CN100435050C - Control method for acrobatic motion of pendulums of under-actuated double pendulum system - Google Patents

Abstract

The present invention relates to a method for controlling the acrobatic motion of pendulums of an under-actuated double-pendulum system, which belongs to the technology of under-actuated system control. The under-actuated double-pendulum system is used to simulate the motion intelligence of human bodies according to motion characteristics of acrobats and piecewise controls the complete set of acrobatic motion composed of motion postures and balance positions of the two pendulums by the motion inertia of the pendulums. A main controller of the complete set of the acrobatic motion is composed of sub controllers (corresponding to control targets in each stage) which are connected in an association pattern mode. The main controller is compiled in the mode that program control codes in real-time operation are input into a corresponding computer control system, and the motion control of a servo motor is realized after the power amplification of outputted control signals through a servo motor driver; then, a dolly is driven, the two pendulums are driven to move, and the two pendulums can accomplish various complete sets of acrobatic motion. The method can be widely used for controlling under-actuated joint type mechanical arms, acrobatic robots, celestial navigation instruments, intelligent toys, etc.

Description

Control method for acrobatic motion of pendulums of under-actuated double pendulum system

One, technical field

The invention belongs to the control technology field of owing drive system, particularly owe to drive the motion planning and the control method of double pendulum system double pendulum bar.

Two, background technology

In the control field, inverted pendulum is the experimental provision of the check control theory of generally acknowledging.As application number is 02257287.2 disclosed " level Four inverted pendulum experiment instrument ", mainly is made up of level Four fork, pedestal, driving-belt, dolly, slide rail, scrambler, servomotor etc.After this experiment instrument is started working from original state (promptly artificially the level Four fork being placed state vertically upward), the scrambler that is connected with forks at different levels detects the angle of each fork and vertical direction, and its measurement result is passed to controller (i.e. " mathematics circular " the 6th phase in 2003 " fuzzy control theory and the application in inverted pendulum control thereof " paper disclosed " becoming the adaptive fuzzy controller of domain ").Controller is handled the signal that records, and produces control signal output, by the servo driver drives servomotor.Servomotor makes moving of car by driving-belt, realizes being in the stable control of handstand state level Four fork.This experiment instrument provides measuring means for the research of control theory, the resolution policy that the control corresponding method provides multistage oscillator system surely to put control, but do not have tangible engineering significance.

In automation field,, be one and owe driving, multivariate, non-linear, cross coupling complicated system as the reversible pendulum system of controlling object.Control to inverted pendulum is a very classical and challenging research topic.Owe to drive in the control of reversible pendulum system existing, in " adaptive fuzzy controller of change domain " real-time stabilization control to the level Four inverted pendulum, domain diminishes along with error and shrinks (also can expand along with the error increase) as described above.The Adaptive Fuzzy Control that becomes domain is a kind of approximate linear control method that turns to the basis.Under the constant prerequisite of rule format, domain shrinks and is equivalent to increase rule, and also be the interpolation node encryption, thereby improved precision, be a kind of dynamic pointwise convergent interpolator.So, improved the control accuracy of fuzzy controller based on the fuzzy controller that becomes domain.Because under handstand state, owe to drive near the only motion among a small circle the point that stands upside down of handstand fork, it is significant improving precision.But the motion control for fork from sag point pendulum to the point that stands upside down owes to drive because of it has, characteristics such as non-linear and controlled target task complexity on a large scale, and existing control methods such as application fuzzy control can't realize.To owing to drive the grand movement control of reversible pendulum system, be the difficult problem in the automation field always.

Three, summary of the invention

The objective of the invention is weak point, a kind of control method of owing to drive the fork acrobatics action of double pendulum system is provided at existing reversible pendulum system control method.This method can solve a difficult problem of owing to drive the grand movement control of double pendulum system, pushes reversible pendulum system to practical engineering application from experimental provision.

The inventive method is achieved in that a kind of control method for acrobatic motion of pendulums of under-actuated double pendulum system, utilize existing dolly double pendulum system (as shown in Figure 2), this system comprises: interior fork (interior bar), outside lever (outer bar), dolly, angular transducer, ac/dc motor and controller etc.Between the outer bar and interior bar, interior bar and dolly of straight line dolly double pendulum system, all the turning axle by the band rolling bearing flexibly connects, and is equiped with angular encoder or rotational potentiometer respectively on turning axle, so that monitor the corner of inside and outside bar and vertical direction respectively.In the control program of servomotor, be mounted with control program according to this method establishment.The acrobatics action of two bars according to acrobat's action feature, is simulated the kinaesthesia intelligence of human body, utilizes the motional inertia of fork, and the complete acrobatics action of being made up of the equilibrium position and the athletic posture of two forks is controlled stage by stage.The master controller of complete acrobatics action by the sub-controller of each stage controlled target correspondence, is formed by connecting through association is graphic.Master controller is compiled into the programmed control code of real time execution, be input in the corresponding calculated machine control system, the control signal of output is after the motor servo driver power amplification, realize the motion control of servomotor, and then driving trolley, drive the motion of two forks, make two forks finish various complete acrobatics actions, realized owing to drive the accurately purpose of control of double pendulum system grand movement.

A kind of control method for acrobatic motion of pendulums of under-actuated double pendulum system utilizes and owes to drive double pendulum system and controller, controls by computer program, realizes the concrete grammar step following (as shown in Figure 1) of control:

Determining of (1) two bar complete acrobatics action controlled target

1) two bar stable equilibrium position assembled state and control methods thereof

Utilization owes to drive the double pendulum system, according to acrobat's action feature, by the approximate linear control method that turns to the basis, each stable equilibrium position assembled state of two bars is controlled.Its four basic assembled state and control method are as follows: (as shown in Figure 3, Figure 4)

1. interior bar downwards-the outer bar self-stabilization equilibrium state (shown in Fig. 3-1) of (down-down) downwards;

The original state that this state begins to carry out the acrobatics action as the double pendulum system is carried out initialization according to this original state to control system by program and is demarcated.In the complete acrobatics action of layout when being the target of action sequence with this state: when deviation is big, the displacement of the pivot angle of inside and outside bar and dolly is adopted pound pound control (the i.e. feature threshold values of the displacement of the pivot angle of the inside and outside bar of foundation and dolly of open loop, determine two fixed amounts, the control mode that output quantity is switched mutually between these two fixed amounts); In deviation hour, the positive feedback or the degenerative proportion differential of closed loop are adopted in the displacement of the pivot angle of inside and outside bar and dolly respectively, and the motion of dolly is controlled by the linear superposition between them, make two bars reach this state as soon as possible.

2. interior bar downwards-the outer bar not self-stabilization equilibrium state (shown in Fig. 3-2) of (down-up) upwards

In the complete acrobatics action of layout, when being the target of action sequence with this state, interior bar and interior bar angle vertically downward, outer bar and outer bar angle vertically upward, all (the α angle is the physical location of fork and the angle between the moving target position with interior at α, when its size is controlled the fork equilibrium state for controller, the maximum angular that the fork that allows departs from), internally, the positive feedback or the negative feedback proportion differential of closed loop adopted in the pivot angle of outer bar and the displacement of dolly respectively, and the motion of dolly is controlled by the linear superposition between them, thereby finish internal bar vertically downward, the control of outer bar equilibrium state vertically upward, its control procedure such as Fig. 4-1,4-2, shown in the 4-3.

3. interior bar upwards-the outer bar not self-stabilization equilibrium state (shown in Fig. 3-3) of (up-up) upwards

In the complete acrobatics action of layout, when being the target of action sequence with this state, in, outer bar with in, outer bar is vertically upward angle all, all (the α angle is the physical location of fork and the angle between the moving target position with interior at α, when its size is controlled the fork equilibrium state for controller, the maximum angular that the fork that allows departs from), internally, the positive feedback or the negative feedback proportion differential of closed loop adopted in the pivot angle of outer bar and the displacement of dolly respectively, and the motion of dolly is controlled by the linear superposition between them, thereby finish internal bar vertically upward, also vertically upward the control of equilibrium state of outer bar, its control procedure such as Fig. 4-7,4-8, shown in the 4-9.

4. interior bar upwards-the outer bar not self-stabilization equilibrium state (as shown in Figure 3-4) of (up-down) downwards

In the complete acrobatics action of layout, when being the target of action sequence with this state, interior bar and interior bar angle vertically upward, outer bar and outer bar angle vertically downward, all (the α angle is the physical location of fork and the angle between the moving target position with interior at α, when its size is controlled the fork equilibrium state for controller, the maximum angular that the fork that allows departs from), internally, the positive and negative feedback proportional differential of closed loop is adopted in the pivot angle of outer bar and the displacement of dolly respectively, and the motion of dolly is controlled by the linear superposition between them, thereby finish internal bar vertically upward, the control of outer bar equilibrium state vertically downward, its control procedure such as Fig. 4-10,4-11, shown in the 4-12.

2) two bars action basic exercise attitude and control method thereof

Utilization owes to drive the double pendulum system, and according to acrobat's action feature, the kinaesthesia intelligence of simulation human body is controlled the various athletic postures of two bars by program.Its 12 basic exercise attitudes and control method are as follows: (as shown in Figure 4)

1. interior bar downwards-outer bar puts (down-swing-up)

To the 1st athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), the control system of double pendulum is by the positive feedback proportional control, and the vibration of the outer bar of control is put.Simultaneously, the control system of double pendulum makes interior bar maintenance attitude vertically downward by the proportion differential control of plus or minus feedback, and the displacement of dolly is remained near the initial position.The control of this athletic posture is finished in the displacement of the linear superposition control dolly by above-mentioned three control actions.

2. interior bar downwards-outer bar turn clockwise (down-R-rotate)

To the 2nd athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), interior bar downwards-outer bar is upwards when (down-up), dolly moves to left, outer bar is freely dropped from right-hand, start the outer bar process that turns clockwise, when outer bar barycenter is lower than its turning axle, positive feedback control with external bar pivot angle, outwards bar injects energy, to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy.When bar made progress outside outer bar rotation is got back to, the control system of double pendulum was by positive feedback or the control of degenerative proportion differential, and bar keeps attitude vertically downward in making, and the displacement of dolly is remained near the initial position.

3. interior bar downwards-outer bar is rotated counterclockwise (down-L-rotate)

To the 3rd athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar downwards-outer bar is upwards when (down-up), dolly moves to right, outer bar is freely dropped from left, start outer bar and be rotated counterclockwise control, when outer bar barycenter is lower than its rotating shaft, positive feedback control with external bar pivot angle, outwards bar injects energy, to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy.When bar made progress outside outer bar rotation is got back to, the control system of double pendulum was by positive feedback or the control of degenerative proportion differential, and bar keeps attitude vertically downward in making, and the displacement of dolly is remained near the initial position.

4. interior bar upwards-outer bar puts (up-swing-up)

To the 4th athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), the control system of double pendulum is by the positive feedback proportional control, and the vibration of the outer bar of control is put.Simultaneously, the control system of double pendulum makes interior bar maintenance attitude vertically upward by the positive feedback or the control of degenerative proportion differential of closed loop, and the displacement of dolly is remained near the initial position.The control of this athletic posture is finished in the displacement of the linear superposition control dolly by above-mentioned three control actions.

5. interior bar upwards-outer bar turn clockwise (up-R-rotate)

To the 5th athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar upwards-outer bar is upwards when (up-up), dolly moves to left, outer bar is freely dropped from right-hand, start the control that turns clockwise of outer bar, when outer bar barycenter is lower than its turning axle, positive feedback control with external bar pivot angle, outwards bar injects energy, to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy.When bar made progress outside outer bar rotation is got back to, the control system of double pendulum was by positive feedback or the control of degenerative proportion differential, and bar keeps attitude vertically downward in making, and the displacement of dolly is remained near the initial position.

6. interior bar upwards-outer bar is rotated counterclockwise (up-L-rotate)

To the 6th athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar upwards-outer bar is upwards when (up-up), dolly moves to right, outer bar is freely dropped from left, start outer bar and be rotated counterclockwise control, when outer bar barycenter is lower than its turning axle, positive feedback control with external bar pivot angle, outwards bar injects energy, to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy.When bar made progress outside outer bar rotation is got back to, the control system of double pendulum was by positive feedback or the control of degenerative proportion differential, and bar keeps attitude vertically downward in making, and the displacement of dolly is remained near the initial position.

7. interior bar downwards-outer bar downwards-two bars put (down-down-swing-up) simultaneously

To the 7th athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar downwards-outer bar is downwards when (down-down), the control system of double pendulum is by the positive feedback proportional control, and bar and the vibration simultaneously of outer bar are put in the control.Simultaneously,, the angle of two bars and the position of dolly are controlled, made two forks become the attitude vibration of near linear to put by the positive feedback or the degenerative proportion differential of closed loop.At this moment the linear superposition of three control actions has constituted moving of car has been controlled.

8. interior bar upwards-outer bar-two bars turn clockwise simultaneously (up-up-R-rotate) upwards

To the 8th athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar upwards-outer bar is upwards when (up-up), dolly moves to left, two bars are freely dropped from right-hand simultaneously, start the control that turns clockwise of two bars, when two bar barycenter are lower than its turning axle, with positive feedback control to two bar pivot angles, inject energy simultaneously to two bars, to replenish the energy loss that causes because of friction in the rotation of two bars, the number of times that two bars rotate simultaneously is decided by to inject the size of energy.When interior bar and the rotation of outer bar were got back to vertically upward simultaneously, the control system of double pendulum was controlled by the positive feedback or the degenerative proportion differential of closed loop, makes interior bar, outer bar keep attitude vertically upward simultaneously, and the displacement of dolly is remained near the initial position.

9. interior bar upwards-outer bar upwards-two bars be rotated counterclockwise (up-up-L-rotate) simultaneously

To the 9th athletic posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar upwards-outer bar is upwards when (up-up), dolly moves to right, two bars are freely dropped from left simultaneously, start two bars and be rotated counterclockwise control, when two bar barycenter are lower than its turning axle, with positive feedback control to two bar pivot angles, inject energy simultaneously to two bars, to replenish the energy loss that causes because of friction in the rotation of two bars, the number of times that two bars rotate simultaneously is decided by to inject the size of energy.When interior bar and the rotation of outer bar were got back to vertically upward simultaneously, the control system of double pendulum was controlled by the positive feedback or the degenerative proportion differential of closed loop, makes interior bar, outer bar keep attitude vertically upward simultaneously, and the displacement of dolly is remained near the initial position.

10. interior bar downwards-outer bar upwards-two bars put (down-up-swing-up) simultaneously

To the 10th movement posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar downwards-outer bar is upwards when (down-up), at first make the double pendulum bar depart from (down-up) position with less moving of car, then according to the position and the athletic posture feature of two forks, proportional controlling means by positive feedback, the bar vibration is put in making, simultaneously, adopt with degenerative proportion differential control method, keep outer bar and interior bar to be the attitude of certain included angle and relative motion and to vibrate simultaneously and put.The motion control of dolly is made of the linear superposition of above-mentioned positive and negative FEEDBACK CONTROL all the time.

Interior bar upwards-outer bar-two bars turn clockwise simultaneously (up-down-R-rotate) downwards

To the 11st movement posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar upwards-outer bar is downwards when (up-down), angle by bar and outer bar in the negative feedback control, dolly moves to left simultaneously, two bars are freely dropped from right-hand, start the control that turns clockwise of two bars, in two bar barycenter are lower than during the bar turning axle, adopt the positive feedback proportional control to inject energy to two bars, replenish the energy loss that causes because of friction in the rotation, the number of times that two bars rotate simultaneously is decided by to inject the size of energy.In interior bar and the rotation of outer bar are got back to bar make progress-when outer bar is downward, the control system of double pendulum is by the positive feedback or the control of degenerative proportion differential of closed loop, bar keeps up-attitude that outer bar keeps down in making, and the displacement of dolly is remained near the initial position.

Interior bar upwards-outer bar downwards-two bars be rotated counterclockwise (up-down-L-rotate) simultaneously

To the 12nd movement posture controlled target in the present invention's two forks, 12 basic exercise attitudes controlled target synoptic diagram (as Fig. 4), when interior bar upwards-outer bar is downwards when (up-down), angle by bar and outer bar in the negative feedback control, dolly moves to right simultaneously, two bars are freely dropped from left, start two bars and be rotated counterclockwise control, in two bar barycenter are lower than during the bar turning axle, adopt the positive feedback proportional control to inject energy to two bars, replenish the energy loss that causes because of friction in the rotation, the number of times that two bars rotate simultaneously is decided by to inject the size of energy.In interior bar and the rotation of outer bar are got back to bar make progress-when outer bar is downward, the control system of double pendulum is by the positive feedback or the control of degenerative proportion differential of closed loop, bar keeps up-attitude that outer bar keeps down in making, and the displacement of dolly is remained near the initial position.

The control method of above-mentioned four home position assembled state and 12 basic exercise attitudes has guaranteed the feasibility that complete acrobatics action realizes.Simultaneously, with the control method that simple and direct positive negative feedback combines, guaranteed the real-time and the reliability of control.

3) the complete acrobatics action of two bars controlled target determines and the control task decomposition

1. two bars complete acrobatics action controlled target determines

Utilization owes to drive the double pendulum system, simulation acrobat's action, characteristics according to complete acrobatics action, according to comprehensive, the creativeness of acrobatics art and the requirement of fragrance, in conjunction with the (1)-1) the equilibrium position assembled state and (1)-2 in step) 12 basic exercise attitudes and the conversion and the joining relation mutually in step, by computer aided program, the various complete acrobatics actions of layout, and determine corresponding complete acrobatics action controlled target.The quantity of complete acrobatics action controlled target is by the action number decision of corresponding complete acrobatics action.Wherein each acrobatics action has showed from a certain equilibrium position assembled state, experiences the motion process of a certain basic exercise attitude, arrives another kind of equilibrium position assembled state or gets back to original equilibrium position assembled state.(specifically seeing embodiment 1 for details).

2. the control task of the complete acrobatics action of two bars controlled target is decomposed

According to the (1)-3)-the 1. complete acrobatics action of the two bars controlled target determined of step, sequence of movement according to each complete acrobatics action controlled target, by program the sub-controlled target in each stage is resolved in each action respectively, and the corresponding sub-controller of sub-controlled target in each stage is set.The controlled target in each stage is achieved by the control of corresponding sub-controller.Simultaneously, also to determine by the action order, realize taking over seamlessly between each action with the controlled target that is connected and corresponding total sequence controller (promptly related graphic) is set, thereby finish nonlinear Control and the complete acrobatics Autonomous Control of moving of double pendulum system on a large scale.(2) control of complete acrobatics action controlled target

1) modeling of controlled device double pendulum system and parameter identification

1. owe to drive the foundation of double pendulum system mathematic model structure

Set up the mathematical model structure of owing to drive the double pendulum system with the Lagrange's equation in newton-Euler method or the analytical mechanics.The model structure form of setting up is the second order nonlinear differential equation:

$M\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)=F$ In the formula: q=(x, θ ₁, θ ₂) ^T, $\stackrel{\·}{q}={(\stackrel{\·}{x},{\stackrel{\·}{\mathrm{\θ}}}_1,{\stackrel{\·}{\mathrm{\θ}}}_2)}^T$

2. in computing machine, make up the upright double pendulum system mathematic model corresponding numerical model of owing to drive

Use numerical analysis method, according to the (2)-1)-1. the mathematical model set up is set up corresponding numerical model the step in computing machine, and determine kinetic parameter in the mathematical model by preliminary physical measurement.In Computer Simulation, find the solution the differential equation with the quadravalence runge kutta method of fixed step size.

3. the identification of double pendulum system equivalent model parameter

For making the (2)-1)-2. go on foot numerical simulation model and the practical object in computing machine, set up to accomplish basically identical, so that quicken to finish the transition of control experiment from the Computer Simulation to the material object, adopt evolutionary programming algorithm logarithm value realistic model in kinetic parameter adjust, make its can with the practical object equivalence.The steps include: at first to set up the input and output response and the (2)-1 of owing to drive the double pendulum system of reflection actual measurement)-2. go on foot the fitness function of other evolutionary programming algorithm of input and output difference in response of the numerical model of in computing machine, setting up, use evolutionary programming algorithm then these kinetic parameters are optimized, accomplish basically identical until the input and output response of numerical simulation model and the input and output response of practical object.Be not easy to the friction factor that accurately obtains with mensuration in the model, also in above genetic evolution calculation process, be determined, thereby obtain be can with the equivalent numerical of practical object basically identical, therefore the work such as evaluation definite, the system works quality of the effective control parameter of controller all can be finished by the numerical simulation experiment, make the simulation study of back to real-time control very strong directive significance be arranged.

2) complete acrobatics action master controller and each acrobatics are moved determining of corresponding sub-controller controlled variable and optimizing

To the (1)-3) the complete acrobatics action controlled target determined of step, decompose obtain each stage by stage controlled target and each corresponding sub-controller is set and guarantee to take over seamlessly between each action be connected related graphic, guaranteed the rationality of whole complete acrobatics movement controller structure and the feasibility of complete acrobatics action realization.But, wherein have a large amount of handoff features parameters and controlled variable to determine and to optimize.The present invention realizes determining of above-mentioned each sub-controller and related graphic parameter by evolutionary programming algorithm and optimizes, to realize that fast, accurately complete acrobatics action is the fitness function that target is set up evolutionary programming algorithm, use evolutionary programming algorithm then these features and controlled variable are optimized, until the accurate realization of complete acrobatics action.This method can obtain the feasible controlled variable that many groups are finished each control task by computing machine easily reliably, makes the equivalence substantially of realistic model and practical object, thereby reduces the debugging work load of control experiment in kind widely.

3) assessment and the judgement of control experiment in kind and experimental result

To the (1)-3) each each sub-controller and total sequence controller of controlled target stage by stage of being provided with of step, work out corresponding controlled target stage by stage, behind the control program of energy real time execution, in controller that is input to the controller formed by the PC system or forms by embedded system or the controller formed by PC system and embedded system, in its controller, be provided with motion control card, rotation to servomotor in the system is controlled, the displacement of the rotation driving trolley by servomotor drives the location status and the athletic posture of two forks that flexibly connect with dolly.Owe to drive in the exercise testing that double pendulum system material object carries out complete acrobatics action in control, write down the situation of environmental interference and the effect of control in real time.In experimentation, at any time The simulation experiment result and full-scale investigation result are analyzed and relatively reach assessment and judge: when also not finishing the controlled target of complete acrobatics action, repeat each step in (2) step, controller parameter or control program are adjusted again; When finishing the controlled target of complete acrobatics action, finish control experiment in kind.Thereby finish the control of owing to drive the complete acrobatics action of double pendulum system.

The present invention adopts the decomposition control of above-mentioned many controlled target and multi-modal control to realize the control method of complicated controlled target, has succinctly reliably, is convenient to simulate acrobat's health kinaesthesia intelligence, and is convenient to realize the outstanding advantage of non-linear grand movement control.The present invention can be widely used in owing to drive the control of devices such as joint type mechanical arm, acrobatics robot, sky aircraft and intelligent toy.

Four, description of drawings

Fig. 1 program flow chart of the present invention;

The existing driving trolley double pendulum system architecture synoptic diagram of owing of Fig. 2;

Among the figure: 1. ac/dc servomotor, 2. pedestal (dolly), 3. driving-belt, 4. slide rail, 5. angular encoder, 6. in fork, 7. outside lever.

Fig. 3 the present invention two fork equilibrium position assembled state controlled target synoptic diagram;

Among the figure: 1. in bar downwards-outer bar (down-down) downwards, 2. in bar downwards-outer bar upwards (down-up), 3. in bar upwards-outer bar upwards (up-up), 4. in bar upwards-outer bar (up-down) downwards.

12 basic exercise attitudes of Fig. 4 the present invention two forks controlled target synoptic diagram;

Among the figure: 1. in bar downwards-outer bar puts (down-swing-up), 2. interior bar downwards-outer bar turn clockwise (down-R-rotate), 3. interior bar downwards-outer bar is rotated counterclockwise (down-L-rotate), 4. interior bar upwards-outer bar puts (up-swing-up), 5. interior bar upwards-outer bar turn clockwise (up-R-rotate), 6. interior bar upwards-outer bar is rotated counterclockwise (up-L-rotate), 7. interior bar downwards-outer bar downwards-two bars put (down-down-swing-up) simultaneously, 8. interior bar upwards-outer bar-two bars turn clockwise simultaneously (up-up-R-rotate) upwards, 9. interior bar upwards-outer bar upwards-two bars be rotated counterclockwise (up-up-L-rotate) simultaneously, 10. interior bar downwards-outer bar upwards-two bars put (down-up-swing-up) simultaneously, 11. interior bar upwards-outer bar downwards-two bars turn clockwise simultaneously (up-down-R-rotate), in 12. bars upwards-outer bar downwards-two bars be rotated counterclockwise (up-down-L-rotate) simultaneously.

The hardware system composition frame chart of Fig. 5 PC system controller of the present invention;

Among the figure: 8.PC system, 9. motion control card, 10. motor servo controller, 11. ac/dc servomotors, 12. double pendulum systems, 14.PC machine.

The controller hardware block diagram of system of Fig. 6 embedded system of the present invention;

Among the figure: 10. motor servo controller, 11. ac/dc servomotors, 12. double pendulum systems, 13. embedded systems.

The controller hardware block diagram of system that Fig. 7 PC of the present invention and embedded system constitute;

Among the figure: 10. motor servo controller, 11. ac/dc servomotors, 12. double pendulum systems, 13. embedded systems, 14.PC machine.

Fig. 8 is the program flow chart of the complete acrobatics action of the decomposition of present embodiment 1 controlled target;

Fig. 9 moves controlled target synoptic diagram stage by stage for the complete acrobatics of decomposition of present embodiment 1;

Figure 10 is the program flow chart of the complete acrobatics action of the decomposition of present embodiment 2 controlled target;

Figure 11 moves controlled target synoptic diagram stage by stage for the complete acrobatics of decomposition of present embodiment 2.

Five, embodiment

Below in conjunction with embodiment, further specify the present invention.

Embodiment 1

Shown in Fig. 8～9, a kind of control method for acrobatic motion of pendulums of under-actuated double pendulum system utilizes and to owe to drive double pendulum system and controller, and is as follows to the method step of the decomposition of the complete acrobatics action of first cover that arranged and control by program:

1) layout and the decomposition of controlled target stage by stage that complete acrobatics is moved

To the complete acrobatics action of first cover controlled target that has arranged by computing machine, by its sequence of movement (as shown in Figure 8), adopt to open and close that ring combines and the control mode of positive negative feedback combination should be overlapped acrobatics by program and moved controlled target and be decomposed into 15 stage controlled target, as shown in Figure 9, and 15 15 sub-controllers of controlled target correspondence stage by stage are set, its method step that decomposes complete acrobatics action controlled target is as follows:

1. first stage controlled target, from the 1st location status of system, promptly bar downwards-outer bar downwards the naturally stable location status of (down-down) begin, through interior bar downwards-the 1st kind of basic exercise attitude that outer bar put (down-swing-up) arrive in bar downwards-make progress the 2nd location status of (down-up) of outer bar also stablize;

2. second stage controlled target, through interior bar downwards-turn clockwise the 2nd kind of basic exercise attitude in (down-R-rotate) 720 ° (two weeks) of outer bar, in getting back to bar downwards-outer bar the 2nd location status of (down-up) and stable upwards;

3. three phases controlled target, through interior bar downwards-outer bar is rotated counterclockwise the 3rd kind of basic exercise attitude of (down-L-rotate) 720 ° (two weeks), in getting back to bar downwards-outer bar the 2nd location status of (down-up) and stable upwards;

4. four-stage controlled target, through interior bar downwards-outer bar upwards-two bars put simultaneously in the 10th kind of basic exercise attitude to the of (down-up-swing-up) bar upwards-outer bar downwards 4 location statuss of (up-down) also stablize;

5. the 5th stage controlled target, through interior bar upwards-the 4th kind of basic exercise attitude that outer bar put (up-swing-up) to interior bar upwards-outer bar upwards the 3rd location status of (up-up) also stablize;

6. the 6th stage controlled target, through interior bar upwards-turn clockwise the 5th kind of basic exercise attitude in (up-R-rotate) 1080 ° (three weeks) of outer bar, in getting back to bar upwards-outer bar the 3rd location status of (up-up) and stable upwards;

7. the 7th stage controlled target, through interior bar upwards-outer bar is rotated counterclockwise the 6th kind of basic exercise attitude of (up-L-rotate) 1080 ° (three weeks), in getting back to bar upwards-outer bar the 3rd location status of (up-up) and stable upwards;

8. the 8th stage controlled target, through interior bar upwards-turn clockwise the 5th kind of basic exercise attitude in (up-R-rotate) 720 ° (two weeks) of outer bar, in getting back to bar upwards-outer bar the 3rd location status of (up-up) and stable upwards;

9. the 9th stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously the 8th kind of basic exercise attitude of (up-up-R-rotate) 180 ° (half cycles) of-two bars upwards, to interior bar downwards-outer bar the 1st location status of (down-down) and stable downwards;

10. the tenth stage controlled target, through interior bar downwards-outer bar downwards-two bars the 7th kind of basic exercise attitude of having put (down-down-swing-up) simultaneously to interior bar upwards-outer bar upwards (up-up) the 3rd location status and stablize;

The 11 stage controlled target, through interior bar upwards-outer bar in upwards-two bars the 9th kind of basic exercise attitude being rotated counterclockwise (up-up-L-rotate) 360 ° (week) simultaneously got back to bar upwards-outer bar upwards (up-up) the 3rd location status and stablize;

The 12 stage controlled target, through interior bar upwards-outer bar (up-R-rotate) the 5th kind of basic exercise attitude in 540 ° (weeks half) that turn clockwise, to interior bar upwards-outer bar the 4th location status of (up-down) and stable downwards;

The tenth three phases controlled target, through interior bar upwards-outer bar downwards-two bars be rotated counterclockwise the 12nd kind of basic exercise attitude of (up-down-R-rotate) 720 ° (two weeks) simultaneously, in getting back to bar upwards-outer bar the 4th location status of (up-down) and stable downwards;

The tenth four-stage controlled target, through interior bar upwards-outer bar-two bars (up-down-R-rotate) the 11st kind of basic exercise attitude in 540 ° (weeks half) that turn clockwise simultaneously downwards, to interior bar downwards-outer bar the 2nd location status of (down-up) and stable upwards;

The 15 stage controlled target, through interior bar downwards-outer bar (down-R-rotate) the 2nd kind of basic exercise attitude in 900 ° (two weeks half) that turn clockwise, to interior bar downwards-outer bar the 1st location status of (down-down) and stable downwards, finish this cover and move.

2) control of complete acrobatics action controlled target

1. the modeling of controlled device double pendulum system and parameter identification

If state variable is: q=[x θ ₁θ ₂] ^T, (wherein: x is the dolly displacement, θ ₁Be interior fork angle, θ ₂Be the outside lever angle).The motion model that the application Lagrange's equation obtains dolly double pendulum system is:

$M\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)=F$

In the formula: $M\left(q\right)=\left[\begin{array}{ccc}M+{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">m</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">m</figure-callout>}}_2+m_0& (m_1{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+m_{2}L+m_{0}L)\cos \left({\mathrm{\&theta;}}_1\right)& m_2{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_2\cos \left({\mathrm{\&theta;}}_2\right)\\ (m_1{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+m_{2}L+m_{0}L)\cos \left({\mathrm{\&theta;}}_1\right)& (m_1{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">J</figure-callout>}}_1+m_2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+m_0{L}^2)& {\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{<figure-callout\; id="2"\; label="Ll"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">Ll</figure-callout>}}_2\cos ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)\\ m_2{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_2\cos \left({\mathrm{\&theta;}}_2\right)& {\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{<figure-callout\; id="2"\; label="Ll"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">Ll</figure-callout>}}_2\cos ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)& (m_2{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^2+J_2)\end{array}\right]$

$C(q,\stackrel{\&CenterDot;}{q})=\left[\begin{array}{ccc}f& -(m_1{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+m_{2}L+m_{0}L){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\sin \left({\mathrm{\&theta;}}_1\right)& -m_2{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2\sin \left({\mathrm{\&theta;}}_2\right)\\ 0& {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">c</figure-callout>}}_1+c_2& {\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{<figure-callout\; id="2"\; label="Ll"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">Ll</figure-callout>}}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2\sin ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">c</figure-callout>}}_2\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{<figure-callout\; id="2"\; label="Ll"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">Ll</figure-callout>}}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\sin ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)-c_2& {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">c</figure-callout>}}_2\end{array}\right]$

$g\left(q\right)=\left[\begin{array}{c}0\\ -(m_{0}L+m_1{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+m_{2}L)g\left(\sin {\mathrm{\&theta;}}_1\right)\\ -{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{<figure-callout\; id="2"\; label="gl"\; filenames="C20061005435500251.png,C20061005435500261.png"\; state="\{\{state\}\}">gl</figure-callout>}}_2\sin \left({\mathrm{\&theta;}}_2\right)\end{array}\right]$

F＝[u·0 0] ^T

Concrete parameter in the following formula in the physical significance of each symbol and the enforcement sees the following form:

Realize the double pendulum system value model of quick computing with the C Programming with Pascal Language according to following formula in computing machine, separate second order differential equation with the quadravalence runge kutta method of fixed step size, simulation time is consistent with real-time control at interval, gets 5ms.

Further, allow fork freely fall, write down the exercise data of inside and outside fork from the top.To the given acceleration signal of servomotor output, note the exercise data of fork and dolly.

Utilize evolutionary programming algorithm to make up the search model parameter at random, make the numerical model free movement of similarity condition in the emulation and exercise data in kind approaching, a wherein immediate group model parameter is exactly the result of identification of Model Parameters.Simulation study has been had and consistent controlling object in kind, thus the debugging of control method first in computing machine emulation realize, and then be transplanted in the control system in kind and go, control efficiency is improved greatly.

2. controller parameter determines and optimization

To the 1st) step decomposes obtain 15 controlled target stage by stage, and 15 corresponding sub-controllers are set, and guaranteed the rationality of controller architecture.But wherein there is a large amount of controlled variable to determine.According to 15 stage controlled target that decomposited, and work out 15 corresponding multi-modal control programs respectively, by to the Simulation Control effect of numerical model in the computing machine and the comparison between the expection controlled target, utilize evolutionary programming algorithm to determine and optimize the controlled variable of these 15 controllers.

This method can not only obtain the many groups of feasible controlled variable that can finish each control task by computing machine easily easily, and can reduce debugging work load widely.Because allow failure in the simulation calculation, and execution speed is fast more a lot of than full-scale investigation, so this step is compared with classic method, can save a large amount of hand labours.

3) assessment and the judgement of control experiment in kind and experimental result

With the 1st) step decompose 15 sub-controllers of 15 stage controlled target obtaining and by the 2nd)-2. the step is optimized the parameter of 15 sub-controllers that obtain, insert in the PC system of pci interface, by GT-400-SV motion control card (solid high-tech company, Shenzhen product) the output control signal that is installed in the PC system, after the motor servo driver power amplification, realize the motion control of servomotor.Simultaneously, motion control card also can receive the various status informations of double pendulum systems such as dolly position, inside and outside swinging angle of swinging rod, feeds back to controller.

On this basis, owe to drive the control method of the double pendulum system fork first cover acrobatics action, press the program circuit shown in the program flow diagram (as Fig. 8) of the complete acrobatics action of the decomposition of present embodiment controlled target, be compiled into the control program of real time execution, and be presented in the PC system, finish motion control to the complete acrobatics action of double pendulum bar system in kind first cover.In material object control experiment, add environmental interference and write down relevant control effect in real time, to controlling outcome evaluation and judgement: when not finishing the controlled target of combination, repeat the 2nd) step, controller parameter or control program are adjusted again; When finishing the controlled target of complete acrobatics action, finish to adjust, thereby finish the apery motion control of owing to drive the first cover acrobatics action of double pendulum system in kind.

Embodiment 2:

Shown in Figure 10～11, a kind of control method for acrobatic motion of pendulums of under-actuated double pendulum system utilizes and to owe to drive double pendulum system and controller, and is as follows to the method step of the decomposition of the complete acrobatics action of second cover that arranged and control by program:

1) to the decomposition of complete acrobatics action controlled target

To the complete acrobatics action of second condom that arranges by computing machine controlled target, by its sequence of movement (as shown in figure 10), adopt to open and close that ring combines and the control mode of positive negative feedback combination should be overlapped acrobatics by program and moved controlled target and be decomposed into 15 stage controlled target, as shown in figure 11, and 15 15 sub-controllers of controlled target correspondence stage by stage are set, its method step that decomposes complete acrobatics action controlled target is as follows:

1. first stage controlled target, from the 1st location status of system, promptly bar downwards-outer bar downwards the naturally stable location status of (down-down) begin, through interior bar downwards-outer bar in-two bars the 7th kind of basic exercise attitude of having put (down-down-swing-up) simultaneously arrives downwards bar upwards-outer bar upwards the 3rd location status of (up-up) also stablize;

2. second stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously the 8th kind of basic exercise attitude in (up-up-R-rotate) 720 ° (two weeks) of-two bars upwards, in getting back to bar upwards-outer bar the 3rd location status of (up-up) and stable upwards;

3. three phases controlled target, through interior bar upwards-outer bar upwards-two bars be rotated counterclockwise the 9th kind of basic exercise attitude of (up-up-L-rotate) 1080 ° (three weeks) simultaneously, in getting back to bar upwards-outer bar the 3rd location status of (up-up) and stable upwards;

4. four-stage controlled target, through interior bar upwards-turn clockwise the 5th kind of basic exercise attitude in (up-R-rotate) 720 ° (two weeks) of outer bar, in getting back to bar upwards-outer bar the 3rd location status of (up-up) and stable upwards;

5. the 5th stage controlled target, through interior bar upwards-outer bar is rotated counterclockwise (up-L-rotate) 900 ° the 6th kind of basic exercise attitude in (two weeks half), to interior bar upwards-outer bar the 4th location status of (up-down) and stable downwards;

6. the 6th stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously the 11st kind of basic exercise attitude in (up-down-R-rotate) 1080 ° (three weeks) of-two bars downwards, in getting back to bar upwards-outer bar the 4th location status of (up-down) and stable downwards;

7. the 7th stage controlled target, through interior bar upwards-outer bar downwards-two bars be rotated counterclockwise the 12nd kind of basic exercise attitude of (up-down-L-rotate) 1080 ° (three weeks) simultaneously, in getting back to bar upwards-outer bar the 4th location status of (up-down) and stable downwards;

8. the 8th stage controlled target, through interior bar upwards-outer bar-two bars (up-down-R-rotate) the 11st kind of basic exercise attitude in 900 ° (two weeks half) that turn clockwise simultaneously downwards, to interior bar downwards-outer bar the 2nd location status of (down-up) and stable upwards;

9. the 9th stage controlled target, through interior bar downwards-turn clockwise the 2nd kind of basic exercise attitude in (down-R-rotate) 720 ° (two weeks) of outer bar, in getting back to bar downwards-outer bar the 2nd location status of (down-up) and stable upwards;

10. the tenth stage controlled target, through interior bar downwards-outer bar is rotated counterclockwise (down-L-rotate) 1260 ° the 3rd kind of basic exercise attitude in (three weeks half), to interior bar downwards-outer bar the 1st location status of (down-down) and stable downwards;

The 11 stage controlled target, through interior bar downwards-outer bar put the 1st kind of basic exercise attitude of (down-swing-up), to interior bar downwards-outer bar upwards the 2nd location status of (down-up) also stablize;

The 12 stage controlled target, through interior bar downwards-outer bar-two bars the 10th kind of basic exercise attitude of having put (down-up-swing-up) simultaneously upwards, to interior bar upwards-outer bar downwards (up-down) the 4th location status and stablize;

The tenth three phases controlled target, through interior bar upwards-outer bar put the 4th kind of basic exercise attitude of (up-swing-up), to interior bar upwards-outer bar upwards the 3rd location status of (up-up) also stablize;

The tenth four-stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously the 8th kind of basic exercise attitude in (up-up-R-rotate) 1080 ° (three weeks) of-two bars upwards, in getting back to bar upwards-outer bar the 3rd location status of (up-up) and stable upwards;

The 15 stage controlled target, through interior bar upwards-outer bar upwards-two bars be rotated counterclockwise (up-up-L-rotate) 1260 ° the 9th kind of elemental motion in (three weeks half) simultaneously, in getting back to bar downwards-outer bar the 1st location status of (down-down) and stable downwards, finish this cover and move.

2) control of complete acrobatics action controlled target

1. the modeling of controlled device double pendulum system and parameter identification

The foundation of modelling by mechanism, numerical simulation model and identification of Model Parameters, with embodiment 1 2)-1. go on foot identical.

2. controller parameter determines and optimization

Determining and optimization method of controller parameter, with embodiment 1 the 2nd)-2. go on foot identically, but because the controlled target difference, the fitness function in the evolutionary programming algorithm is different with the optimization control parameter of being tried to achieve.

3) assessment and the judgement of control experiment in kind and experimental result

With the 1st) step decompose each sub-controller of 15 stage controlled target obtaining and by the 2nd)-2. the step is optimized the parameter of 15 sub-controllers that obtain, insert the controller hardware system (as Fig. 7) of PC system and embedded system, in embedded system, be provided with the motion control arithmetic module of bottom and the program module of communicating by letter with PC, the control signal of embedded system output, after the motor servo driver power amplification, realize the motion control of servomotor, simultaneously, embedded system also receives the dolly position, the status information of double pendulum systems such as inside and outside swinging angle of swinging rod feeds back to controller.

On this basis, owe to drive the double pendulum system second cover acrobatics method of controlling operation, press the program circuit shown in the program flow diagram (as Figure 10) of the complete acrobatics action of the decomposition of present embodiment controlled target, be compiled into the control program of real time execution, and be presented in the embedded system, finish the acrobatics of double pendulum bar action control, the PC system communicates by letter with embedded system, realizes the supervision of double pendulum system running state and tension management function such as control task is set; In material object control experiment, add environmental interference and write down relevant control effect in real time, to controlling outcome evaluation and judgement: when not finishing the controlled target of combination, repeat the 2nd) step, controller parameter or control program are adjusted again; When finishing the controlled target of complete acrobatics action, finish to adjust, thereby finish the apery motion control of owing to drive the second cover acrobatics action of double pendulum system in kind.

Claims (3)

1. a control method for acrobatic motion of pendulums of under-actuated double pendulum system utilizes and owes to drive double pendulum system and controller, controls by computer program, it is characterized in that concrete method step is as follows:

Determining of (1) two bar complete acrobatics action controlled target

1) two bar stable equilibrium position assembled state and control methods

Utilization owes to drive the double pendulum system, according to acrobat's action feature, by the approximate linear control method that turns to the basis, each stable equilibrium position assembled state of two bars is controlled, and its four basicly stable equilibrium position assembled state and control method are as follows:

1. interior bar downwards-the downward self-stabilization equilibrium state of outer bar

The original state that this state begins to carry out the acrobatics action as the double pendulum system is carried out initialization according to this original state to control system by program and is demarcated; In the complete acrobatics action of layout, when being the target of action sequence: when deviation is big, adopt the pound pound of open loop to control to the pivot angle of inside and outside bar and the displacement of dolly with this state; In deviation hour, the positive feedback or the degenerative proportion differential of closed loop are adopted in the displacement of the pivot angle of inside and outside bar and dolly respectively, and the motion of dolly is controlled by the linear superposition between them;

2. interior bar downwards-not self-stabilization equilibrium state that outer bar makes progress

In the complete acrobatics action of layout, when being the target of action sequence with this state, interior bar and interior bar angle, outer bar and outer bar angle vertically upward vertically downward, all in the physical location and the angle α between the moving target position of fork, the displacement of the pivot angle of inside and outside bar and dolly is adopted the positive feedback or the negative feedback proportion differential of closed loop respectively, and by the linear superposition between them motion of dolly is controlled, thereby finish internal bar vertically downward, the control of outer bar equilibrium state vertically upward;

3. interior bar upwards-not self-stabilization equilibrium state that outer bar makes progress

In the complete acrobatics action of layout, when being the target of action sequence with this state, inside and outside bar and inside and outside bar be vertically upward angle all, all in the physical location and the angle α between the moving target position of fork, the displacement of the pivot angle of inside and outside bar and dolly is adopted the positive feedback or the negative feedback proportion differential of closed loop respectively, and by the linear superposition between them motion of dolly is controlled, thereby finish internal bar vertically upward, also vertically upward the control of equilibrium state of outer bar;

4. interior bar makes progress-the downward not self-stabilization equilibrium state of outer bar

In the complete acrobatics action of layout, when being the target of action sequence with this state, interior bar and interior bar angle, outer bar and outer bar angle vertically downward vertically upward, all in the physical location and the angle α between the moving target position of fork, the displacement of the pivot angle of inside and outside bar and dolly is adopted the positive and negative feedback proportional differential of closed loop respectively, and the motion of dolly is controlled by the linear superposition between them, thereby finish internal bar vertically upward, the control of outer bar equilibrium state vertically downward;

2) two bars action basic exercise attitude and control method thereof

Utilization owes to drive the double pendulum system, and according to acrobat's action feature, the kinaesthesia intelligence of simulation human body is controlled the various athletic postures of two bars by program, and its 12 basic exercise attitudes and control method are as follows:

1. interior bar downwards-outer bar puts

To the 1st athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, the control system of double pendulum is by the positive feedback proportional control, the vibration of the outer bar of control is put, simultaneously, the control system of double pendulum makes interior bar maintenance attitude vertically downward by the positive feedback or the control of negative feedback proportion differential of closed loop, the displacement of dolly is remained near the initial position, linear superposition by above-mentioned three control actions, the control of this athletic posture is finished in the displacement of control dolly;

2. interior bar downwards-outer bar turns clockwise

To the 2nd athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, interior bar downwards-when outer bar makes progress, dolly moves to left, outer bar is freely dropped from right-hand, start the control that turns clockwise of outer bar, when outer bar barycenter is lower than its turning axle, positive feedback control by external bar pivot angle, outwards bar injects energy, and to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy; When bar made progress outside outer bar rotation is got back to, the control system of double pendulum was by positive feedback or the control of degenerative proportion differential, and bar keeps attitude vertically downward in making, and the displacement of dolly is remained near the initial position;

3. interior bar downwards-outer bar is rotated counterclockwise

To the 3rd athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar downwards-when outer bar makes progress, dolly moves to right, outer bar is freely dropped from left, start outer bar and be rotated counterclockwise control, when outer bar barycenter is lower than its turning axle, positive feedback control by external bar pivot angle, outwards bar injects energy, to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy, when bar makes progress outside outer bar rotation is got back to, the control system of double pendulum is by positive feedback or the control of degenerative proportion differential, and bar keeps attitude vertically downward in making, and the displacement of dolly is remained near the initial position;

4. interior bar upwards-outer bar puts

To the 4th athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, the control system of double pendulum is by the positive feedback proportional control, the vibration of the outer bar of control is put, simultaneously, the control system of double pendulum is by the positive feedback or the control of degenerative proportion differential of closed loop, bar keeps attitude vertically upward in making, the displacement of dolly is remained near the initial position, linear superposition by above-mentioned three control actions, the control of this athletic posture is finished in the displacement of control dolly;

5. interior bar upwards-outer bar turns clockwise

To the 5th athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar upwards-when outer bar makes progress, dolly moves to left, outer bar is freely dropped from right-hand, start the control that turns clockwise of outer bar, when outer bar barycenter is lower than its turning axle, positive feedback control by external bar pivot angle, outwards bar injects energy, to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy, when bar makes progress outside outer bar rotation is got back to, the control system of double pendulum is by the positive feedback or the control of degenerative proportion differential of closed loop, and bar keeps attitude vertically upward in making, and the displacement of dolly is remained near the initial position;

6. interior bar upwards-outer bar is rotated counterclockwise

To the 6th athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar upwards-when outer bar makes progress, dolly moves to right, outer bar is freely dropped from left, start outer bar and be rotated counterclockwise control, when outer bar barycenter is lower than its turning axle, positive feedback control by external bar pivot angle, outwards bar injects energy, to replenish the energy loss that causes because of friction in the outer bar rotation, the number of times of outer bar rotation is decided by to inject the size of energy, when bar makes progress outside outer bar rotation is got back to, the control system of double pendulum is by the positive feedback or the control of degenerative proportion differential of closed loop, and bar keeps attitude vertically upward in making, and the displacement of dolly is remained near the initial position;

7. interior bar downwards-outer bar downwards-two bars put simultaneously

To the 7th athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar downwards-when outer bar is downward, the control system of double pendulum is by the positive feedback proportional control, bar and the vibration simultaneously of outer bar are put in the control, simultaneously, positive feedback or degenerative proportion differential by closed loop, the angle of two bars and the position of dolly are controlled, make two forks become the attitude vibration of near linear to put, at this moment the linear superposition of three control actions has constituted the motion control to dolly;

8. interior bar upwards-outer bar upwards-two bars turn clockwise simultaneously

To the 8th athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar upwards-when outer bar makes progress, dolly moves to left, two bars are freely dropped from right-hand simultaneously, start the control that turns clockwise simultaneously of two bars, when two bar barycenter are lower than its turning axle, by positive feedback control to two bar pivot angles, inject energy simultaneously to two bars, to replenish the energy loss that causes because of friction in the rotation of two bars, the number of times that two bars rotate simultaneously is decided by to inject the size of energy, when interior bar and outer bar rotate when getting back to vertically upward simultaneously, the control system of double pendulum makes interior bar by the positive feedback or the control of degenerative proportion differential of closed loop, outer bar keeps attitude vertically upward simultaneously, and the displacement of dolly is remained near the initial position;

9. interior bar upwards-outer bar upwards-two bars be rotated counterclockwise simultaneously

To the 9th athletic posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar upwards-when outer bar makes progress, dolly moves to right, two bars are freely dropped from left simultaneously, start two bars and be rotated counterclockwise control simultaneously, when two bar barycenter are lower than its turning axle, by positive feedback control to two bar pivot angles, inject energy simultaneously to two bars, to replenish the energy loss that causes because of friction in the rotation of two bars, the number of times that two bars rotate simultaneously is decided by to inject the size of energy, when interior bar and outer bar rotate when getting back to vertically upward simultaneously, the control system of double pendulum makes interior bar by the positive feedback or the control of degenerative proportion differential of closed loop, outer bar keeps attitude vertically upward simultaneously, and the displacement of dolly is remained near the initial position;

10. interior bar downwards-outer bar upwards-two bars put simultaneously

To the 10th movement posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar downwards-when outer bar makes progress, at first make double pendulum bar deviation position with less moving of car, then according to the position and the athletic posture feature of two forks, proportional control by positive feedback, the bar vibration is put in making, simultaneously, degenerative proportion differential control by closed loop, keep outer bar and interior bar to be the attitude of certain included angle and relative motion, and vibration is put simultaneously, and the motion control of dolly is made of the linear superposition of above-mentioned positive and negative FEEDBACK CONTROL all the time;

Interior bar upwards-outer bar downwards-two bars turn clockwise simultaneously

To the 11st movement posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar upwards-when outer bar is downward, angle by bar and outer bar in the negative feedback control, dolly moves to left simultaneously, two bars are freely dropped from right-hand, start the control that turns clockwise of two bars, in two bar barycenter are lower than during the bar turning axle, inject energy by the positive feedback proportional control to two bars, replenish the energy loss that causes because of friction in the rotation, the number of times that two bars rotate simultaneously is decided by to inject the size of energy, in interior bar and the rotation of outer bar are got back to bar make progress-when outer bar is downward, positive feedback or the degenerative proportion differential control of the control system of double pendulum by closed loop, bar keeps up-attitude that outer bar keeps down in making, and the displacement of dolly is remained near the initial position;

Interior bar upwards-outer bar downwards-two bars be rotated counterclockwise simultaneously

To the 12nd movement posture controlled target in 12 basic exercise attitudes of the present invention's two forks controlled target synoptic diagram, when interior bar upwards-when outer bar is downward, angle by bar and outer bar in the negative feedback control, dolly moves to right simultaneously, two bars are freely dropped from left, start two bars and be rotated counterclockwise control, in two bar barycenter are lower than during the bar turning axle, inject energy by the positive feedback proportional control to two bars, replenish the energy loss that causes because of friction in the rotation, the number of times that two bars rotate simultaneously is decided by to inject the size of energy, in interior bar and the rotation of outer bar are got back to bar make progress-when outer bar is downward, positive feedback or the degenerative proportion differential control of the control system of double pendulum by closed loop, bar keeps up-attitude that outer bar keeps down in making, and the displacement of dolly is remained near the initial position;

3) the complete acrobatics action of two bars controlled target determines and the control task decomposition

1. two bars complete acrobatics action controlled target determines

Utilization owes to drive the double pendulum system, simulation acrobat's action, characteristics according to complete acrobatics action, comprehensive according to the acrobatics art, the requirement of creativeness and fragrance, in conjunction with the (1)-1) the equilibrium position assembled state and (1)-2 in step) 12 basic exercise attitudes and the conversion and the joining relation mutually in step, pass through computer aided program, the various complete acrobatics actions of layout, and definite corresponding complete acrobatics action controlled target, the quantity of complete acrobatics action controlled target, action number decision by corresponding complete acrobatics action, wherein each acrobatics action has showed from a certain equilibrium position assembled state, experience the motion process of a certain basic exercise attitude, arrive another kind of equilibrium position assembled state or get back to original equilibrium position assembled state;

2. the control task of the complete acrobatics action of two bars controlled target is decomposed

According to the (1)-3)-the 1. complete acrobatics action of the two bars controlled target determined of step, sequence of movement according to each complete acrobatics action controlled target, by program the sub-controlled target in each stage is resolved in each action respectively, and the corresponding sub-controller of sub-controlled target of each stage is set, the sub-controlled target in each stage is achieved by the control of corresponding sub-controller, also to determine by the action order, realize taking over seamlessly between each action with the controlled target that is connected and be provided with corresponding related graphic, thereby realize nonlinear Control and the complete acrobatics Autonomous Control of moving of double pendulum system on a large scale in;

(2) control of complete acrobatics action controlled target

1) modeling of controlled device double pendulum system and parameter identification

1. owe to drive the foundation of double pendulum system mathematic model structure

Set up the mathematical model structure of owing to drive the double pendulum system with the Lagrange's equation in newton-Euler method or the analytical mechanics, the model structure form of foundation is the second order nonlinear differential equation:

$M\left(q\right)\stackrel{\&CenterDot;\&CenterDot;}{q}+C(q,\stackrel{\&CenterDot;}{q})\stackrel{\&CenterDot;}{q}+G\left(q\right)=F$

In the formula: q=(x, θ ₁, θ ₂) ^T, $\stackrel{\&CenterDot;}{q}={(\stackrel{\&CenterDot;}{x},{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1,{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2)}^T$

$M\left(q\right)=\left[\begin{array}{ccc}M+m_1+m_2+m_0& (m_1{l}_1+m_{2}L+m_{0}L)\cos \left({\mathrm{\&theta;}}_1\right)& m_2{l}_2\cos \left({\mathrm{\&theta;}}_2\right)\\ (m_1{l}_1+m_{2}L+m_{0}L)\cos \left({\mathrm{\&theta;}}_1\right)& (m_1{l}_1^2+J_1+m_2{L}^2+m_0{L}^2)& m_{2}L{l}_2\cos ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)\\ m_2{l}_2\cos \left({\mathrm{\&theta;}}_2\right)& m_{2}L{l}_2\cos ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)& (m_2{l}_2^2+J_2)\end{array}\right]$

$C(q,\stackrel{\&CenterDot;}{q})=\left[\begin{array}{ccc}f& -(m_1{l}_1+m_{2}L+m_{0}L){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\sin \left({\mathrm{\&theta;}}_1\right)& -m_2{l}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2\sin \left({\mathrm{\&theta;}}_2\right)\\ 0& c_1+c_2& m_{2}L{l}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2\sin ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)-c_2\\ 0& -m_{2}L{l}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\sin ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)-c_2& c_2\end{array}\right]$

$G\left(q\right)=\left[\begin{array}{c}0\\ -(m_{0}L+m_1{l}_1+m_{2}L)g\left(\sin {\mathrm{\&theta;}}_1\right)\\ -m_{2}g{l}_2\sin \left({\mathrm{\&theta;}}_2\right)\end{array}\right]$

F＝[u 0 0] ^T

Concrete parameter in the following formula in the physical significance of each symbol and the enforcement sees the following form:

The dolly mass M Interior fork quality m ₁ Outside lever quality m ₂ Scrambler quality m ₀ Interior fork barycenter arrives rotating shaft apart from l ₁ The outside lever barycenter arrives rotating shaft apart from l ₂ Dolly horizontal shift x Inside and outside fork length L Dolly-track friction coefficient f Interior fork pendulum angle θ ₁rad Fork pivoting friction coefficient f ₁、f ₂ Outside lever pendulum angle θ ₂rad Inside and outside fork moment of inertia J ₁、J ₂ Level applies control uN

2. in computing machine, make up and owe to drive double pendulum system mathematic model corresponding numerical model

Use numerical analysis method, according to the (2)-1)-the 1. mathematical model set up of step, in computing machine, set up corresponding numerical model, and determine kinetic parameter in the mathematical model by preliminary physical measurement, in Computer Simulation, find the solution the differential equation with the quadravalence runge kutta method of fixed step size;

3. the identification of double pendulum system equivalent model parameter

At first according to the input and output response and the (2)-1 of owing to drive the double pendulum system of reflection actual measurement)-input and output that 2. go on foot the numerical model of in computing machine, the setting up difference between responding, set up the fitness function of corresponding evolutionary programming algorithm, using evolutionary programming algorithm then adjusts to the kinetic parameter in the model, accomplish basically identical until the input and output response of numerical simulation model and the input and output response of practical object, be not easy to the friction factor that accurately obtains with mensuration in the model, also in above genetic evolution calculation process, be determined, thereby obtain be can with the equivalent numerical of practical object basically identical, so the determining of the effective control parameter of controller, the appraisal of system works quality all can be finished by the numerical simulation experiment;

2) complete acrobatics is moved determining of each sub-controller and related graphic parameter and optimizing

To the (1)-3) the complete acrobatics action controlled target determined of step, decompose obtain each stage by stage controlled target and each corresponding sub-controller is set and guarantee to take over seamlessly between each action be connected related graphic, realize determining and optimization of above-mentioned each sub-controller and related graphic parameter by evolutionary programming algorithm;

3) assessment and the judgement of control experiment in kind and experimental result

To the (1)-3) go on foot each sub-controller of setting with related graphic, after the control program of establishment energy real time execution, in controller that is input to the controller formed by the PC system or forms by embedded system or the controller formed by PC system and embedded system, in its controller, be provided with motion control card, rotation to servomotor in the system is controlled, the displacement of the rotation driving trolley by servomotor, the location status and the athletic posture of two forks that control and dolly flexibly connect, owing to drive double pendulum system material object in control carries out in the experiment of complete acrobatics action, write down the situation of environmental interference and the effect of control in real time, in experimentation, at any time The simulation experiment result and full-scale investigation result are analyzed and relatively reach assessment and judge: when not finishing the controlled target of complete acrobatics action, repeat each step in (2) step, controller parameter or control program are adjusted again; When finishing the controlled target of complete acrobatics action, finish control experiment in kind, thereby finish the control of owing to drive the complete acrobatics action of double pendulum system.

2. according to the described control method for acrobatic motion of pendulums of under-actuated double pendulum system of claim 1, it is characterized in that a kind of control method for acrobatic motion of pendulums of under-actuated double pendulum system, utilization owes to drive double pendulum system and controller, and is as follows to the method step of the decomposition of the complete acrobatics of first cover action that arranged and control by program:

1) to the decomposition of complete acrobatics action controlled target

To the complete acrobatics action of first cover controlled target that has arranged by computing machine, by its sequence of movement, adopt to open and close that ring combines and the control mode of positive negative feedback combination, should overlap acrobatics action controlled target by program and be decomposed into 15 stage controlled target, and 15 sub-controllers of 15 stage controlled target correspondences are set, its decomposition and control method step are as follows:

1. first stage controlled target, from the 1st location status of double pendulum system, promptly bar downwards-the downward naturally stable location status of outer bar begins, through interior bar downwards-the 1st kind of basic exercise attitude that outer bar put, in arriving bar downwards-the 2nd location status that outer bar makes progress also stablize;

2. second stage controlled target, through interior bar downwards-turn clockwise 720 ° the 2nd kind of basic exercise attitude of outer bar, in getting back to bar downwards-the 2nd location status that outer bar makes progress and stable;

3. three phases controlled target, through interior bar downwards-outer bar is rotated counterclockwise 720 ° the 3rd kind of basic exercise attitude, in getting back to bar downwards-the 2nd location status that outer bar makes progress and stable;

4. four-stage controlled target, through interior bar downwards-outer bar upwards in-two bars the 10th kind of basic exercise attitude to the of having put simultaneously bar upwards-4 downward location statuss of outer bar also stablize;

5. the 5th stage controlled target, through interior bar upwards-the 4th kind of basic exercise attitude that outer bar put to interior bar make progress-the 3rd location status that outer bar makes progress also stablize;

6. the 6th stage controlled target, through interior bar upwards-turn clockwise 1080 ° the 5th kind of basic exercise attitude of outer bar, in getting back to bar upwards-the 3rd location status that outer bar makes progress and stable;

7. the 7th stage controlled target, through interior bar upwards-outer bar is rotated counterclockwise 1080 ° the 6th kind of basic exercise attitude, in getting back to bar upwards-the 3rd location status that outer bar makes progress and stable;

8. the 8th stage controlled target, through interior bar upwards-turn clockwise 720 ° the 5th kind of basic exercise attitude of outer bar, in getting back to bar upwards-the 3rd location status that outer bar makes progress and stable;

9. the 9th stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously 180 ° the 8th kind of basic exercise attitude of-two bars upwards, to interior bar downwards-downward the 1st location status of outer bar and stable;

10. the tenth stage controlled target, through interior bar downwards-outer bar downwards-two bars the 7th kind of basic exercise attitude of having put simultaneously to interior bar upwards-the 3rd location status that outer bar makes progress also stablize;

The 11 stage controlled target, through interior bar upwards-outer bar upwards-two bars be rotated counterclockwise simultaneously 360 ° the 9th kind of basic exercise attitude get back in bar upwards-the 3rd location status that outer bar makes progress and stablizing;

The 12 stage controlled target, through interior bar upwards-turn clockwise 40 ° the 5th kind of basic exercise attitude of outer bar, to interior bar upwards-downward the 4th location status of outer bar and stable;

The tenth three phases controlled target, through interior bar upwards-outer bar downwards-two bars be rotated counterclockwise 20 ° the 12nd kind of basic exercise attitude simultaneously, in getting back to bar upwards-downward the 4th location status of outer bar and stable;

The tenth four-stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously 540 ° the 11st kind of basic exercise attitude of-two bars downwards, to interior bar downwards-the 2nd location status that outer bar makes progress and stablizing;

The 15 stage controlled target, through interior bar downwards-turn clockwise 900 ° the 2nd kind of basic exercise attitude of outer bar, to interior bar downwards-downward the 1st location status of outer bar and stable, finish this cover and move;

2) control of complete acrobatics action controlled target

1. the modeling of controlled device double pendulum system and parameter identification

If state variable is: q=[x θ ₁θ ₂] ^T, in the formula: x is the dolly displacement, θ ₁Be interior fork angle, θ ₂Be the outside lever angle, the motion model that the application Lagrange's equation gets dolly double pendulum system is:

$M\left(q\right)\stackrel{\&CenterDot;\&CenterDot;}{q}+C(q,\stackrel{\&CenterDot;}{q})\stackrel{\&CenterDot;}{q}+G\left(q\right)=F$

In the formula: $M\left(q\right)=\left[\begin{array}{ccc}M+m_1+m_2+m_0& (m_1{l}_1+m_{2}L+m_{0}L)\cos \left({\mathrm{\&theta;}}_1\right)& m_2{l}_2\cos \left({\mathrm{\&theta;}}_2\right)\\ (m_1{l}_1+m_{2}L+m_{0}L)\cos \left({\mathrm{\&theta;}}_1\right)& (m_1{l}_1^2+J_1+m_2{L}^2+m_0{L}^2)& m_{2}L{l}_2\cos ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)\\ m_2{l}_2\cos \left({\mathrm{\&theta;}}_2\right)& m_{2}L{l}_2\cos ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)& (m_2{l}_2^2+J_2)\end{array}\right]$

$C(q,\stackrel{\&CenterDot;}{q})=\left[\begin{array}{ccc}f& -(m_1{l}_1+m_{2}L+m_{0}L){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\sin \left({\mathrm{\&theta;}}_1\right)& -m_2{l}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2\sin \left({\mathrm{\&theta;}}_2\right)\\ 0& c_1+c_2& m_{2}L{l}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2\sin ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)-c_2\\ 0& -m_{2}L{l}_2{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\sin ({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_2)-c_2& c_2\end{array}\right]$

$G\left(q\right)=\left[\begin{array}{c}0\\ -(m_{0}L+m_1{l}_1+m_{2}L)g\left(\sin {\mathrm{\&theta;}}_1\right)\\ -m_{2}g{l}_2\sin \left({\mathrm{\&theta;}}_2\right)\end{array}\right]$

F＝[u 0 0] ^T

Concrete parameter in the following formula in the physical significance of each symbol and the enforcement sees the following form:

According to following formula, in computing machine, realize the double pendulum system value model of quick computing with the C Programming with Pascal Language, separate above-mentioned second order differential equation with the quadravalence runge kutta method of fixed step size, simulation time is consistent with real-time control at interval, gets 5ms;

Further, allow fork freely fall, write down the exercise data of inside and outside fork,, note the exercise data of fork and dolly to the given acceleration signal of servomotor output from the top;

Utilize evolutionary programming algorithm to make up the search model parameter at random, make the numerical model free movement of similarity condition in the emulation and free-moving data in kind approaching, a wherein immediate group model parameter is exactly the result of identification of Model Parameters;

2. controller parameter determines and optimization

To the 1st) go on foot and decompose 15 stage controlled target that obtain, 15 corresponding sub-controllers are set, and work out 15 corresponding multi-modal control programs respectively, by to the Simulation Control effect of numerical model in the computing machine and the comparison between the expection controlled target, utilize evolutionary programming algorithm to determine and optimize the controlled variable of these 15 controllers;

3) assessment and the judgement of control experiment in kind and experimental result

With the 1st) step decompose 15 sub-controllers of 15 stage controlled target obtaining and by the 2nd)-2. the step is optimized the parameter of 15 sub-controllers that obtain, insert in the PC system of pci interface, by the GT-400-SV motion control card output control signal that is installed in the PC system, after the motor servo driver power amplification, realize the motion control of servomotor, simultaneously, motion control card also can receive the various status informations of dolly position, inside and outside swinging angle of swinging rod double pendulum system, feeds back to controller;

On this basis, owe to drive the control method of the double pendulum system first cover acrobatics action, press the program circuit shown in the program flow diagram of the complete acrobatics action of the decomposition of present embodiment 1 controlled target, be compiled into the control program of real time execution, and be presented in the PC system, finish owing to drive the motion control of the complete acrobatics action of double pendulum system in kind first cover; In material object control experiment, add environmental interference and write down relevant control effect in real time, to controlling outcome evaluation and judgement: when not finishing the controlled target of combination, repeat the 2nd) step, controller parameter or control program are adjusted again; When finishing the controlled target of complete acrobatics action, finish to adjust, thereby finish the apery motion control of owing to drive the first cover acrobatics action of double pendulum system in kind.

3. according to the described control method for acrobatic motion of pendulums of under-actuated double pendulum system of claim 1, it is characterized in that a kind of control method for acrobatic motion of pendulums of under-actuated double pendulum system, utilization owes to drive double pendulum system and controller, and is as follows to the method step of the decomposition of the complete acrobatics of second cover action that arranged and control by program:

1) to the decomposition of complete acrobatics action controlled target

To the complete acrobatics action of second cover controlled target that has arranged by computing machine, by its sequence of movement, adopt to open and close that ring combines and the control mode of positive negative feedback combination, should overlap acrobatics action controlled target by program and be decomposed into 15 stage controlled target, and 15 sub-controllers of 15 stage controlled target correspondences are set, its decomposition and control method step are as follows:

1. first stage controlled target, from the 1st location status of system, promptly bar downwards-the downward naturally stable location status of outer bar begins, through interior bar downwards-outer bar in-two bars the 7th kind of basic exercise attitude of having put simultaneously arrives downwards bar upwards-the 3rd location status that outer bar makes progress also stablize;

2. second stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously 720 ° the 8th kind of basic exercise attitude of-two bars upwards, in getting back to bar upwards-the 3rd location status that outer bar makes progress and stable;

3. three phases controlled target, through interior bar upwards-outer bar upwards-two bars be rotated counterclockwise 1080 ° the 9th kind of basic exercise attitude simultaneously, in getting back to bar upwards-the 3rd location status that outer bar makes progress and stable;

4. four-stage controlled target, through interior bar upwards-turn clockwise 720 ° the 5th kind of basic exercise attitude of outer bar, in getting back to bar upwards-the 3rd location status that outer bar makes progress and stable;

5. the 5th stage controlled target, through interior bar upwards-outer bar is rotated counterclockwise 900 ° the 6th kind of basic exercise attitude, to interior bar upwards-downward the 4th location status of outer bar and stable;

6. the 6th stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously 1080 ° the 11st kind of basic exercise attitude of-two bars downwards, in getting back to bar upwards-downward the 4th location status of outer bar and stable;

7. the 7th stage controlled target, through interior bar upwards-outer bar downwards-two bars be rotated counterclockwise 1080 ° the 12nd kind of basic exercise attitude simultaneously, in getting back to bar upwards-downward the 4th location status of outer bar and stable;

8. the 8th stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously 900 ° the 11st kind of basic exercise attitude of-two bars downwards, to interior bar downwards-the 2nd location status that outer bar makes progress and stablizing;

9. the 9th stage controlled target, through interior bar downwards-turn clockwise 720 ° the 2nd kind of basic exercise attitude of outer bar, in getting back to bar downwards-the 2nd location status that outer bar makes progress and stable;

10. the tenth stage controlled target, through interior bar downwards-outer bar is rotated counterclockwise 1260 ° the 3rd kind of basic exercise attitude, to interior bar downwards-downward the 1st location status of outer bar and stable;

The 11 stage controlled target, through interior bar downwards-the 1st kind of basic exercise attitude that outer bar put, to interior bar downward-the 2nd location status that outer bar makes progress also stablize;

The 12 stage controlled target, through interior bar downwards-outer bar-two bars the 10th kind of basic exercise attitude of having put simultaneously upwards, to interior bar upwards-downward the 4th location status of outer bar and stablizing;

The tenth three phases controlled target, through interior bar upwards-the 4th kind of basic exercise attitude that outer bar put, to interior bar make progress-the 3rd location status that outer bar makes progress also stablize;

The tenth four-stage controlled target, through interior bar upwards-outer bar turn clockwise simultaneously 1080 ° the 8th kind of basic exercise attitude of-two bars upwards, in getting back to bar upwards-the 3rd location status that outer bar makes progress and stable;

The 15 stage controlled target, through interior bar upwards-outer bar upwards-two bars be rotated counterclockwise 1260 ° the 9th kind of elemental motion simultaneously, in getting back to bar downwards-downward the 1st location status of outer bar and stable, finish this cover and move;

2) control of complete acrobatics action controlled target

1. the modeling of controlled device double pendulum system and parameter identification

The foundation of modelling by mechanism, numerical simulation model and identification of Model Parameters, with claim 2 2)-1. go on foot identical;

2. controller parameter determines and optimization

Determining and optimization method of controller parameter, with claim 2 the 2nd)-2. go on foot identical, but because controlled target with, the fitness function in the evolutionary programming algorithm is different with the optimization control parameter of being tried to achieve;

3) assessment and the judgement of control experiment in kind and experimental result

With the 1st) step decompose 15 sub-controllers of 15 stage controlled target obtaining and by the 2nd)-2. the step is optimized the parameter of 15 sub-controllers that obtain, insert in the controller of PC system and embedded system composition, in embedded system, be provided with bottom the motion control arithmetic module and with the program module of PC system communication, the control signal of embedded system output, after the motor servo driver power amplification, realize the motion control of servomotor, simultaneously, embedded system also receives the dolly position, the status information of inside and outside swinging angle of swinging rod double pendulum system feeds back to controller;

On this basis, owe to drive the double pendulum system second cover acrobatics method of controlling operation, press the program circuit shown in the program flow diagram of the complete acrobatics action of the decomposition of present embodiment 2 controlled target, be compiled into the control program of real time execution, and be presented in the embedded system, finish the acrobatics action control to the double pendulum bar, the PC system communicates by letter with embedded system, realizes the double pendulum system running state is monitored and be provided with control task tension management function; In material object control experiment, add environmental interference and write down relevant control effect in real time, to controlling outcome evaluation and judgement: when not finishing the controlled target of combination, repeat the 2nd) step, controller parameter or control program are adjusted again; When finishing the controlled target of complete acrobatics action, finish to adjust, thereby finish the apery motion control of owing to drive the second cover acrobatics action of double pendulum system in kind.

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