CN118123850B - A deformation sensing and trajectory tracking method and system for a long flexible hydraulic mechanical arm - Google Patents

Abstract

The present invention discloses a deformation sensing and trajectory tracking method and system for a long flexible hydraulic mechanical arm. The method first establishes a boom deformation curve for theoretical reference based on a cantilever beam model, and constructs the boom deformation curve using a quartic polynomial according to the curve characteristics. By extracting the inclination information of any three locations of the boom, an inclination observer based on a discrete-time Lumberg state observer is designed to reduce the inclination measurement error caused by boom vibration. Then, the polynomial coefficients are solved according to the Kramer rule, and finally the deflection of the boom end is calculated according to the constructed curve, which is converted into a joint compensation angle, and the trajectory is corrected using the independent compensation principle. The method proposed in the present invention can accurately sense the static deformation of the boom of a long flexible hydraulic mechanical arm, avoiding the problem of low calculation accuracy caused by the use of structural parameter approximations in traditional deflection solutions. In addition, the sensed deformation information is applied to the underlying trajectory tracking control, which can realize precise and automated operation of the long flexible arm end.

Description

A deformation sensing and trajectory tracking method and system for a long flexible hydraulic mechanical arm

Technical Field

The present invention relates to the technical field of automated precision operation of long flexible boom engineering machinery, and in particular to a deformation sensing and trajectory tracking method and system for a long flexible hydraulic mechanical arm.

Background technique

The long flexible hydraulic mechanical arm is the core operating mechanism of long-arm construction machinery. The arm is mainly driven by a multi-stage series hydraulic cylinder. Due to its advantages such as wide operating range and high power-to-weight ratio, it is widely used in special operations such as construction, high-altitude cleaning, and industrial production. At the same time, informatization and intelligence are driving the transformation of long-arm construction machinery from the traditional multi-person collaboration and joint control mode to the less-person, automated operation mode.

However, this type of operating mechanism usually also has significant characteristics such as weak rigidity and high inertia. In the extended state, the boom will produce elastic deformation due to its own gravity and external load. The deformation deflection of each boom section is accumulated through multiple joints and eventually produces obvious end position errors. Taking the long flexible hydraulic mechanical arm of a concrete placing boom as an example, in the process of controlling the automatic placing of the mechanical arm, if the trajectory tracking algorithm based on the rigidity assumption is continued to be used, the end position error caused by the deformation of the boom will not be avoided, which will seriously reduce the placing accuracy and even cause the boom or the end hose to collide with surrounding buildings, causing safety accidents.

At present, the mainstream idea to improve the operation accuracy of the end of a long flexible arm is to compensate for the deformation of the arm, so it is particularly important to obtain the deformation data of the arm. The existing arm deformation calculation methods are mainly divided into two categories: one is to calculate the arm deflection by establishing a flexible multi-body dynamic model of the robotic arm; the other is to conduct finite element simulation analysis on the robotic arm under full posture conditions to establish an arm deformation database. Although these two methods have shown certain effects in improving trajectory accuracy, they both rely on sufficiently accurate mathematical or simulation models, which requires a priori known control object structural parameters and considers a large number of boundary conditions. Therefore, in principle, the two methods are only applicable to the research object itself and are not universal in practical applications. To this end, from the perspective of improving the accuracy of automated operations and the universality and extensibility of the method, based on the idea of information fusion of multi-posture data of the arm, the present invention proposes a method for static deformation perception and trajectory tracking of the arm.

Summary of the invention

The purpose of the present invention is to propose a deformation sensing and trajectory tracking method and system for a long flexible hydraulic mechanical arm in view of the shortcomings of the existing technical methods, which mainly solves the problems of low calculation accuracy and poor practicality of the method when directly using the approximate values of the arm structure parameters to model/simulate the calculation of the end deformation. In addition, considering the adverse effect of the arm vibration on the sensor measurement accuracy, the deformation data is corrected by designing an inclination observer, and the calculated accurate joint compensation angle is independently embedded in the joint trajectory tracking strategy based on PID, which solves the problem of low end motion accuracy caused by the trajectory tracking algorithm based on the traditional rigid assumption.

The technical solution adopted by the present invention is: in the first aspect, the present invention provides a deformation sensing and trajectory tracking method for a long flexible hydraulic mechanical arm, the method comprising the following steps:

Step 1, based on the joint torque of the long flexible hydraulic mechanical arm under the action of gravity, simplify the arm into a cantilever beam model;

Step 2: According to the characteristics of the cantilever beam model, a quartic polynomial is used to construct the overall deformation curve of the boom, and the analytical expression of the tangent value of the inclination angle at any point of the boom is obtained by differentiation;

Step 3, based on the end angular velocity signal of the boom vibration process, a discrete-time Lumberg state observer model is used to design a boom inclination angle observer, which can accurately feedback the inclination angle information at any point of the boom in real time;

Step 4: Based on the inclination information, the Kramer rule is used to calculate the unique solution of the coefficient of the analytical formula of the inclination tangent value, and then the deformation profile curve of the boom is obtained;

Step 5, calculate the deflection of each arm end to predict the joint deviation angle caused by deformation, and in the trajectory tracking process of the long flexible arm automatic operation, adopt the principle of joint independent compensation to compensate the joint angle corresponding to the corresponding end deflection at each sampling moment, and correct the end trajectory in real time.

Furthermore, in step 1, the boom is simplified into a cantilever beam model. Based on the characteristics of the cantilever beam model, the deflection at any position of the boom and the deformation position present a quartic function relationship. According to this relationship, a quartic polynomial is used in step 2 to construct a deformation profile curve, as follows:

in, The first value calculated for the constructed curve Boom The deflection at the point, , , Respectively The arm deformation curve corresponds to the coefficients of the polynomial. By differentiating the curve with respect to the deformation position, the analytical expression of the tangent value of the inclination angle at any point can be obtained.

Furthermore, in step 3, the angular velocity signal of the end of the boom during vibration is collected, and the boom inclination angle observer is designed based on the discrete time Lumberg state observer model. The inclination angle observer is specifically as follows:

in, for The estimated value of the inclination angle at the moment, for The estimated value of the inclination angle at the moment, for The tilt sensor measurement value at the moment, is the sampling time, for The bias estimate of the angular velocity measured by the inertial measurement unit at time, for The bias estimate of the angular velocity measured by the inertial measurement unit at time, for The angular velocity measured by the inertial measurement unit at the moment, is the tilt observer gain, is the bias estimator gain.

Furthermore, in step 4, the inclination sensor and the inertial measurement unit feedback data are combined, and the inclination observer in step 3 is used to obtain the accurate inclination values of any three points on the same section of the boom at each moment, and then substitute them into the analytical expression of the inclination tangent value obtained in step 2, and calculate the unique solution of the analytical expression coefficient according to Cramer's rule, and finally obtain the expression of the boom deformation profile curve at the current moment.

Furthermore, in step 5, according to the deformation profile curve expression of step 4, the deflection of the boom end at the current moment is obtained as the arc length corresponding to the boom rotation angle, so that the joint deviation angle is calculated back through the arc length formula in mathematical concepts.

Furthermore, in step 5, in the trajectory tracking process of the long flexible arm automatic operation, the independent compensation principle is adopted. When the PID controller is used to track the expected joint trajectory, the joint is compensated for the corresponding deviation angle at each sampling moment, thereby ensuring the end trajectory tracking accuracy. The formula for compensating the deviation angle of the joint is as follows:

in, for Moment Compensation angle of the arm joint, for Rebuilding the moment The end deflection calculated from the arm deformation profile curve, For the The length of the arm, , and They are The time is Coefficient of the deformation profile curve constructed by the arm.

In a second aspect, the present invention also provides a long flexible hydraulic mechanical arm deformation perception and trajectory tracking system, the system comprising a model simplification module, a deformation curve construction module, a tilt angle observer design module, a deformation profile curve solving module and a trajectory tracking module;

The model simplification module is used to simplify the arm frame into a cantilever beam model based on the joint torque of the long flexible hydraulic mechanical arm arm frame under the action of gravity;

The deformation curve construction module is used to construct the overall deformation curve of the boom using a quartic polynomial according to the cantilever beam model characteristics, and differentiate to obtain an analytical expression of the tangent value of the inclination angle at any point of the boom;

The inclination angle observer design module is used to design the inclination angle observer of the boom based on the terminal angular velocity signal of the boom vibration process, adopt the discrete time Lumberg state observer model, and accurately feedback the inclination angle information at any point of the boom in real time;

The deformation contour curve solving module is used to calculate the unique solution of the coefficient of the analytical formula of the inclination tangent value based on the inclination information using the Cramer's rule, and then obtain the boom deformation contour curve;

The trajectory tracking module is used to calculate the deflection of each arm end to predict the joint deviation angle caused by deformation, and in the trajectory tracking process of the long flexible arm automatic operation, the joint independent compensation principle is adopted to compensate the joint angle corresponding to the corresponding end deflection at each sampling moment, and correct the end trajectory in real time.

In the third aspect, the present invention also provides a deformation sensing and trajectory tracking device for a long flexible hydraulic robotic arm, comprising a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, the deformation sensing and trajectory tracking method for a long flexible hydraulic robotic arm is implemented.

In a fourth aspect, the present invention further provides a computer-readable storage medium having a program stored thereon, and when the program is executed by a processor, the method for deformation sensing and trajectory tracking of a long flexible hydraulic robotic arm is implemented.

In a fifth aspect, the present invention further provides a computer program product, including a computer program, which, when executed by a processor, implements the deformation sensing and trajectory tracking method of a long flexible hydraulic robotic arm.

The beneficial effects of the present invention are:

(1) The present invention proposes a method for deformation perception and trajectory tracking of a long flexible arm with multi-posture information fusion, which solves the problems of inaccurate deformation calculation, low trajectory tracking accuracy, and poor practicality of the traditional method, which relies on dynamic theory modeling or full-posture dynamics simulation to obtain the deformation of the flexible arm and compensates for the deformation based on a single posture information feedback control framework.

(2) The arm deformation sensing scheme adopted in the present invention gives full play to the advantages of sensor data fusion in engineering applications. The basic form of the arm deformation contour curve is analyzed based on the cantilever beam deflection model. The end deflection can be accurately solved only by any three inclination angles of the arm, and the deviation of each joint can be compensated independently, which can effectively improve the end trajectory tracking accuracy and reduce the difficulty of practical application.

(3) In order to solve the common problem that the self-vibration of the flexible arm after being excited easily leads to a decrease in the measurement data accuracy of the inclination sensor, the present invention proposes a design method of the inclination observer based on the discrete-time Romberg model, which can effectively reduce the adverse effect of vibration on the inclination measurement error.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

FIG1 is a flow chart of a long flexible arm deformation perception and trajectory tracking method based on multi-posture information fusion.

FIG2 is a schematic diagram of the structure of a four-degree-of-freedom long flexible hydraulic mechanical arm of a 13m concrete placing boom.

FIG3 is a schematic diagram of a cantilever beam model equivalent to a cantilever beam model subjected to a torque-uniformly distributed load combination.

FIG4 is a schematic diagram of the sensor layout scheme of the multi-posture information fusion framework.

FIG5 is a schematic diagram of a long flexible arm trajectory tracking strategy based on multi-posture information fusion deformation perception.

FIG6 is a comparison diagram of the actual end trajectory curve and the expected end trajectory in the process of making the long flexible hydraulic mechanical arm track a straight line trajectory using the method proposed by the present invention and the comparison method.

FIG. 7 is a curve diagram showing the error variation of the end in the vertical direction when the long flexible hydraulic mechanical arm tracks a straight line trajectory using the method proposed by the present invention and the comparative method.

FIG8 is a structural diagram of a deformation sensing and trajectory tracking device for a long flexible hydraulic mechanical arm provided by the present invention.

Detailed ways

In order to more clearly illustrate the use process of the present invention, it is further described below in conjunction with the drawings and embodiments, but the content of the present invention is not limited to the presented examples.

The embodiment of the present invention proposes a deformation sensing and trajectory tracking method and system for a long flexible hydraulic mechanical arm. The method first establishes a reference arm deformation contour curve based on the cantilever beam principle assumption, constructs the arm deformation curve using a quartic polynomial according to the curve characteristics, and uses an inclination sensor to extract the inclination information of any three positions of the arm. Further, in combination with the vibration signal measured by the inertial measurement unit, a arm inclination observer is designed based on the discrete time Lumberg state observer model to reduce the measurement error of the inclination sensor caused by vibration. Then the inclination angle is substituted into the analytical expression of the inclination tangent value, the unique solution of the analytical expression coefficient is solved according to the Kramer method, and the deflection of each arm end is calculated. Finally, the arm end deflection is converted into a joint compensation angle, and the independent compensation principle is used to correct the deviation in real time during the joint trajectory tracking process, thereby effectively improving the motion accuracy of the mechanical arm end. For the specific process, refer to Figure 1.

This embodiment takes a 13m concrete placing boom's four-degree-of-freedom long flexible hydraulic mechanical arm as an example, as shown in FIG2 . Usually, the first joint is responsible for completing the rotational motion, and the arm deformation is negligibly affected by the joint. Therefore, it is regarded as a planar three-degree-of-freedom long flexible hydraulic mechanical arm composed of two, three, and four joints. The specific implementation steps of the method of the present invention are as follows:

Step 1: In Cartesian space, derive the joint torque generated by the gravity of the robot arm at each end of the boom and the uniformly distributed load on the boom, and equate the force state of the boom to the cantilever beam model shown in Figure 3 (subject to the combined effect of torque and uniformly distributed load), and then establish the boom deformation profile curve equation for reference.

The gravity generates joint torque at the end of each arm:

In the formula, is the joint torque vector, is the torque component generated by the gravity of the robot arm at each joint, is the Jacobian matrix, The forces on each arm are as follows:

in, , , are the center of mass positions of each boom, , , are the masses of each boom, , are the lengths of each arm, , , are the angles of the 1st, 2nd, and 3rd joints, is the acceleration due to gravity.

The calculation formula for the uniformly distributed load on the boom is:

in, for The uniform load on the boom is is the equivalent density, for Equivalent cross-sectional area of the boom, for The length of the arm, for The cosine of the arm joint angle in world coordinates.

The deformation profile curve equation for reference established after the boom is equivalent to a cantilever beam model is:

in, for Boom The deflection at the point, is the elastic modulus of the boom material, for Boom moment of inertia, For gravity Torque at the end of the boom.

Step 2, based on the theoretical characteristics analysis of the boom deformation contour curve established in step 1, it can be seen that the deflection at any position of the boom and the deformation position present a quartic function relationship. The boom deformation contour curve is reconstructed using a quartic polynomial, and the curve is differentiated with respect to the deformation position to derive an analytical expression for the tangent value of the inclination angle at any point of the boom.

The reconstructed arm deformation profile curve is:

in, The formula calculated using this Boom The deflection at the point, , , They are The boom deformation curve corresponds to the coefficients of the polynomial.

The analytical formula of the tangent value of the inclination angle at any point of the boom is:

in, for Boom The inclination angle at the point.

Step 3: Use the inertial measurement unit to collect the angular velocity signal of the end of the boom during vibration, and design the boom inclination angle observer based on the discrete-time Lumberg state observer model to reduce the measurement error of the inclination sensor caused by vibration.

The tilt angle observer is:

in, for The estimated value of the inclination angle at the moment, for The estimated value of the inclination angle at the moment, for The tilt sensor measurement value at the moment, is the sampling time, for The bias estimate of the angular velocity measured by the inertial measurement unit at time, for The bias estimate of the angular velocity measured by the inertial measurement unit at time, for The angular velocity measured by the inertial measurement unit at the moment, is the tilt observer gain, is the bias estimator gain.

Step 4, using the multi-posture information fusion framework based on the flexible manipulator electro-hydraulic control system shown in Figure 4 to collect multi-posture information feedback data, including joint posture signals, boom vibration information collected by the inertial measurement unit, and boom deformation information collected by the inclination sensor, wherein the joint posture signals and boom vibration information are used as basic information, and the boom vibration information is used for auxiliary correction to obtain deformation perception data; the observer in step 3 is used to correct the inclination basic data collected at each moment, and the accurate inclination values of any three points on the same section of the boom at the current moment are substituted into the inclination tangent value analytical formula constructed in step 2, and the linear equation group is processed according to Cramer's rule to calculate the unique solution of the analytical coefficients to obtain the deformation contour curve expression of the boom at the current moment.

The linear equations are:

in, is the equation coefficient matrix, is the constant term matrix, The analytical coefficient vectors and matrices are as follows:

in, , and They are Any three points on the arm , , The inclination of the position, , and are analytical coefficients respectively.

The unique solution of the analytical coefficient is specifically:

The deformation profile curve expression of the boom at the current moment is:

Step 5: Set the arm end deflection at any time As the arc length corresponding to the arm rotation angle, the joint deviation angle is calculated back through the arc length formula in the mathematical concept. The trajectory tracking strategy shown in Figure 5 is used, the independent compensation principle is adopted, and the feedback signal of the feedback data of the multi-pose information is combined. The trajectory tracking controller based on PID control tracks the expected joint trajectory at each sampling moment, and the corresponding deviation angle is compensated for the joint. The joint trajectory is corrected in real time based on the flexible manipulator electro-hydraulic control system to complete the preset trajectory tracking of the end.

The deviation angle compensated to the joint is:

in, for time The compensation angle of the joint, for Rebuilding at all times The end deflection calculated from the arm deformation profile curve, , and They are Time is Coefficient of the deformation curve of the boom construction.

Embodiment: The deformation sensing and trajectory tracking method of the long flexible hydraulic mechanical arm of the embodiment is adopted, and a four-degree-of-freedom long flexible hydraulic mechanical arm of a 13m concrete placing boom shown in FIG2 is used to provide a specific experimental plan.

First, according to step 1 of the embodiment, the deformation contour curve equation of the boom is established based on the cantilever beam model, and then the deformation contour curve of the boom is reconstructed using a quartic polynomial according to step 2. The sensor layout scheme shown in Figure 4 is used to feedback multiple posture information of the boom at the current moment, and the accurate inclination information of the installation position of the inclination sensor on the boom, the deformation contour curve of each section of the boom, and the joint deviation angle caused by the deformation are calculated in sequence according to steps 3, 4, and 5. Thereafter, in the trajectory tracking process of the automatic operation of the long flexible hydraulic mechanical arm, the joint independent compensation principle is adopted to compensate the joint deviation angles calculated at each time of use to the corresponding joints, correct the joint trajectory in real time, and complete the preset trajectory tracking of the end.

Comparative example: Using the same process as step 1 of the embodiment, the arm deformation contour curve equation is established based on the cantilever beam model, the expected joint trajectory is used to directly calculate the joint deviation angle caused by the deformation, and the expected joint trajectory is corrected, and then the PID controller is directly used to track the pre-corrected joint trajectory to complete the terminal preset trajectory tracking.

Effect detection: The present invention presets a section of terminal straight line trajectory, and uses the deformation sensing and trajectory tracking methods in the embodiment and the comparative example to track the straight line trajectory. Under the two methods, the comparison between the actual terminal trajectory curve and the expected terminal trajectory curve is shown in Figure 6, and the error change curve of the terminal of the long flexible hydraulic mechanical arm in the vertical direction is shown in Figure 7. From the results shown in Figures 6 and 7, it can be seen that the deformation sensing and trajectory tracking method of the long flexible hydraulic mechanical arm proposed in the present invention can more accurately sense the arm deformation information compared with the comparative method, and brings beneficial effects to the improvement of the terminal trajectory tracking accuracy, and the absolute positioning error in the vertical direction is reduced from ±150mm to ±25mm.

Corresponding to the aforementioned embodiment of a method for deformation sensing and trajectory tracking of a long flexible hydraulic mechanical arm, the present invention also provides an embodiment of a system for deformation sensing and trajectory tracking of a long flexible hydraulic mechanical arm.

Corresponding to the above-mentioned embodiment of a method for sensing deformation and tracking trajectory of a long flexible hydraulic mechanical arm, the present invention also provides an embodiment of a device for sensing deformation and tracking trajectory of a long flexible hydraulic mechanical arm. The system includes a model simplification module, a deformation curve construction module, an inclination observer design module, a deformation profile curve solving module and a trajectory tracking module; the specific implementation process of each module can refer to the steps of the above-mentioned embodiment of a method for sensing deformation and tracking trajectory of a long flexible hydraulic mechanical arm.

The model simplification module is used to simplify the arm frame into a cantilever beam model based on the joint torque of the long flexible hydraulic mechanical arm arm frame under the action of gravity;

The deformation curve construction module is used to construct the overall deformation curve of the boom using a quartic polynomial according to the cantilever beam model characteristics, and differentiate to obtain an analytical expression of the tangent value of the inclination angle at any point of the boom;

The inclination angle observer design module is used to design the inclination angle observer of the boom based on the terminal angular velocity signal of the boom vibration process, adopt the discrete time Lumberg state observer model, and accurately feedback the inclination angle information at any point of the boom in real time;

The deformation contour curve solving module is used to calculate the unique solution of the coefficient of the analytical formula of the inclination tangent value based on the inclination information using the Cramer's rule, and then obtain the boom deformation contour curve;

The trajectory tracking module is used to calculate the deflection of each arm end to predict the joint deviation angle caused by deformation, and in the trajectory tracking process of the long flexible arm automatic operation, the joint independent compensation principle is adopted to compensate the joint angle corresponding to the corresponding end deflection at each sampling moment, and correct the end trajectory in real time.

Referring to Figure 8, an embodiment of the present invention provides a long flexible hydraulic robotic arm deformation sensing and trajectory tracking device, including a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it is used to implement a long flexible hydraulic robotic arm deformation sensing and trajectory tracking method in the above embodiment.

The embodiment of the deformation sensing and trajectory tracking device of a long flexible hydraulic mechanical arm provided by the present invention can be applied to any device with data processing capability, and the any device with data processing capability can be a device or apparatus such as a computer. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capability in which it is located to read the corresponding computer program instructions in the non-volatile memory into the memory and run it. From the hardware level, as shown in Figure 8, it is a hardware structure diagram of any device with data processing capability in which the deformation sensing and trajectory tracking device of a long flexible hydraulic mechanical arm provided by the present invention is located. In addition to the processor, memory, network interface, and non-volatile memory shown in Figure 8, any device with data processing capability in which the device in the embodiment is located can also include other hardware according to the actual function of the device with data processing capability, which will not be described in detail.

The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of the present invention. Ordinary technicians in this field can understand and implement it without paying creative work.

An embodiment of the present invention further provides a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, a deformation sensing and trajectory tracking method of a long flexible hydraulic mechanical arm in the above embodiment is implemented.

The computer-readable storage medium may be an internal storage unit of any device with data processing capability described in any of the aforementioned embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device of any device with data processing capability, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capability. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, and may also be used to temporarily store data that has been output or is to be output.

The present invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, the method for sensing deformation and tracking trajectory of a long flexible hydraulic mechanical arm is implemented.

The above description is only a preferred implementation case of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the basic principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims (10)

1. The deformation sensing and track tracking method for the long flexible hydraulic mechanical arm is characterized by comprising the following steps of:

step 1, simplifying an arm support into an arm support Liang Moxing based on joint torque of the arm support of a long flexible hydraulic mechanical arm under the action of gravity;

Step 2, constructing an integral deformation curve of the cantilever crane by adopting a fourth-time polynomial according to the model characteristics of the cantilever crane, and differentiating to obtain an inclination tangent value analysis type at any point of the cantilever crane;

Step 3, designing an arm support inclination angle observer by adopting a discrete time Luneberg state observer model based on a terminal angular velocity signal in the arm support vibration process, and accurately feeding back inclination angle information at any point of the arm support in real time;

Step 4, calculating a unique solution of the inclination tangent value analytic coefficient based on the inclination information by utilizing the Kreimer rule, and further obtaining a deformation profile curve of the arm support;

And 5, calculating the deflection of the tail end of each arm support to predict the joint deflection angle caused by deformation, adopting a joint independent compensation principle in the track tracking process of the automatic operation of the long flexible arm, and respectively compensating the joint angle corresponding to the deflection of the corresponding tail end at each sampling moment to correct the tail end track in real time.

2. The method for sensing deformation and tracking the track of the long flexible hydraulic mechanical arm according to claim 1, wherein in the step 1, the arm support is simplified into the cantilever Liang Moxing, based on the characteristics of a cantilever beam model, the deformation profile curve is constructed by adopting a fourth-order polynomial according to the four-order functional relation between the deflection of any position of the arm support and the deformation position, and the method is specifically as follows:

；

Wherein, Calculated for the constructed curveArm supportThe deflection at the point(s),、、Respectively the firstAnd (3) obtaining the analytic expression of the inclination tangent value of any point by differentiating the curve relative to the deformation position according to the coefficient of the polynomial corresponding to the arm support deformation curve.

3. The method for sensing deformation and tracking the track of the long flexible hydraulic mechanical arm according to claim 1, wherein the step 3 is characterized in that an angular velocity signal of the tail end in the vibration process of the arm support is collected, and an arm support inclination angle observer is designed based on a discrete time Luneberg state observer model, wherein the inclination angle observer is specifically as follows:

；

Wherein, Is thatThe time-of-day tilt angle estimate,Is thatThe time-of-day tilt angle estimate,Is thatThe measurement value of the moment inclination angle sensor,In order to sample the time of the sample,Is thatThe moment inertial measurement unit measures an offset estimate of the angular velocity,Is thatThe moment inertial measurement unit measures an offset estimate of the angular velocity,Is thatThe angular velocity measured by the moment of inertia measurement unit,For the gain of the tilt angle observer,For biasing the estimator gain.

4. The method for sensing deformation and tracking the track of the long flexible hydraulic mechanical arm according to claim 1, wherein in the step 4, the inclination angle observer in the step 3 is adopted to obtain accurate inclination angle values of any three parts on the same section of arm support at each moment by combining the inclination angle sensor and the feedback data of the inertia measurement unit, and then the accurate inclination angle values are substituted into the inclination angle tangent value analytic expression obtained in the step 2, the analytic expression coefficient unique solution is calculated according to the Kramer rule, and finally the deformation profile curve expression of the arm support at the current moment is obtained.

5. The method for sensing deformation and tracking the track of the long flexible hydraulic mechanical arm according to claim 1, wherein in the step 5, according to the deformation contour curve expression in the step 4, the deflection of the tail end of the arm support at the current moment is obtained as the corresponding arc length of the angle of the arm support, so that the joint deflection angle is reversely calculated through an arc length formula in a mathematical concept.

6. The method for sensing deformation and tracking the track of the long flexible hydraulic mechanical arm according to claim 1, wherein in the step 5, in the track tracking process of the long flexible arm automatic operation, an independent compensation principle is adopted, when a PID controller is utilized to track a desired joint track, a corresponding deviation angle is compensated for the joint at each sampling moment, so that the tracking precision of the tail end track is ensured, and the deviation angle formula for the joint is compensated, and is specifically as follows:

；

Wherein, Is thatTime of day (time)The compensation angle of the arm support joint,Is thatTime of day reconstructionThe deflection of the tail end calculated by the arm support deformation profile curve,Is the firstThe length of the arm support,、AndRespectively isThe moment is the firstThe coefficient of the deformation profile curve constructed by the arm support.

7. The deformation sensing and track tracking system of the long flexible hydraulic mechanical arm is characterized by comprising a model simplifying module, a deformation curve constructing module, an inclination angle observer design module, a deformation contour curve solving module and a track tracking module;

the model simplifying module is used for simplifying the arm support into a cantilever Liang Moxing based on joint torque of the long flexible hydraulic mechanical arm support under the action of gravity;

The deformation curve construction module is used for constructing an integral deformation curve of the cantilever crane by adopting a fourth-order polynomial according to the characteristics of the cantilever beam model, and differentiating to obtain an inclination tangent value analysis type at any point of the cantilever crane;

The inclination angle observer design module is used for designing an inclination angle observer of the arm support by adopting a discrete time Luneberg state observer model based on a terminal angular velocity signal in the vibration process of the arm support, and accurately feeding back inclination angle information at any point of the arm support in real time;

the deformation profile curve solving module is used for calculating an inclination tangent value analytic type unique solution based on inclination information by utilizing a Kreimer rule, so as to obtain an arm support deformation profile curve;

The track tracking module is used for calculating the deflection of the tail end of each arm support to predict the joint deflection angle caused by deformation, and in the track tracking process of the automatic operation of the long flexible arm, the joint independent compensation principle is adopted, the joint angles corresponding to the deflection of the corresponding tail end are respectively compensated at each sampling moment, and the tail end track is corrected in real time.

8. A long flexible hydraulic mechanical arm deformation sensing and track tracking device, comprising a memory and one or more processors, wherein executable codes are stored in the memory, and the processor executes the executable codes to realize the long flexible hydraulic mechanical arm deformation sensing and track tracking method according to any one of claims 1-6.

9. A computer readable storage medium having a program stored thereon, wherein the program, when executed by a processor, implements a long flexible hydromechanical arm deformation sensing and trajectory tracking method according to any one of claims 1-6.

10. A computer program product comprising a computer program which, when executed by a processor, implements a long flexible hydromechanical arm deformation sensing and trajectory tracking method according to any one of claims 1-6.