CN113485389A - Underwater robot three-dimensional trajectory tracking control method based on self-adaptive prediction - Google Patents
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Abstract
The invention discloses an underwater robot three-dimensional trajectory tracking control method based on self-adaptive prediction, which comprises the following steps: according to the actual working condition of the underwater robot, the actual motion model of the underwater robot in the three-dimensional space is properly simplified; step two: according to the expected track of the current task, the information of the expected track is transmitted to the AUV, and after data are acquired through relevant equipment of the AUV, current position information eta is obtainedd＝[xd(t)yd(t)zd(t)]TAttitude information psid(t) velocity information vd＝[ud(t)vd(t)wd(t)rd(t)]TFurther providing a control model for tracking the three-dimensional track of the underwater robot; u (t) is the advancing and retreating speed of the AUV, v (t) is the surging speed of the AUV, w (t) represents the floating and submerging speed of the AUV, and r (t) represents the yawing speed of the AUV; when the underwater robot reaches a new position, recalculating the next optimal input based on the current actual state and the expected trajectory, and iterating in each control cycleAnd the control system is used for realizing the continuous control of the controlled object and ensuring the control precision.
Description
Technical Field
The invention belongs to the technical field of motion control of unmanned autonomous underwater robots, and particularly relates to an underwater robot three-dimensional trajectory tracking control method based on self-adaptive prediction.
Background
Unmanned autonomous underwater robots have attracted considerable attention by researchers as an enabler for humans to explore and develop the ocean. In recent years, underwater robots are widely used in the fields of science, industry, commerce, military and the like. The method mainly comprises the steps of marine surveying and mapping, deep sea exploration, marine oil and gas development, pipeline maintenance, marine rescue, underwater target tracking, patrol and the like. For better application in the above-mentioned situations, precise control of underwater robots is of great importance. However, the underwater robot propulsion system has the influence of factors such as nonlinearity, strong coupling, external uncertain disturbance and the like, so that the underwater robot high-precision path tracking control technology becomes a challenging research hotspot.
System constraints caused by physical or safety limitations are widely present in all control systems. The predictive control method acts as a closed-loop optimal control strategy and provides a systematic way to handle input and state constraints, as compared to other control methods. However, the parameters of the prediction model in the prediction control do not change according to time, and a strong nonlinear system such as an underwater robot system changes violently with time, so that the prediction accuracy of a linear discrete equation adopted in the prediction control is possibly greatly reduced, and the control performance of the prediction control is greatly reduced. In addition, some current technologies only perform some simple simulation simulations aiming at the trajectory tracking of the underwater robot, and have a large difference from the actual working condition.
Disclosure of Invention
The invention provides a self-adaptive prediction-based underwater robot three-dimensional trajectory tracking control method for realizing accurate trajectory tracking control in an AUV three-dimensional space, wherein input and state constraints are explicitly considered in the method, and then the trajectory tracking problem is converted into a standard quadratic programming problem which has the input and state constraints and can be calculated on line. When the underwater robot reaches a new position, the optimal input of the next moment is recalculated based on the current actual state and the expected track, and then the iteration is carried out in each control cycle, so that the continuous control on the controlled object is realized. Then, in order to eliminate errors generated in the nonlinear model linearization process of the underwater robot by the traditional predictive control and solve the problem of poor robustness of the controller under the strong nonlinear working condition, the method utilizes a Kalman filtering algorithm to adjust and control time domain model parameters on the basis of a predictive control algorithm, compensates nonlinear time-varying characteristic quantity of the time domain model parameters, and realizes the self-adaptive predictive control. The control precision, the anti-interference performance and the robustness of the underwater robot during track tracking are improved.
In order to achieve the purpose, the invention provides the following technical scheme: a three-dimensional track tracking control method of an underwater robot based on self-adaptive prediction is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: according to the actual working condition of the underwater robot, the actual motion model of the underwater robot in the three-dimensional space is properly simplified;
step two: according to the expected track of the current task, the information of the expected track is transmitted to the AUV, and after data are acquired through relevant equipment of the AUV, current position information eta is obtainedd＝[xd(t)yd(t)zd(t)]TAttitude information psid(t) velocity information vd＝[ud(t)vd(t)wd(t)rd(t)]TFurther providing a control model for tracking the three-dimensional track of the underwater robot; u (t) is the advancing and retreating speed of the AUV, v (t) is the surging speed of the AUV, w (t) represents the floating and submerging speed of the AUV, and r (t) represents the yawing speed of the AUV;
step three: using the current position information eta obtained in the step twod＝[xd(t)yd(t)zd(t)]TAttitude information psid(t) and velocity information vd＝[ud(t)vd(t)wd(t)rd(t)]TFurther listing a state equation and linearizing the state equation to obtain a linear time invariant equation through a position error model between the column-written AUV mathematical model and the track tracking reference track;
step four: discretizing the state equation after linearization in the third step, further writing a predictive control equation, and designing a predictive controller;
step five: according to the designed controller, the constraints of speed, rotation angle and the like of the underwater robot in the actual operation process are considered; giving out an optimized objective function with constraints and calculating a forward and backward speed control law ud(t), the rate of control of surge velocity vd(t), the floating and submerging speed control rate wd(t), yaw rate control rate rd(t)；
Step six: and aiming at the error between the model linearization and the actual system control model in the step two and solving the problem of poor robustness of the controller under the strong nonlinear working condition, further correcting the model parameters for predictive control in the control time domain by adopting a Kalman filtering algorithm, compensating the nonlinear time-varying characteristic quantity of the model parameters, and realizing the self-adaptive predictive control.
Preferably, in the step one, the underwater robot motion model is simplified relatively based on the actual working condition of the underwater robot, and in the step one, the simplified kinematics model for tracking the three-dimensional trajectory of the underwater robot is as follows:
and in the second step, based on the physical model of the underwater robot moving in the three-dimensional space, the control model of the underwater robot is obtained according to the position information, the posture information and the speed information of the underwater robot.
And in the third step, an error model is obtained according to the actual position and the track tracking requirement of the underwater robot and the reference track.
In the third step, a state equation linearization is further established based on the underwater robot position error model to obtain a linear time invariant equation; in step three, the linear time-invariant equation is:
in the fourth step, based on the underwater robot trajectory tracking control system, the antecedent Euler method is adopted to discretize the linear time invariant equation, and then the predictive controller is designed according to the predictive control method.
In the fifth step, based on the underwater robot track tracking control system, an optimized objective function of the prediction controller is given:
preferably, in the sixth step, based on the underwater robot trajectory tracking control system, aiming at the defects in the traditional predictive control and solving the problem of poor robustness of the controller under the strong nonlinear working condition, an optimization algorithm is provided to adjust model parameters:
the control models adopted by the predictive control used in each control period are all the optimal models which accord with the current working conditions, so that the self-adaptive predictive control is realized, and the control effect is optimized.
Preferably, in order to solve the problem that a certain error exists during linearization of a design initial model of the predictive controller of the underwater robot in the third step, online identification is carried out on the system, and the linearization model is continuously updated and corrected, so that self-adaptive predictive control is realized.
Compared with the prior art, the invention has the beneficial effects that: the underwater robot control system is suitable for an underwater robot, and the control model is simple and effective; input and state constraint are defined aiming at physical limits of states such as upper and lower limits of speed input, a yaw angle and the like in the actual motion process of the underwater robot, and a track tracking problem is converted into a mathematical problem with input and state constraint;
when the underwater robot reaches a new position, recalculating the next optimal input based on the current actual state and the expected track, and performing iteration in each control period to realize continuous control on the controlled object and ensure the control precision;
in order to eliminate the error influence in the nonlinear model linearization process of the underwater robot and solve the problem of poor robustness of the controller under the strong nonlinear working condition, on the basis of a predictive control algorithm, a Kalman filtering algorithm is used for adjusting and controlling time domain model parameters, nonlinear time-varying characteristic quantity of the time domain model parameters is compensated, adaptive predictive control is realized, and the control effect is further improved.
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FIG. 1 is an inertial and body coordinate system of operation of an underwater robot in an embodiment of the present invention;
FIG. 2 is a flow chart of the predictive control concept in an embodiment of the invention;
FIG. 3 is a block diagram of an adaptive prediction control in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example (b): a three-dimensional track tracking control method of an underwater robot based on self-adaptive prediction comprises the following specific steps:
the method comprises the following steps: analyzing the actual working condition of the underwater robot track tracking, and simplifying a motion model;
the motion of the underwater robot can be described in 6 degrees of freedom, i.e. 3 translational components and 3 rotational components; the translation component comprises a surging x, a surging y and a heaving z which describe the position of the underwater robot, and the rotation component comprises a rolling phi, a pitching theta and a yawing psi; in the path tracking of the underwater robot, an inertial coordinate system E-eta zeta xi and a body coordinate system O-xyz are respectively established, and a relation between the two coordinate systems is established; the AUV moves in space under water with six degrees of freedom, and a coordinate system is shown in figure 1;
the motion of the underwater robot in a body coordinate system (O-xyz) can be expressed by linear motion along three axes and rotational motion around the three axes, and the dynamic model equation is as follows:
where M is the inertial matrix due to the rigid body and the additional mass; c (v) is a coriolis force matrix; d (v) is a fluid damping matrix; g (η) is the restoring force vector generated by gravity and buoyancy; τ is the drive force and moment acting on the AUV; v ═ uv w pqr ] T, wherein each element is the linear velocity and the angular velocity of the AUV on three axes of the body coordinate system respectively;
for the track tracking control of the underwater robot, the influence of the heading angle psi on the control effect is great, the underwater turbulence is less, and the roll angle phi and the pitch angle theta are extremely small; to simplify the calculation, it can be ignored (i.e., Φ — 0, θ — 0); the equation is properly simplified, and only the tracking control problems of four degrees of freedom, namely surging x, surging y, heaving z and yawing psi, are considered in the track tracking process.
Step two: according to the simplified three-dimensional motion model, a three-dimensional track tracking control model of the underwater robot is given;
the simplified velocity vector in the geodetic coordinate system is
The linear velocity vector under the body coordinate system is v ═ u v w r]And T. The corresponding relation is as follows:
setting the actual states of the underwater robot as eta ═ x (T), y (T), z (T), ψ (T) at a certain time T; the reference path is the known quantity η d ═ xd (T) yd (T) zd (T) ψ d (T) T; the track tracking actually controls the actual advancing and retreating speed u, the longitudinal moving speed v, the floating and submerging speed w and the yawing angular speed r of the underwater robot, so that the error e eta (t) of the actual path eta of the underwater robot and the determined expected path eta d is gradually reduced to zero (t) (-) eta (t); i.e. there is an error when the time t goes to infinity:
trajectory tracking is equivalent to solving the mathematical problem shown in equation (3).
Step three: linearizing the simplified tracking control nonlinear model, and writing a state equation in a column;
the reference path of the AUV is set by the upper computer, and the actual position and direction eta of the AUV at a certain moment and the position and direction eta d set by the upper computer are input to the navigation system to be processed to obtain the state error
As can be seen from equation (2), the input to the motion control system of the underwater robot can be regarded as v ═ u v w r]T, state eta ═ x y z psi]T, given a reference state of η d ═ xd yd zd ψ d]T, reference speed Vd ═ ud wd rd]T; after the kinematic equation is approximately linearized, a linear time invariant equation can be obtained:
in the formula (I), the compound is shown in the specification,
step four: discretizing a trajectory tracking control state equation of the column-writing underwater robot, then column-writing a predictive control equation, and designing a predictive controller;
because the MPC controller needs a discrete model for optimization, the formula (4) is discretized by adopting an Euler discretization method to obtain:
in the formula Ak＝I+aT,BkI is the fourth order identity matrix and T is the sampling time.
According to the basic principle of predictive control, setting a prediction time domain as Np and a control time domain as NC; assuming equation (5) predicts the Np steps forward at each time, for convenience of description, the predicted state sequence and control sequence are as shown in equation (6):
wherein
And
a state vector and an input vector at the time k + i (i ═ 1 · Np) predicted at the time k, respectively; the prediction control model is obtained according to equations (5) and (6):
X(k)＝A(k)x(k)+B(k)U(k) (7)
in the formula (11)
Step five: adding actual constraints such as speed, bow and roll angle and the like received by the underwater robot in the running process into an optimized objective function, and solving the optimized objective function;
the underwater robot is constrained by a steering angle, an installation direction of an electric propulsion motor and a rotating speed in the actual movement process, so that a state vector and an input vector always meet constraint conditions, namely:
umin≤U(k)≤umax
Xmin≤X(k)≤Xmax (8)
where umin, Xmin, umax, and Xmax are the minimum and maximum values of the input vector and the state vector, respectively.
The vector form written after the formula (7) is substituted into the formula (8) is as follows:
LU(k)≤l (9)
in the formula
The optimization controller can enable the underwater robot to track the expected path quickly and stably, and the following optimization objective functions are adopted in the method:
wherein X (k), U (k) are the same as those in formula (6), Q ═ diag (Q (0),. cndot. cndot.)) and R ═ diag (R (0),. cndot. cndot.))
From equations (7), (9) and (10), the optimization objective function with constraints can be derived as:
wherein H ═ 2(bt (k) qb (k)) + R, f ═ 2bt (k) (a (k) x (k) -xd (k)); l, L are the same as in formula (9);
this is a standard Quadratic Programming (QP) problem and the variables are the optimal control inputs u (k) to the underwater robot; the solution to the optimal input for the underwater robot trajectory tracking is to solve the Quadratic Programming (QP) problem.
Step six: aiming at the defects in the traditional predictive control and solving the problem that the robustness of the controller is poor under the strong nonlinear working condition, an algorithm is further designed to adjust model parameters, and the self-adaptive predictive control is realized.
Because the path tracking kinematic equation of the underwater robot is a strong nonlinear equation, certain error exists between the prediction controller and an actual system during design initial model linearization, and the error is larger and larger in the running process of the underwater robot, so that the control effect is poor; in order to solve the error generated in the model linearization process, the method adopts the following method to carry out online identification on the system, continuously updates and corrects the linearization model, and realizes self-adaptive prediction control; therefore, the prediction model equation can well describe the state of the underwater robot during real-time track tracking, so that the control effect is more superior to that of the traditional prediction control; the control block diagram is shown in FIG. 3; .
1. According to the equation (5), the discretized mathematical model of the system is:
wherein Ak, Bk are the same as in formula (5), c (k) ═ 1110] T.V (k), and w (k) are system noise and measurement noise, respectively;
2. predicting the state vector, i.e. from the inputs u (k) and the last state estimate
To predict the state vector at time (k +1), we shall:
in the formula, Ts is sampling period, "#" represents state estimation, and "" represents a predicted value;
3. calculating an output corresponding to the predicted quantity
Namely, the method comprises the following steps:
4. calculating an error covariance matrix, namely:
in the formula, Q is a covariance matrix of system noise;
5. the gain matrix K (K +1) of KF is calculated, i.e. there is:
wherein R is a zero matrix of fourth order;
6. obtaining optimized state estimates
Namely, the method comprises the following steps:
7. for the next estimation, an estimation error covariance matrix is pre-calculated, that is:
after the calculation is finished, the optimized state estimator obtained by the formula (15) is used
And (3) giving an equation (7), so that a model which is in accordance with the current working condition is used when the next period of control is carried out, the self-adaptive prediction control is realized, and the control effect is optimized.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (9)
1. A three-dimensional track tracking control method of an underwater robot based on self-adaptive prediction is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: according to the actual working condition of the underwater robot, the actual motion model of the underwater robot in the three-dimensional space is properly simplified;
step two: according to the expected track of the current task, the information of the expected track is transmitted to the AUV, and after data are acquired through relevant equipment of the AUV, current position information eta is obtainedd＝[xd(t) yd(t) zd(t)]TAttitude information psid(t) velocity information vd＝[ud(t) vd(t) wd(t) rd(t)]TFurther providing a control model for tracking the three-dimensional track of the underwater robot; u (t) is the advancing and retreating speed of the AUV, v (t) is the surging speed of the AUV, w (t) represents the floating and submerging speed of the AUV, and r (t) represents the yawing speed of the AUV;
step three: using the current position information eta obtained in the step twod＝[xd(t) yd(t) zd(t)]TAttitude information psid(t) and velocity information vd＝[ud(t) vd(t) wd(t) rd(t)]TFurther listing a state equation and linearizing the state equation to obtain a linear time invariant equation through a position error model between the column-written AUV mathematical model and the track tracking reference track;
step four: discretizing the state equation after linearization in the third step, further writing a predictive control equation, and designing a predictive controller;
step five: according to the designed controller, the constraints of speed, rotation angle and the like of the underwater robot in the actual operation process are considered; giving out an optimized objective function with constraints and calculating a forward and backward speed control law ud(t), the rate of control of surge velocity vd(t), the floating and submerging speed control rate wd(t), yaw rate control rate rd(t)；
Step six: and aiming at the error between the model linearization and the actual system control model in the step two and solving the problem of poor robustness of the controller under the strong nonlinear working condition, further correcting the model parameters for predictive control in the control time domain by adopting a Kalman filtering algorithm, compensating the nonlinear time-varying characteristic quantity of the model parameters, and realizing the self-adaptive predictive control.
2. The underwater robot three-dimensional trajectory tracking control method based on adaptive prediction as claimed in claim 1, wherein: in the first step, the motion model of the underwater robot is relatively simplified based on the actual working condition of the underwater robot, and in the first step, the simplified kinematic model for tracking the three-dimensional track of the underwater robot is as follows:
3. the underwater robot three-dimensional trajectory tracking control method based on adaptive prediction as claimed in claim 1, wherein: and in the second step, based on the physical model of the underwater robot moving in the three-dimensional space, the control model of the underwater robot is obtained according to the position information, the posture information and the speed information of the underwater robot.
4. The underwater robot three-dimensional trajectory tracking control method based on adaptive prediction as claimed in claim 1, wherein: and in the third step, an error model is obtained according to the actual position and the track tracking requirement of the underwater robot and the reference track.
5. The underwater robot three-dimensional trajectory tracking control method based on adaptive prediction as claimed in claim 1, wherein: in the third step, a state equation linearization is further established based on the underwater robot position error model to obtain a linear time invariant equation; in step three, the linear time-invariant equation is:
6. the underwater robot three-dimensional trajectory tracking control method based on adaptive prediction as claimed in claim 1, wherein: in the fourth step, based on the underwater robot trajectory tracking control system, the antecedent Euler method is adopted to discretize the linear time invariant equation, and then the predictive controller is designed according to the predictive control method.
7. The underwater robot three-dimensional trajectory tracking control method based on adaptive prediction as claimed in claim 1, wherein: in the fifth step, based on the underwater robot track tracking control system, an optimized objective function of the prediction controller is given:
and then, constraining the amplitude values of the state variable and the input variable, and further giving out an optimized objective function with constraint:
8. the underwater robot three-dimensional trajectory tracking control method based on adaptive prediction as claimed in claim 1, wherein: in the sixth step, based on the underwater robot trajectory tracking control system, aiming at the defects in the traditional predictive control and solving the problem of poor robustness of the controller under the strong nonlinear working condition, an optimization algorithm is provided to adjust model parameters:
and realizing self-adaptive prediction control.
9. The adaptive prediction based underwater robot three-dimensional trajectory tracking control method according to claims 1-8, characterized in that: in order to solve the problem that certain errors exist in the linearization of the design initial model of the prediction controller of the underwater robot in the third step, the system is identified on line, and the linearization model is updated and corrected continuously, so that the self-adaptive prediction control is realized.
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| CN114019798A (en) * | 2021-11-03 | 2022-02-08 | 中国科学院深圳先进技术研究院 | Robot trajectory tracking control method, magnetic medical robot and storage medium |
| CN114147710A (en) * | 2021-11-27 | 2022-03-08 | 深圳市优必选科技股份有限公司 | Robot control method, device, robot and storage medium |
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