A high-precision PID trajectory tracking control method for a space manipulator
By combining a nonlinear disturbance observer with PID control and using gradient optimization algorithms to optimize PID parameters, the problem of high-precision control of a free-floating space robotic arm was solved, achieving high-precision trajectory tracking and constraint satisfaction, and adapting to complex space environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN UNIV
- Filing Date
- 2026-02-06
- Publication Date
- 2026-06-12
AI Technical Summary
In the high-precision control of free-floating space robotic arms, existing technologies suffer from chattering issues in sliding mode control, limited anti-disturbance capabilities in adaptive control, and computationally complex and poorly versatile neural network control, making it difficult to meet the multi-constraint operation requirements in complex space environments.
A high-precision PID trajectory tracking control method is designed by adopting a composite architecture of nonlinear disturbance observer and PID control. This method estimates and compensates for unmodeled dynamic and spatial environmental disturbances in real time, optimizes PID parameters by combining gradient optimization algorithm, and explicitly incorporates joint angle, angular velocity and control torque constraints.
It significantly improves trajectory tracking accuracy, avoids jitter, ensures that the robotic arm moves within a safe range, adapts to different task scenarios, and has high engineering application value and versatility.
Smart Images
Figure CN122194609A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of spacecraft control technology, and more specifically, to a high-precision PID trajectory tracking control method for a space robotic arm. Background Technology
[0002] With the diversification and increasing complexity of space missions (such as on-orbit satellite maintenance, space debris capture, and deployment of interplanetary exploration equipment), free-floating space robotic arms have become core equipment for space operations, and their high-precision trajectory tracking control is crucial to ensuring mission success. The operational performance of free-floating space robotic arms directly depends on their comprehensive ability to cope with the strong coupling characteristics of the system, uncertainties (unmodeled dynamics, space environment disturbances), and multiple physical constraints (angle, angular velocity, actuator torque constraints). When the engineering practicality of control strategies is similar, control schemes that can effectively balance tracking accuracy, constraint satisfaction, and uncertainty suppression can often significantly improve the reliability and success rate of space missions.
[0003] Research on high-precision control of free-floating space robotic arms at home and abroad mainly focuses on sliding mode control, adaptive control and neural network control methods. However, these methods cannot achieve good control results in the following aspects: (1) Although sliding mode control has strong robustness, traditional sliding mode has inherent chattering problems, which can easily break through the actuator torque constraint and is difficult to accurately adapt to the strong coupling dynamic characteristics of the free-floating space robotic arm base and joints, and cannot fully utilize the maneuver potential of the robotic arm; (2) Although the adaptive control-based scheme can cope with some parameter uncertainties, it has limited ability to suppress unmodeled dynamics and sudden spatial disturbances. It is only applicable to simplified dynamic models and is difficult to match the multi-constraint operation requirements in complex spatial environments. It can only complete simple point-to-point positioning tasks; (3) Similar to adaptive control, although neural network control can approximate complex nonlinear dynamics, it has problems of high computational complexity and strong dependence on training samples. When the number of robotic arm joints, load mass or task scenario changes, the network needs to be retrained, resulting in poor versatility and engineering implementation. Summary of the Invention
[0004] The present invention provides a high-precision PID trajectory tracking control method for a space robotic arm, which can solve the above-mentioned problems.
[0005] To solve the above problems, the technical solution adopted by the present invention is as follows:
[0006] A high-precision PID trajectory tracking control method for a space robotic arm includes:
[0007] Step S1: Establish a rotational motion dynamics model for the free-flying space robotic arm. The dynamics model includes an inertia matrix, a Coriolis matrix, a control torque term, and system uncertainty terms with unmodeled dynamics and external disturbances.
[0008] Step S2: Construct a nonlinear perturbation observer and use the nonlinear perturbation observer to estimate the system uncertainty in the dynamic model in real time to obtain the estimated value of the system uncertainty;
[0009] Step S3: Based on the estimated value of the system uncertainty, design a PID composite controller. The PID composite controller includes proportional, derivative, and integral feedback terms, as well as compensation terms for the system dynamic characteristics and uncertainties.
[0010] Step S4: Establish a PID parameter optimization problem, construct the objective function in the integral form of the trajectory tracking error, take the joint angle, joint angular velocity and control torque of the robotic arm as physical constraints, and use the proportional coefficient matrix, differential coefficient matrix and integral coefficient matrix of the PID composite controller as optimization variables;
[0011] Step S5: Transform the physical constraints into finite-dimensional constraints using the constraint transcription method, and calculate the gradients of the objective function and the physical constraints with respect to the optimization variables;
[0012] Step S6: Using the calculated gradient, solve for the optimal PID control parameters through an iterative optimization algorithm, and input the optimal PID control parameters into the PID composite controller to realize trajectory tracking control of the free-flying space robotic arm.
[0013] Further, in step S1, the rotational motion dynamics model of the free-flying space robotic arm is as follows:
[0014]
[0015] in, In a broad sense, For generalized speed, For generalized acceleration, The inertia matrix, For Coriolis matrix, To control the torque, This represents system uncertainty.
[0016] Furthermore, in step S2, the nonlinear disturbance observer is constructed as follows:
[0017]
[0018] in, For system uncertainty The estimated value, For state estimators, As an auxiliary momentum term, and , Let be the observer gain matrix, and , It is a diagonal matrix. It is a positive parameter.
[0019] Further, in step S3, the PID composite controller is:
[0020]
[0021] in, For the desired trajectory, For the desired angular acceleration, To track errors, The derivative of the tracking error; , , These are the proportional, derivative, and integral coefficient matrices of the PID composite controller, respectively, and all are diagonal matrices; the control law of the PID composite controller is introduced... The term compensates for the uncertainty of the estimate, and by introducing The term applies linearization compensation to the Coriolis force.
[0022] Furthermore, in step S5, the constrained transcription method transforms the original inequality constraints into equality constraints by introducing a constraint approximation function. The specific transformation formula is as follows:
[0023]
[0024] in, Indicates the first One constraint For terminal time, This is the one-sided inequality form of the original constraint. These are the constraint values after transcription. and It is a positive adjustment parameter. This is a constrained approximation function.
[0025] Furthermore, in step S5, the method for calculating the gradient of the objective function with respect to the optimization variables includes:
[0026] Define the costate variables of the objective function This satisfies the following differential equation:
[0027]
[0028] Where A is the state matrix of the closed-loop system, and , It is an n×n identity matrix; based on costate variables Calculate the objective function J with respect to the PID parameters. , , gradient:
[0029]
[0030] in, Costate variables The last n-dimensional components.
[0031] Further, in step S5, the method for calculating the gradient of the physical constraints with respect to the optimization variables includes:
[0032] For angle constraints, angular velocity constraints, and control torque constraints, calculate the transcribed constraints separately. The gradient of the PID parameters; the post-transcriptional constraints Regarding the proportionality coefficient matrix The gradient is:
[0033]
[0034] The post-transcriptional constraints Regarding the differential coefficient matrix The gradient is:
[0035]
[0036] The post-transcriptional constraints Regarding the integral coefficient matrix The gradient is:
[0037]
[0038] Where j represents the joint index corresponding to the constraint. This represents the j-th component of the vector.
[0039] Further, in step S6, the iterative optimization algorithm specifically includes:
[0040] Step S61: Initialize PID parameters and adjustment parameters , And set adjustment parameters minimum threshold ;
[0041] Step S62: Determine the current adjustment parameter Is it less than the minimum threshold? If so, output the current PID parameters as the optimal parameters; otherwise, execute step S63.
[0042] Step S63: Using the current PID parameters as the initial point, solve the constrained optimization problem using the calculated gradient;
[0043] Step S64: Verify whether the solution results satisfy all physical constraints. If they do, decrease the adjustment parameters. and Then update the PID parameters and return to step S62. If the condition is not met, simply decrease the adjustment parameter. Return to step S63.
[0044] Compared with the prior art, the beneficial effects of the present invention are:
[0045] (1) The present invention adopts a composite architecture of nonlinear disturbance observer and PID control. By estimating and compensating for unmodeled dynamic and spatial environmental disturbances in real time through the nonlinear disturbance observer, the problem of weak anti-disturbance capability of traditional adaptive control is effectively solved; at the same time, the composite architecture avoids the chattering phenomenon of sliding mode control, can give full play to the maneuver potential of the robotic arm, and significantly improve the trajectory tracking accuracy.
[0046] (2) This invention explicitly incorporates physical constraints such as joint angle, angular velocity, and control torque into the PID parameter optimization process. By converting continuous time constraints into finite-dimensional constraints through constraint transcription and solving them in combination with gradient optimization algorithms, it ensures that the motion state and actuator output of the robotic arm are always within a safe range when performing high-dynamic tasks, effectively avoiding system failures or task failures caused by violation of constraints.
[0047] (3) Compared with neural network control, this invention uses a simple and mature PID controller as the core, which does not require complex network training and a large amount of sample data. By adaptively adjusting the PID parameters (proportional, derivative, and integral coefficients) through a gradient-based parameter optimization method, this method can flexibly adapt to different task scenarios, load changes and robotic arm configurations, and has extremely high engineering application value and versatility.
[0048] (4) This invention introduces costate variables and sensitivity equations to accurately calculate the gradient information of the objective function and various physical constraints with respect to the PID parameters. Compared with heuristic algorithms, this gradient-based search strategy has a faster convergence speed and can more accurately find the optimal control parameters that minimize the tracking error under strict constraints.
[0049] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, embodiments of the present invention are described below in detail with reference to the accompanying drawings. Attached Figure Description
[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0051] Figure 1 This is a flowchart of the high-precision PID trajectory tracking control method for the space robotic arm described in this invention;
[0052] Figure 2 The pose angle tracking curves of the base, joint 1, and joint 2 in the simulation case of the method of the present invention are shown.
[0053] Figure 3 The following are the attitude angular velocity tracking curves of the base, joint 1, and joint 2 in the simulation case of the method of the present invention;
[0054] Figure 4 The pose angle error curves of the base, joint 1, and joint 2 in the simulation case of the method of the present invention are shown.
[0055] Figure 5 The following are the attitude angular velocity error curves of the base, joint 1, and joint 2 in the simulation case of the method of the present invention;
[0056] Figure 6 The image shows the control torque curve of a freely floating space robotic arm in a simulation example of the method of this invention. Detailed Implementation
[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.
[0058] This invention provides a high-precision PID trajectory tracking control method for a space robotic arm. Addressing the challenges of strongly coupled dynamics, parameter uncertainties, external disturbances, and multiple physical constraints (joint angles, angular velocities, and control torque) in free-flying space robotic arms, this method proposes a composite control architecture based on a nonlinear disturbance observer and PID control, and adaptively optimizes the PID parameters using a gradient-based optimization algorithm.
[0059] like Figure 1 As shown, the method in this embodiment mainly includes the following steps:
[0060] Step S1: Establish a rotational motion dynamics model for the free-flying space robotic arm.
[0061] Based on the Newton-Euler equations and the Lagrange equations, the rotational motion dynamics model of the free-flying space robotic arm is established as follows:
[0062] (1)
[0063] in, The attitude is a generalized attitude (including the base attitude angle and joint angle). N is the number of joints; For generalized velocity (angular velocity); This refers to generalized acceleration (angular acceleration). Here is the system's inertia matrix; This is the Coriolis matrix, representing the output torque of the actuator; To control the torque; This refers to system uncertainty, which includes unmodeled dynamics and external environmental disturbances.
[0064] To facilitate subsequent observer design and stability verification, the system uncertainty is addressed. Make the following assumptions:
[0065] (1) The uncertainty d is bounded, that is ,in It is a positive number;
[0066] (2) Slowly changing signal d within a short sampling period .
[0067] And set the following physical constraints:
[0068] (1) Angle constraint: , ;
[0069] (2) Angular velocity constraint: , ;
[0070] (3) Actuator constraints: , ;
[0071] Our control objective is to design a PID controller and a nonlinear disturbance observer to enable the free-floating space robot's attitude q to track the desired trajectory. ,satisfy:
[0072] Tracking error Asymptotically converges to 0;
[0073] All physical constraints are strictly satisfied;
[0074] System uncertainty has been effectively suppressed.
[0075] Step S2: Construct a nonlinear perturbation observer and estimate the system uncertainty.
[0076] To eliminate the impact of system uncertainties on control accuracy, a nonlinear disturbance observer is constructed as follows:
[0077] (2)
[0078] in: This is an estimate of the system uncertainty d; For estimating the internal state of the observer; For auxiliary momentum term; The observer gain matrix; It is a diagonal matrix. Positive parameters that satisfy the stability condition; It is the inverse of the inertia matrix.
[0079] Stability analysis: defining observation error .like (in These are the elements of the inertial correlation constant matrix. (where the maximum Euler angular velocity is), then the estimation error of the nonlinear perturbation observer... It asymptotically converges to 0. This indicates that the observer can accurately estimate the system uncertainty.
[0080] Step S3: Design a PID composite controller.
[0081] Combined with the estimated value output by the nonlinear perturbation observer Design a PID composite controller that includes feedforward compensation:
[0082] (3)
[0083] in: For the desired trajectory, The desired angular acceleration; To track errors, The derivative of the tracking error; This is the PID proportional coefficient matrix (diagonal matrix). This is the PID differential coefficient matrix (diagonal matrix). This is the PID integral coefficient matrix (diagonal matrix); Item Used to offset system uncertainties; Item Used for linearizing compensation for the Coriolis force effect.
[0084] For the dynamic model (1) and the PID composite controller (3) based on the nonlinear disturbance observer, if appropriate PID parameters are selected... The tracking error of the closed-loop system It asymptotically converges to 0. The proof of the closed-loop stability is as follows:
[0085] Substituting the PID composite controller (3) into the dynamic model (1), the closed-loop error equation is obtained:
[0086] (4)
[0087] Constructing Lyapunov functions:
[0088] (5)
[0089] Depend on Positive definiteness and The positive definiteness of it indicates that For all non-zero Established.
[0090] Taking the time derivative of the Lyapunov function (5), we get...
[0091] (6)
[0092] Will Substitute, utilize and nonlinear disturbance observer Simplifying, we get:
[0093] (7)
[0094] Based on the properties of the Coriolis force matrix Opposing the claim, therefore ,therefore:
[0095] (8)
[0096] because All are positive definite matrices, therefore And only if hour By applying LaSalle's invariant set principle, the tracking error of the closed-loop system... The system asymptotically converges to 0 and becomes asymptotically stable.
[0097] Step S4: Establish the PID parameter optimization problem.
[0098] The PID parameter optimization problem aims to minimize trajectory tracking error, using the joint angles, angular velocities, and control torque of the robotic arm as physical constraints. The proportional coefficient matrix, derivative coefficient matrix, and integral coefficient matrix of the PID composite controller are used as optimization variables, as detailed below:
[0099] (9)
[0100] in, This is the terminal time.
[0101] Step S5: Constrained transcription and gradient calculation.
[0102] This invention employs a constraint transcription method to transform the physical constraints into finite-dimensional constraints, and calculates the gradients of the objective function and the physical constraints with respect to the optimization variables.
[0103] 1. Restricted transcription
[0104] The constrained transcription method transforms the original inequality constraints into equality constraints by introducing a constraint approximation function. The specific transformation formula is as follows:
[0105] (10)
[0106] in, Indicates the first One constraint For terminal time, This is the one-sided inequality form of the original constraint. These are the constraint values after transcription. and It is a positive adjustment parameter. This is a constrained approximation function.
[0107] 2. Calculation of the gradient of the objective function
[0108] Define the state matrix A of the closed-loop system:
[0109]
[0110] in, It is an n×n identity matrix.
[0111] Define the costate variables corresponding to the objective function. (A 2n-dimensional vector) that satisfies the differential equation:
[0112] (11)
[0113] make for The last n-dimensional components. The objective function J with respect to the PID parameters. , , The gradient is:
[0114] (12)
[0115] 3. Physical constraint gradient calculation
[0116] For each post-transcriptional constraint The gradient calculation with respect to the PID parameters is as follows:
[0117] Regarding the proportionality coefficient matrix gradient:
[0118] (13)
[0119] Regarding the differential coefficient matrix gradient:
[0120] (14)
[0121] Regarding the integral coefficient matrix gradient:
[0122] (15)
[0123] Where j represents the joint index corresponding to the constraint. Let j represent the j-th component of the vector. The sensitivity of the state to the parameters (e.g., ...) in the above formula... This can be obtained by solving the corresponding sensitivity differential equation.
[0124] Step S6: Iterative optimization solution.
[0125] This invention utilizes the calculated gradient to solve for the optimal PID control parameters through an iterative optimization algorithm, and inputs the optimal PID control parameters into the PID composite controller to achieve trajectory tracking control of a free-flying space robotic arm.
[0126] Iterative optimization algorithms specifically include:
[0127] Step S61: Initialize PID parameters and adjustment parameters , Set threshold ;
[0128] Step S62: Determine the current adjustment parameter Is it less than the minimum threshold? If so, output the current PID parameters as the optimal parameters. Otherwise, proceed to step S63;
[0129] Step S63: Using the current PID parameters as the initial point, solve the constrained optimization problem using the calculated gradient. ;
[0130] Step S64: Verify constraint satisfaction. If all Then update , Update the PID parameters and return to step S62; otherwise, let Return to step S63.
[0131] In the simulation examples of the method of this invention, the model parameters of the free-floating space manipulator are shown in Table 1, and the specific values of tracking the desired trajectory, the nonlinear disturbance observer, and the PID controller are shown in Table 2. The simulation environment is Matlab 2019a, and the optimization problem is solved using Miser.
[0132] Table 1
[0133] Parameter values significance The system's inertia matrix Coriolis force matrix of the system Mass of base, mass of link 1, mass of link 2, length of link 1, length of link 2, moment of inertia of base, moment of inertia of link 1, moment of inertia of link 2
[0134] Table 2
[0135] Parameter values significance ， Initial attitude angle and angular velocity Uncertainty Attitude angle upper and lower limits Attitude angular velocity upper and lower limits Control torque upper and lower limits Attitude Expected Trajectory Optimized Optimized Optimized
[0136] Depend on Figure 2 The attitude angle tracking curves shown are Figure 3 The attitude angular velocity tracking curve shown can be seen from the PID controller's output. The attitude angle q and attitude angular velocity... Able to respond quickly and track the desired trajectory After establishing the optimal control problem, solving for the optimal PID controller parameters using control parameterization ensures that the corresponding physical constraints are not violated during the tracking process; Figure 4 The attitude angle error curves shown are Figure 5 The attitude angular velocity error curve shown demonstrates that the optimal parameters can effectively reduce tracking error and achieve high-precision tracking control; Figure 6 The control torque curve of the free-floating space robotic arm shown indicates that, through optimal control parameter adjustment, the control torque does not violate the constraints.
[0137] In summary, the embodiments of the present invention effectively suppress system uncertainty through a nonlinear disturbance observer, and achieve high-precision trajectory tracking under strict constraints of angle, angular velocity and control torque through a gradient-based parameter optimization method.
[0138] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A high-precision PID trajectory tracking control method for a space robotic arm, characterized in that, include: Step S1: Establish a rotational motion dynamics model for the free-flying space robotic arm. The dynamics model includes an inertia matrix, a Coriolis matrix, a control torque term, and system uncertainty terms with unmodeled dynamics and external disturbances. Step S2: Construct a nonlinear perturbation observer and use the nonlinear perturbation observer to estimate the system uncertainty in the dynamic model in real time to obtain the estimated value of the system uncertainty; Step S3: Based on the estimated value of the system uncertainty, design a PID composite controller. The PID composite controller includes proportional, derivative, and integral feedback terms, as well as compensation terms for the system dynamic characteristics and uncertainties. Step S4: Establish a PID parameter optimization problem, construct the objective function in the integral form of the trajectory tracking error, take the joint angle, joint angular velocity and control torque of the robotic arm as physical constraints, and use the proportional coefficient matrix, differential coefficient matrix and integral coefficient matrix of the PID composite controller as optimization variables; Step S5: Transform the physical constraints into finite-dimensional constraints using the constraint transcription method, and calculate the gradients of the objective function and the physical constraints with respect to the optimization variables; Step S6: Using the calculated gradient, solve for the optimal PID control parameters through an iterative optimization algorithm, and input the optimal PID control parameters into the PID composite controller to realize trajectory tracking control of the free-flying space robotic arm.
2. The high-precision PID trajectory tracking control method for a space robotic arm according to claim 1, characterized in that, In step S1, the rotational motion dynamics model of the free-flying space robotic arm is as follows: in, In a broad sense, For generalized speed, For generalized acceleration, The inertia matrix, For Coriolis matrix, To control the torque, This represents system uncertainty.
3. The high-precision PID trajectory tracking control method for a space robotic arm according to claim 2, characterized in that, In step S2, the nonlinear disturbance observer is constructed as follows: in, For system uncertainty The estimated value, For state estimators, As an auxiliary momentum term, and , Let be the observer gain matrix, and , It is a diagonal matrix. It is a positive parameter.
4. The high-precision PID trajectory tracking control method for a space robotic arm according to claim 3, characterized in that, In step S3, the PID composite controller is: in, For the desired trajectory, For the desired angular acceleration, To track errors, The derivative of the tracking error; , , These are the proportional, derivative, and integral coefficient matrices of the PID composite controller, respectively, and all are diagonal matrices; the control law of the PID composite controller is introduced... The term compensates for the uncertainty of the estimate, and by introducing The term applies linearization compensation to the Coriolis force.
5. The high-precision PID trajectory tracking control method for a space robotic arm according to claim 1, characterized in that, In step S5, the constrained transcription method transforms the original inequality constraints into equality constraints by introducing a constraint approximation function. The specific transformation formula is as follows: in, Indicates the first One constraint For terminal time, This is the one-sided inequality form of the original constraint. These are the constraint values after transcription. and It is a positive adjustment parameter. This is a constrained approximation function.
6. The high-precision PID trajectory tracking control method for a space robotic arm according to claim 5, characterized in that, In step S5, the method for calculating the gradient of the objective function with respect to the optimization variables includes: Define the costate variables of the objective function This satisfies the following differential equation: Where A is the state matrix of the closed-loop system, and , It is an n×n identity matrix; based on costate variables Calculate the objective function J with respect to the PID parameters. , , gradient: in, Costate variables The last n-dimensional components.
7. The high-precision PID trajectory tracking control method for a space robotic arm according to claim 5, characterized in that, In step S5, the method for calculating the gradient of the physical constraints with respect to the optimization variables includes: For angle constraints, angular velocity constraints, and control torque constraints, calculate the transcribed constraints separately. The gradient of the PID parameters; the post-transcriptional constraints Regarding the proportionality coefficient matrix The gradient is: The post-transcriptional constraints Regarding the differential coefficient matrix The gradient is: The post-transcriptional constraints Regarding the integral coefficient matrix The gradient is: Where j represents the joint index corresponding to the constraint. This represents the j-th component of the vector.
8. The high-precision PID trajectory tracking control method for a space robotic arm according to claim 1, characterized in that, In step S6, the iterative optimization algorithm specifically includes: Step S61: Initialize PID parameters and adjustment parameters , And set adjustment parameters minimum threshold ; Step S62: Determine the current adjustment parameter Is it less than the minimum threshold? If so, output the current PID parameters as the optimal parameters; otherwise, execute step S63. Step S63: Using the current PID parameters as the initial point, solve the constrained optimization problem using the calculated gradient; Step S64: Verify whether the solution results satisfy all physical constraints. If they do, decrease the adjustment parameters. and Then update the PID parameters and return to step S62. If the condition is not met, simply decrease the adjustment parameter. Return to step S63.