Universal position control method for multi-configuration double-passive-joint plane three-connecting-rod mechanical arm

Abstract

The invention belongs to the technical field of robot motion control, and particularly relates to a universal position control method for a multi-configuration double-passive-joint plane three-connecting-rod mechanical arm. The problem of tail end position control caused by incomplete constraint, state coupling and nonlinear characteristics of one type of underactuated systems of the double-passive-joint mechanical arm is solved, the three-configuration universality is achieved, and the fault-tolerant capability and control efficiency of the system can be remarkably improved; the method is especially suitable for trajectory planning and optimization control of high-under-actuated and strong-coupling mechanical systems in a zero-gravity or microgravity environment, such as spacecraft mechanical arms and deep sea operation robots.

Description

Technical Field

[0001] This invention relates to the field of robot motion control, specifically to a general position control method for a multi-configuration dual passive joint planar three-bar manipulator. Background Technology

[0002] Underactuated mechanical systems, with their advantages of fewer actuation devices, lighter structural weight, lower energy consumption, and higher flexibility, have shown great application potential in fields with extremely high requirements for system weight, energy consumption, and reliability, such as on-orbit servicing of spacecraft and deep-sea exploration. Their core control objective is to achieve coordinated multi-degree-of-freedom motion through internal dynamic coupling using control inputs fewer than the system's degrees of freedom—in other words, "controlling many with few, and using force against force." Therefore, the control problem of underactuated systems has always been a key focus and challenge in the fields of robotics and control theory.

[0003] The control strategies for planar underactuated robotic arms vary significantly depending on the number and position of the passive joints and the system constraints.

[0004] For systems containing only one passive joint, existing technologies have proposed a relatively rich array of solutions: (1) For a planar PA (passive-active) complete constraint system, the angular constraint relationship between the active and passive joints can be obtained by integrating the underactuated equations. This allows for the synchronous arrival of the active and passive joints at the target angle when planning the motion of the active joints. For planar PA... n For systems with n≥2, due to angular velocity constraints between active and passive joints, existing methods employ model reduction to decompose the system into multiple virtual PA subsystems. The constraint relationships are then utilized to achieve the global control objective.

[0005] (2) Planar AP (active-passive) systems, lacking angle constraints similar to PA systems, make it difficult to directly establish the mathematical relationship between the active and passive joints. To address this, a control strategy combining Fourier transform and particle swarm optimization (PSO) is needed, along with the introduction of a nonlinear perturbation observer to suppress external disturbances. For planar A systems with second-order nonholonomic characteristics... n For P (n≥2) systems, existing technologies transform them into second-order chain canonical form through coordinate transformation, and then design nonlinear feedback control laws to achieve asymptotic stability.

[0006] (3) In addition, planar three-bar linkage robotic arms (PUM) containing a single passive joint in the middle, such as APAA and AAPA configurations, can be simplified into virtual subsystems, such as virtual PAA and virtual AAP, by energy decay or model reduction, and then the virtual system is controlled step by step to achieve the global goal.

[0007] While there is considerable research on single-passive-joint systems, the control problem of dual-passive-joint systems has been largely neglected due to their more complex nonholonomic constraints and stronger state coupling. For example, in a planar three-bar configuration, if two joints are passive (such as APP, PAP, PPA configurations), the system will be subject to multiple nonholonomic constraints simultaneously, making traditional methods based on virtual subsystem decomposition or constraint integration difficult to apply directly. Existing literature on the control of dual-passive-joint systems mostly focuses on specific configuration designs, lacking a universal control framework. Furthermore, since passive joints cannot be directly driven, their states must be indirectly controlled through the coordinated motion of active joints, which places higher demands on trajectory smoothness and state continuity.

[0008] Therefore, there is an urgent need for a position control method for a dual passive joint robotic arm that can be universal across configurations and take into account both trajectory smoothness and state continuity, so as to improve the system's adaptability and fault tolerance in high reliability scenarios such as aerospace and deep sea. Summary of the Invention

[0009] In view of this, the present invention aims to overcome the shortcomings of the prior art and is based on solving the general position control problem of a dual-passive joint planar three-bar manipulator. It proposes a multi-configuration compatible segmented trajectory optimization control method. By establishing a unified dynamic model for multiple configurations, the integrability boundary conditions of nonholonomic constraints are revealed. A continuous trajectory function with parameterized adjustment capability is constructed. The PSO algorithm is used to achieve global optimization of trajectory parameters across configurations. Combined with a sliding mode control strategy, it overcomes the technical bottleneck of single joint configuration adaptability and breaks through the dual limitations of traditional methods, which rely on the specific position of the passive joint and are limited by the constraint relationship of the single passive joint.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: A general position control method for a multi-configuration dual-passive joint planar three-bar robotic arm includes the following steps: S1. Establish a dynamic model based on the Euler-Lagrange equations, and establish a kinematic model based on the dynamic constraint equations and homogeneous coordinate transformation. Analyze the nonholonomic constraint equations and state coupling characteristics of the system. S2. Based on the target position, the target angle of each joint is solved in reverse, and the particle swarm optimization (PSO) algorithm is used to optimize the target joint angle of the robotic arm with multiple solutions. S3. Design a three-segment continuous trajectory that includes an intermediate angle and variable parameters. The trajectory consists of a first segment, a second segment, and a holding segment. The expressions of the first segment and the second segment of the trajectory each include independently adjustable trajectory parameters. These parameters include at least the intermediate angle, time parameters, and shape adjustment parameters. By adjusting the trajectory parameters, the angular velocity and angular acceleration of the active joint in different motion stages can be independently controlled. S4. Optimize trajectory parameters using the PSO algorithm to ensure that all joint states converge continuously and synchronously to the final state at trajectory switching points. S5. Based on the desired trajectory generated by the optimized parameters, a sliding mode tracking controller is designed in conjunction with Lyapunov stability theory to make the active joint move along the optimized trajectory, indirectly controlling the passive joint, so that the end of the robotic arm converges to the target end position.

[0011] Furthermore, in step S1, the dynamic model is established based on the Euler-Lagrange equations and clearly distinguishes the input torques of active joints and passive joints; the kinematic model is used to describe the mapping relationship between the end position of the robotic arm and the angles of each joint.

[0012] Furthermore, in step S2, the particle swarm optimization (PSO) algorithm constructs an evaluation function based on the distance error between the end effector of the robotic arm and the target position, performs global optimization within the feasible region of the joint space, solves the problem of multiple solutions to the inverse kinematics equations, and quickly selects a set of target joint angles that can achieve precise end effector positioning.

[0013] Furthermore, in step S3, the three continuous trajectories containing variable parameters are composed of fifth-order polynomial basis functions and additional adjustable terms, ensuring the continuity of angles, angular velocities, and even angular accelerations at the starting point, ending point, and intermediate switching points.

[0014] Furthermore, in step S4, when the Particle Swarm Optimization (PSO) algorithm is used to optimize the trajectory parameters, an evaluation function is constructed to specifically evaluate the continuity of the passive joint state. This function quantifies the jump in the passive joint angle and angular velocity before and after the trajectory switching point, guiding the optimization algorithm to search for parameter solutions that make the jump zero.

[0015] Furthermore, in step S5, the designed sliding mode tracking control law can effectively suppress system model uncertainty and coupling interference, ensure the asymptotic convergence of tracking error, and thus ensure the stability of the entire control system.

[0016] Furthermore, the method is applicable to the end-effector position control of planar three-bar dual passive joint robotic arms with three configurations: active-passive-passive APP, passive-active-passive PAP, and passive-passive-active PPA.

[0017] The present invention also provides a computer-readable storage medium storing a computer program thereon, characterized in that the computer program, when executed by a processor, implements the general position control method for the multi-configuration dual passive joint planar three-bar manipulator.

[0018] The beneficial effects of this invention are as follows: (1) A unified theoretical and control framework is proposed, which can effectively handle the dual passive joint configurations of APP, PAP and PPA in three different positions. It breaks through the dependence of traditional methods on specific positions of passive joints and significantly improves the applicability of the method and the fault tolerance of the system.

[0019] (2) The problem of coordinated control of dual passive joints was solved. By using segmented trajectory design and dual-layer PSO optimization strategy, the active joint motion was actively planned and the trajectory parameters that enable the two passive joint states to change smoothly and synchronously were automatically solved. The problem of trajectory design and state coordination caused by strong coupling and non-holonomic constraints in dual passive joint system was successfully solved.

[0020] (3) Sliding mode tracking control is adopted to ensure that the active joint accurately tracks the optimized trajectory. Combined with the globally optimized trajectory parameters, the entire system can reach the target position with high precision.

[0021] (4) Starting from any feasible initial state, this method can find a smooth trajectory that makes the system converge to the target position through intelligent optimization, which overcomes the local uncontrollability problem of such underactuated systems and realizes global position control in the workspace.

[0022] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0023] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 It is the core process for universal position control of multi-configuration dual passive joint planar three-bar robotic arms; Figure 2 This is a schematic diagram of multi-target pose control; Figure 3 This is a schematic diagram of the two-layer PSO optimization process; Figure 4 These are simulation results of the APP configuration control system; Figure 5 These are simulation results of the PAP configuration control system; Figure 6 These are simulation results of the PPA configuration control system. Detailed Implementation

[0024] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0025] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0026] This invention provides a universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm, the core process of which is as follows: Figure 1 As shown, the main steps include: S1. Establish the dynamic and kinematic models of the dual passive joint planar three-bar manipulator, and analyze the nonholonomic constraint equations and state coupling characteristics of the system. S2. Based on the target position, the target angle of each joint is solved in reverse, and the PSO algorithm is used to optimize the target angle for multiple solutions. S3. Design a three-segment continuous trajectory that includes intermediate angles and variable parameters; S4. Optimize trajectory parameters using the PSO algorithm to ensure that all joint states converge continuously and synchronously to the final state at trajectory switching points. S5. A sliding mode tracking controller is designed based on Lyapunov stability theory to enable the active joint to move along the optimized trajectory, thereby indirectly controlling the passive joint and achieving stable convergence of the end position.

[0027] I. A detailed explanation of each step.

[0028] Step 1: Establish a system model and analyze constraint characteristics.

[0029] This step aims to establish a unified dynamic and kinematic model for the three configurations APP, PAP, and PPA, and to analyze their nonholonomic constraint characteristics.

[0030] S1-1. Establish the dynamic model. Establish the dynamic model based on the Euler-Lagrange equations: ; ; ; in, These are the joint's angle, angular velocity, and angular acceleration vectors, respectively. It is an inertial matrix with positive definiteness and symmetry; It is a matrix of Coriolis force and centrifugal force; It is a torque vector; The matrix characterizing the joint driving state, If the i-th joint is an active joint, then , All other elements in the i-th row are 0; if the i-th joint is a passive joint. All elements in the i-th row are 0.

[0031] ; For a dual-passive joint system, the first... The first joint is an active joint, the second... The joint and the first Each of the joints is a passive joint. , These correspond to APP, PAP, and PPA configurations, respectively.

[0032] S1-2. Establish the kinematic model. Based on the dynamic constraint equations in S1-1, establish the kinematic model through homogeneous coordinate transformation: ; in, The length of the link. For joint angle, .

[0033] S1-3. Based on S1-2, derive the relationship between the end-effector position (X,Y) and the joint angles q1, q2, and q3: .

[0034] S1-4. Based on the dynamic model of S1-1 and the kinematic model of S1-2, the integrability of the nonholonomic constraint equations is analyzed, revealing the strong coupling characteristics between the passive and active joint motions. This coupling relationship is the theoretical basis for subsequent trajectory design to indirectly control the passive joints.

[0035] Step 2: Optimize the target angle in reverse based on the PSO algorithm.

[0036] Due to the target end position ( , Solving the joint angle is a multi-solution problem. This step uses the PSO algorithm to quickly filter multiple feasible solutions that satisfy the end-effector target position.

[0037] S2-1. Based on the relationship between the end position and joint angles in S1-3, since the target angles of all joints in the target position have multiple solutions, the PSO algorithm is used to quickly obtain a set of target angles. The evaluation function for target angle optimization is then established. Defined as: ; Where (X,Y) represents the end-effector position calculated from the planned joint angles using a kinematic model. The target location.

[0038] S2-2. Utilize the PSO algorithm to inversely optimize the target angles of each joint, solving the multiple-solution problem of inverse kinematics. The target angle optimization algorithm flow includes: (1) Input target location With robotic arm structural parameters ,in, This represents the mass of the z-th link; This represents the length of the z-th link; Let represent the moment of inertia of the r-th link about its center of mass; Let represent the distance from the z-th joint to the center of mass. Within the feasible region of the joint angles, randomly initialize a particle swarm of N particles. The position of each particle represents a set of candidate joint angles, and its velocity is randomly initialized. Set the individual historical optimality and the swarm's global optimality.

[0039] (2) For each particle, calculate its error value according to S2-1. If a particle's current error is better than its individual historical best, then its current position is updated. The position with the smallest error from all data is selected as the new global optimum.

[0040] (3) Update the velocity and position of each particle according to the standard PSO velocity and position update formula, and repeat (3) until the maximum number of iterations or error is reached. .

[0041] (4) When the algorithm terminates, the position corresponding to the global optimum is the target joint angle obtained by optimization. .

[0042] S2-3. Based on the control target parameters output by the PSO algorithm in S2-2, obtain the initial and final states of the active joint: ; Step 3: Design a parametric segmented continuous trajectory.

[0043] To achieve smooth motion and coordinate active and passive joints, a three-segment continuous trajectory with variable parameters was designed.

[0044] S3-1. Design a three-segment trajectory, introducing intermediate angle and shape variable parameters. The angles, angular velocities, and angular accelerations of the active and passive joints during the control process are solved piecewise.

[0045] (1) The first segment of the trajectory ( ): ; in, This represents the first segment of the angular trajectory of the active joint. This is the initial angle.

[0046] Will Differentiating the angular velocities of the active joints in the first trajectory segment yields the angular velocities. and angular acceleration : ;

[0047] when and At that time, the angle of the active joint angular velocity and angular acceleration They are respectively: ; This indicates that along trajectory one, from arrive The active joint can move from its initial state Upgrade to intermediate state .

[0048] (2) The second segment of the trajectory ( ): ; in, This refers to the second segment of the angle trajectory of the active joint rod. ; Will Differentiating the angular velocities of the active joints in the second trajectory segment yields the angular velocities. and angular acceleration : ; ; when and At that time, the angle of the active joint angular velocity and angular acceleration They are respectively: ; This indicates that along trajectory two, the active joint can... From the target state Move to the middle state .

[0049] (3) The third segment of the trajectory ( ): .

[0050] By adjusting the parameters of the first segment of the trajectory and the second segment trajectory parameters Without changing the starting point of the trajectory, the active joint in and angular velocity during and angular acceleration It can be controlled independently.

[0051] Combining the angles, angular velocities, and angular accelerations of the active joints in the trajectory, and the S1-1 dynamic constraint equations, in The state of the passive joint changes with Change, in The state then follows The change resulted in the endpoints of the two trajectories being at different positions.

[0052] like Figure 2 As shown, by coordinating and adjusting the combination of trajectory parameters, passive joints can exhibit differentiated motion states, thereby achieving multi-target pose control.

[0053] S3-2. Based on the integrability analysis in S1-3, combined with the initial state of the passive joint... and final state ( The state of the passive joint at any given time can be obtained through integration. ; in, The j-th joint is a passive joint, and .

[0054] S3-3. Based on the state function of the passive joint at any time in S3-2, the constraint conditions can be obtained: ; in, , This indicates the angle and angular velocity of the first passive joint at the moment the first segment of the trajectory ends. , This indicates the angle and angular velocity of the first passive joint at the start of the second trajectory segment; , This indicates the end time of the first trajectory segment, the angle of the second passive joint, and the angular velocity. , This indicates the angle and angular velocity of the second passive joint at the start of the second trajectory segment.

[0055] If the conditions are met, then the state of each passive joint. exist The points are continuous, and from arrive The passive joint can swing from the initial state to the target state.

[0056] Step 4: Optimize trajectory parameters based on the PSO algorithm.

[0057] This step aims to find a set of trajectory parameters that satisfy the state continuity condition in S3-3. Figure 3 The diagram shows a two-layer PSO optimization process.

[0058] S4-1. Define the trajectory parameter optimization evaluation function. This is used to measure the state continuity of the passive joint at the switching moment, and the optimization objective is to find the trajectory parameters that minimize the error value. .

[0059] S4-2. Optimize parameters using the PSO algorithm to ensure the continuity of passive joint states at trajectory switching points. The parameter optimization algorithm process includes: (1) Input the initial and final states of all joints. Within a reasonable range of trajectory parameters, initialize the particle swarm. The position of each particle represents a set of candidate parameters.

[0060] (2) For each parameter set represented by a particle, execute S3-1 and S3-2 to calculate the state of all joints at the switching point, and then calculate the evaluation function value according to S4-1. Update the individual optimal and the group optimal, and update the particle position and velocity according to the PSO algorithm.

[0061] (3) Repeat (2) until the maximum number of iterations (100 times) or the error is reached. .

[0062] (4) Output makes Minimum optimized trajectory parameters .

[0063] Step 5: Design a sliding mode tracking controller.

[0064] To ensure that the active joint can accurately track the optimal trajectory generated by Step 3 and Step 4, a sliding mode controller is designed.

[0065] S5-1. Based on S1-2, the endpoint position control of the system is transformed into angle tracking control, and the sliding surface is designed as follows: According to S3-1 and Substitute the values ​​into the sliding surface formula to solve the problem.

[0066] S5-2, Calculation Derivation: ,in This refers to the actual active joint angular velocity. The planned active joint angular velocity. Based on S3-1 Substitute the values ​​into the controller design formula to solve the problem.

[0067] S5-3, Combining Lyapunov functions Design the control law of the controller for: ; ; Sliding surface The controller parameters ensure that the active joints move along the optimized trajectory and the passive joints converge synchronously. , The actual angle of the active joint; , Plan the angular velocity of the active joint; To plan the angular acceleration of the active joint.

[0068] S5-4, Based on the controller design of S4-3, the derivation of V is as follows: ; According to the Lasalle invariance principle, when At that time, that is The active joint tracks the designed optimized trajectory from the initial state to the final state, while the system endpoint moves to the optimized target equilibrium point.

[0069] II. Simulation Verification.

[0070] To verify the effectiveness of the method of the present invention, simulations of the three configurations APP, PAP and PPA were performed in the Simulink environment.

[0071] Controller parameters are set to , , Particle swarm size and dimension N=100 Inertia factor and acceleration constant End-position convergence error Less than rice.

[0072] (1) APP configuration control.

[0073] When the first joint of the PUM is the only active joint, the system is an active-passive-passive APP configuration control system. The initial angle is set as... The endpoint is (0 1.8)m, through Step 2 PSO optimization, the target angles of each joint are obtained; through Step 4 optimization, the trajectory parameters are obtained: ; The simulation results of applying the sliding mode controller in Step 5 are attached. Figure 4 As shown, when , convergence to Under the controller designed in Step 4, the active joint smoothly tracks the optimized trajectory, while the two passive joints continuously change state under strong coupling. The system endpoint moves to the target location. .

[0074] (2) PAP configuration control.

[0075] When the second joint of the PUM is the only active joint, the system is a passive-active-passive PAP configuration control system. The initial angle, initial position, and target position are set as follows: , m and m. The final angle and variable parameters in the planned trajectory are obtained using the PSO algorithm: ; Simulation results are as follows Figure 5 As shown, when , convergence to , convergence to Under the controller designed in Step 4, The system endpoint moves to the target location. The single active joint is effectively controlled, driving the coordinated movement of the two passive joints at the front and rear, and high-precision point control is also achieved at the end of the system.

[0076] (3) PPA configuration control.

[0077] When the third joint of the PUM is the only active joint, the system is a passive-passive-active PPA configuration control system. For the initial state... The initial position is (0,3)m, and the endpoint position is selected. The optimized parameters are obtained as follows: ; Simulation results are as follows Figure 6 As shown, when , convergence to Under the controller designed in Step 4, The system endpoint moves to the target location. The system successfully drove the first two passive joints using joint 3 as the active joint, verifying that the method is also effective for configurations where the active joint is located at the distal end.

[0078] In summary, simulation verification demonstrates that the method of this invention can achieve the control target quickly and smoothly, significantly improving the versatility and effectiveness of dual passive joint robotic arm control for APP, PAP, and PPA configurations. It overcomes the bottleneck of local uncontrollability inherent in traditional PUMs, achieving globally reachable control of the end effector from any initial pose to the target pose. Employing a fifth-order polynomial trajectory and PSO intelligent parameter optimization algorithm ensures continuous angle and angular velocity between the active and passive joints at the switching moment, achieving high control accuracy. .

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm, characterized in that, include: S1. Establish a dynamic model based on the Euler-Lagrange equations, and establish a kinematic model based on the dynamic constraint equations and homogeneous coordinate transformation. Analyze the nonholonomic constraint equations and state coupling characteristics of the system. S2. Based on the target position, the target angle of each joint is solved in reverse, and the particle swarm optimization (PSO) algorithm is used to optimize the target joint angle of the robotic arm with multiple solutions. S3. Design a three-segment continuous trajectory that includes an intermediate angle and variable parameters. The trajectory consists of a first segment, a second segment, and a holding segment. The expressions of the first segment and the second segment of the trajectory each include independently adjustable trajectory parameters. These parameters include at least the intermediate angle, time parameters, and shape adjustment parameters. By adjusting the trajectory parameters, the angular velocity and angular acceleration of the active joint in different motion stages can be independently controlled. S4. Optimize trajectory parameters using the PSO algorithm to ensure that all joint states converge continuously and synchronously to the final state at trajectory switching points. S5. Based on the desired trajectory generated by the optimized parameters, a sliding mode tracking controller is designed in conjunction with Lyapunov stability theory to make the active joint move along the optimized trajectory, indirectly controlling the passive joint, and the end effector of the robotic arm converges to the target end effector position.

2. The universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to claim 1, characterized in that, In step S1, a dynamic model is established based on the Euler-Lagrange equations: ； ； ； in, , , These are the joint's angle, angular velocity, and angular acceleration vectors, respectively. It is an inertial matrix with positive definiteness and symmetry; The matrix represents the Coriolis force and the centrifugal force; It is a torque vector; The coefficient matrix characterizes the joint driving state. If the i-th joint is the active joint, then... , All other elements in the i-th row are 0; if the i-th joint is a passive joint. All elements in the i-th row are 0.

3. The universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to claim 1, characterized in that, In step S1, the end position (X,Y) of the kinematic model and the joint angle The relationship between them is: ； in, For the first Length of the connecting rod.

4. The universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to claim 1, characterized in that, In step S2, when using the PSO algorithm to solve for the target joint angle, the evaluation function for target angle optimization is: ; where, (X Y) is the end-effector position calculated from the candidate joint angles using the kinematic model. The target location.

5. The universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to claim 2, characterized in that, In step S3, the expressions for the three continuous trajectory segments are as follows: (1) The first segment of the trajectory ( In ), the angle of the active joint for: ,in, This is the initial angle; angular velocity of active joint and angular acceleration for: ； ； when and At that time, the angle of the active joint angular velocity and angular acceleration They are respectively: ； (2) The second segment of the trajectory ( In ), the angle of the active joint for: ,in, ; angular velocity of active joint and angular acceleration for: ； ； when and At that time, the angle of the active joint angular velocity and angular acceleration They are respectively: ； (3) The third segment of the trajectory ( In the process, the active joint maintains the target joint angle and its angular velocity is zero. Angle values ​​of each active joint angular velocity and angular acceleration for: 。 6. The universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to claim 5, characterized in that, In step S4, the particle swarm optimization algorithm is used to optimize the trajectory parameters. The evaluation function constructed during optimization. The expression used to measure the state continuity of a passive joint at the switching moment is: ； in, and For integers, the first and The joint is a passive joint. , This indicates the angle and angular velocity of the first passive joint at the end of the first trajectory segment; , This indicates the angle and angular velocity of the first passive joint at the start of the second trajectory segment; , This indicates the angle and angular velocity of the second passive joint at the end of the first trajectory segment. , This indicates the angle and angular velocity of the second passive joint at the beginning of the second trajectory segment.

7. The universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to claim 6, characterized in that, In step S5, the control law of the tracking controller Designed as follows: ； ； Sliding surface For controller parameters; , The actual angle of the active joint; , Plan the angular velocity of the active joint; To plan the angular acceleration of the active joint.

8. The universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to claim 7, characterized in that, Using the sliding mode tracking controller designed in claim 7, the active joint moves along the optimized trajectory.

9. A universal position control method for a multi-configuration dual-passive joint planar three-bar linkage robotic arm according to any one of claims 1 to 8, characterized in that, The method is applicable to the end-effector position control of planar three-bar dual passive joint robotic arms with three configurations: active-passive-passive APP, passive-active-passive PAP, and passive-passive-active PPA.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 8.

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