Double-closed-loop self-adaptive control method for rope-driven hyper-redundant robot
By employing a dual-closed-loop adaptive control method, combining dynamic parameter adaptation and rope joint control, the control challenges of rope-driven redundant robots in complex environments were solved, achieving high-precision and stable motion control and improving the overall performance of the rope-driven redundant robot.
Patent Information
- Application Number
- CN202511310991.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-15
- Publication Date
- 2025-11-21
AI Technical Summary
Controlling rope-driven redundant robots is challenging, especially in complex environments where the nonlinearity of the dynamic model and the tension of the rope affect motion accuracy and stability, making it difficult for traditional control methods to achieve high precision and stability.
A dual-closed-loop adaptive control method is adopted, combining adaptive dynamic parameters and dual-closed-loop control of rope joints. By establishing forward and inverse kinematic models, Newton-Euler equations and adaptive laws, adaptive control torque is designed, and combined with rope tension adjustment, the synchronization error constraint of joints and ropes is achieved.
It improves the control accuracy and system robustness of rope-driven redundant robots, ensures high precision and stability in complex environments, enhances dynamic response capabilities, and meets the requirements of high-precision operation.
Smart Images
Figure CN120985620A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of robot control technology, specifically to a dual-closed-loop adaptive control method for a rope-driven, ultra-redundant robot. Background Technology
[0002] Rope-driven redundant robots are a class of robots with more than the minimum degrees of freedom required to complete a task, whose core actuation relies on the synergistic effect of flexible ropes. These robots achieve complex motion control through the tension variations of multiple ropes, exhibiting high flexibility and adaptability to complex environments. The motion platform of a rope-driven redundant robot is connected to a fixed base via ropes, and the extension and retraction of the ropes are precisely controlled by motors, enabling the robot to achieve precise positioning and attitude adjustment within the workspace. In the field of industrial automation, rope-driven redundant robots can be applied to complex environmental detection scenarios due to their unique advantages. However, the flexibility of the ropes and the characteristic of providing only unidirectional tension in rope-driven redundant robots result in a highly nonlinear system dynamics model, increasing the difficulty of control. Furthermore, the tension state of the ropes directly affects the robot's motion accuracy and stability; therefore, accurate tension algorithms and efficient, stable control algorithms have become the focus of research. Summary of the Invention
[0003] To address the shortcomings of existing technologies, the present invention aims to provide a dual-closed-loop adaptive control method for rope-driven super-redundant robots. This method utilizes a dynamic parameter adaptive method and a dual-closed-loop control method for joints and ropes in rope-driven redundant robots to address the poor performance of rope closed-loop control in traditional control systems. The method achieves synchronized error constraints in both rope control and joint control for robot trajectory control, thereby improving control accuracy.
[0004] To achieve the above objectives, the present invention provides the following technical solution: a double-closed-loop adaptive control method for a rope-driven, ultra-redundant robot, comprising the following steps: (1) Establish the forward and inverse kinematics models of the redundant robot and calculate the relationship between joint angles and rope lengths; (2) Analyze the joint angles, angular velocities and angular accelerations, solve for the linear velocities, linear accelerations and angular accelerations of the redundant robot arm links, and establish the Newton-Euler equations; (3) Separate the parameters of the equation established in step (2) to obtain the linearized equation; (4) Design an adaptive law to adaptively adjust the linearization parameters and solve for the control torque; (5) Solve for the minimum tension solution within the rope tension range using quadratic programming; (6) Combine the tension calculated by the PD controller controlled by the rope to solve for the final control torque.
[0005] In some embodiments, the specific manner of steps (1)-(4) is as follows: Suppose the redundant robot starts from the first... i- 1 section to i The forward kinematics of the segment are represented as follows: (1) in This represents the homogeneous rigid body transformation matrix of the redundant robot from one guide rope disk to the next. h This represents the distance from the center of the universal joint to the center of the guide rope disc. L Represents the length of the arm sleeve, of which , as well as The matrix representation is as follows: (2) The transformation matrix of the redundant robot from the base coordinate system to the end effector is expressed as: (3) Since the redundant continuum robot is driven by ropes, it is necessary to map joint angle changes to rope length changes. A mathematical model is established based on the position of the guide cable hole and the arm sleeve structure. (4) In the formula, L represents the length of the arm sleeve. Represents the first layer of guide rope disc j Layer i The spatial coordinates of the root rope, and further expressed as , among them Represents the corresponding guide rope disc The angle is expressed as: (5) The velocity, angular velocity, linear acceleration, and angular acceleration of each arm link of the redundant robot are expressed by the following recursive formulas: (6) in These are the angular velocity, linear velocity, angular acceleration, and linear acceleration of each robotic arm link. and Representing from the first To the The rotation matrix and translation vector of each, Representing the The rotation axis vector of each robotic arm joint These represent the angular velocity and angular acceleration of the joint rotation, respectively. represent A skew-symmetric matrix of vectors; The redundant robot base itself is stationary; the only force affecting the base is acceleration due to gravity, as shown below: (7) The forces at each joint are determined using Newton's and Euler's formulas: (8) Among them, force Represented as: (9) in Representing the The mass of each robotic arm component Representing the The mass moment at the rotation axis of a robotic arm link Representing the Spatial inertia of each robotic arm link ,at the same time A transformation matrix representing a special structure is expressed as: (10) By linearly separating the mass, mass moment, and inertia in equation (9), equation (9) is transformed into: (11) Since each link is subjected to the superposition of the forces of the following links, the total spatial force of joint i can be expressed as: (12) The matrix in equation (11) is defined as: (13) By superimposing forces from the end effector of the redundant robot forward, each force is transformed into each joint through spatial force transformation, thereby obtaining the torque of the joint rotation axis. The link parameters corresponding to the redundant robot are separated from equation (13) through dynamic parameter linearization, and the linearization matrix is obtained by recursion: (14) (15) This leads to the construction of linearized equations for joint torques and parameters: (16) in , This establishes a linear relationship between joint torque and inertial parameters. In system control, the inertial parameters are continuously corrected through joint errors to achieve dynamic adaptive control. The joint errors... sum of error change rate Represented as: (17) (18) in Represents the desired joint angle. , This refers to the actual joint angle; The dynamic equations of the redundant robotic arm are expressed as follows: (19) in The inertial force representing the robotic arm body, Representing forces such as Coriolis force and centripetal force, This represents the weight of the arm itself, while Represents joint torque; Substituting the torque obtained by linearizing the dynamic parameters into equation (19) yields the following equation: (20) Designing the adaptive rate of a redundant robot system using sliding mode control: (twenty one) in ,at the same time represent The estimated value is initially determined by the inertial parameters of the arm's initial attitude, and then adaptively estimated based on the error generated by trajectory tracking. This yields the torque of the joint, which is mainly divided into two parts: one is the torque obtained through PD control, and the other is the torque obtained through the dynamic adaptive part. (twenty two) Based on Lyapunov stability, the Lyapunov function is designed as an energy function: (twenty three) Taking the derivative of this function, we get: (twenty four) Considering the above properties and substituting them into the control law and adaptive law, we obtain... (25) Therefore, we can conclude that: (26) When time t When it approaches positive infinity, the estimated value as well as They all converge to 0, therefore we know that as time approaches positive infinity...s It will also tend to 0, and through the adaptive control law, the system's velocity and position can both reach zero steady-state closed-loop error.
[0006] In some embodiments, according to steps (5) and (6), the specific manner is as follows: The Jacobian of the rope section is mapped to the torque of the cable tension at the joint: (27) Where the Jacobian matrix is: (28) The tension of the rope can be directly solved using equation (27) (27) and the Jacobi pseudo-inverse. (29) The quadratic programming function is used to set the objective as minimizing tension while simultaneously setting upper and lower limits for the rope tension: (30) The minimum warning force of the rope at the setting is calculated using equation (30). To maximum tension The minimum rope tension that satisfies the condition of equation (27) at the same time; Considering dual-space closed-loop control, with the cable controlling the arm's movement, energy loss occurs during the control of the wire rope's movement. To achieve high-precision control, parameter separation of the motor control, as well as its inertia and friction factors, must be considered. (31) in , , These represent the motor's inertia matrix, viscous friction coefficient, and Coulomb friction force, respectively. The function represents the switching term function, and the above equation can be described as follows based on the rope-driven redundant arm model: (32) The adaptive synchronization term is modified by using the above linearized expression for the dynamic parameters: (33) in It estimates the dynamic parameters, and its derivative is expressed as: (34) Define rope in rope space The error and its derivative are defined as follows: : (35) (36) To ensure that the error deviation between ropes is within a preset range, a synchronization control algorithm is introduced: (37) in Representing the i The synchronization error of the rope root is composed of the integral of the errors of the two adjacent ropes controlled by the same section of the arm and the rope's own error. The proportional coefficient represents the weight of the synchronous control. This yields the final torque for rope control. for: (38) (39) By using the nonlinear solution function to obtain the optimal solution function in the solution space from the forward kinematics equations, and successively approximating the optimal solution with initial values, the forward kinematics equations are transformed into: (40) Solve the following constrained optimization problems using nonlinear constrained optimal solution methods: (41) Among them The function is represented as: (42) After discretizing the trajectory, the inverse kinematics solution is obtained for each point using the algorithm described above. To maintain continuity, the solution from the previous step is used... q The initial solution is used for optimization iteration using nonlinear constraints. Then, the joint angle and the corresponding rope length are used as inputs to provide the control torque in the dual-space closed-loop control to achieve closed-loop control.
[0007] Compared with existing technologies, the beneficial effects of this invention are as follows: By introducing dual-space closed-loop control and adaptive control, the control accuracy and system robustness of the rope-driven redundant serial robot are improved. Closed-loop control of the rope and joints enables the system to perform precise control simultaneously in different spaces, ensuring higher positioning accuracy and stability when the robot performs complex tasks, thus meeting various high-precision operation requirements. Adaptive control, by adjusting dynamic parameters in real time, allows the system to automatically adapt. This effectively improves the robot's adaptability and flexibility, ensuring stable operation in various operating environments. Adaptive adjustment of dynamic parameters reduces the impact of external interference on system performance, thereby improving the system's dynamic response and control performance. Through the combination of dual-space closed-loop control and adaptive control, this technical solution significantly improves the overall performance of the rope-driven redundant serial robot, meeting the high precision and high reliability requirements of complex tasks. The improved control accuracy and system robustness enable the robot to achieve more precise motion control under high-speed and high-acceleration operating conditions, enhancing the system's dynamic response and control performance.
[0008] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. The embodiments of this application will provide a detailed description and understanding of this application. Attached Figure Description
[0009] Figure 1 A simplified structural diagram of a rope-driven redundant robot arm. Figure 2 Flowchart of dual-space closed-loop control for a rope-driven redundant robot; Figure 3 Flowchart of adaptive control of dynamic parameters for joint control section; Figure 4 Overall flowchart of dual closed-loop control for rope-driven redundant robot; Figure 5 This is a schematic diagram of the overall structure of a rope-driven redundant robot. Detailed Implementation
[0010] 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 only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0011] Rope-driven redundant robots face numerous technical challenges and limitations in practical applications due to their unique continuum structure and flexible actuation method. Firstly, while traditional PD (probe control) methods are simple in structure and easy to implement, their performance is poor when dealing with the complex nonlinear dynamics of rope-driven redundant robots. PD controllers tend to cause system response lag when processing robot dynamic responses, making it difficult to achieve high-precision motion control. Furthermore, PD control has limited adaptability to changes in system parameters and external disturbances, easily leading to performance degradation in complex operating environments, failing to meet the requirements of high precision and high stability. Simultaneously, the motion control of rope-driven redundant robots is highly dependent on the tension distribution and synergistic effect of the rope. Since the rope can only provide unidirectional tension, and its tension state directly affects the robot's motion accuracy and stability, traditional control methods struggle to effectively address the rope tension distribution problem. This results in jitter or deviations during robot movement, affecting the accuracy and reliability of task execution.
[0012] To address the aforementioned issues, this application proposes a dynamic parameter-adaptive dual-space closed-loop control strategy. The core of this strategy lies in adjusting control parameters in real time using a dynamic parameter adaptive method to adapt to the dynamic changes and uncertainties of the robot system. This method effectively overcomes control performance problems caused by inaccurate models or environmental changes. The adaptive algorithm automatically adjusts control parameters based on the robot's real-time motion state, ensuring the stability and accuracy of the control system.
[0013] This application employs synchronization error constraints to improve overall control accuracy. The synchronization error constraint mechanism ensures coordination between joint motion and cable tension control, reducing error accumulation caused by asynchrony, thereby significantly improving the robot's positioning accuracy and motion smoothness. Simultaneously, a dual-space closed-loop control method performs precise control at both the joint and cable levels. The joint control level utilizes an adaptive control strategy to improve joint control accuracy, while the cable control level employs a tension adjustment mechanism to ensure that the cable maintains tension while accurately responding to commands. This two-layer control structure significantly improves control accuracy.
[0014] This invention provides a technical solution: a dual-closed-loop adaptive control method for a single-rope driven super-redundant robot, the steps of which are as follows: (1) Establish the forward and inverse kinematics models of the robot and calculate the relationship between joint angles and rope length; (2) Analyze the joint angles, angular velocities and angular accelerations, solve for the linear velocities, linear accelerations and angular accelerations of the robot arm links, and establish the Newton-Euler equations; (3) Separate the parameters of the equation established in step (2) to obtain the linearized equation; (4) Design an adaptive law to adaptively adjust the linearization parameters and solve for the control torque; (5) Solve for the minimum tension solution within the rope tension range using quadratic programming; (6) Combine the tension calculated by the PD controller controlled by the rope to solve for the final control torque.
[0015] Through this technical solution, such as Figure 1 As shown, the controlled rope-driven redundant robot structure includes an arm control base. Internally, servo motors primarily drive ropes 5 via lead screws. These ropes pass through multiple front arm sections 2 and connect to corresponding guide rope reels 1 on the redundant arm sections. The joints consist of two robotic arm sections 2 connected at both ends by U-shaped connectors 4, which in turn connect to a universal joint 3. This structure has two degrees of freedom and is driven and controlled by three ropes through holes in the guide rope reels of corresponding layers. The first arm section passes through the drive ropes of all the arm sections, while the last section connects to its corresponding three ropes. The entire robotic arm consists of multiple arm sections connected in series with universal joints. Figure 5 This is the overall structural diagram of the entire robotic arm.
[0016] like Figure 1 The redundant robot shown starts from the first i-1 Festival i The forward kinematics of the segment are represented as follows: (1) in This represents the rigid body homogeneous transformation matrix from the previous guide rope disk to the next guide rope disk. h This represents the distance from the center of the universal joint to the center of the guide rope disc. L Represents the length of the arm sleeve, of which , as well as The matrix representation is as follows: (2) The transformation matrix of the redundant robot from the base coordinate system to the end effector can be expressed as: (3) Since the redundant continuum robot is driven by ropes, it is necessary to map joint angle changes to rope length changes. A mathematical model is established based on the position of the guide cable hole and the arm sleeve structure. (4) In the formula, L represents the length of the arm sleeve. Represents the first layer of guide rope disc j Layer i The spatial coordinates of the root rope, which can be further represented as , among them Represents the corresponding guide rope disc The angle can be expressed as: (5) Solving the adaptive dynamics feedforward of a redundant robot requires constructing its dynamic equations. These equations need to consider the parameters of the robotic arm and the velocities and accelerations of each link. The velocities, angular velocities, linear accelerations, and angular accelerations of each link in the arm can be expressed by recursive formulas as follows: (6) in These are the angular velocity, linear velocity, angular acceleration, and linear acceleration of each link in the robotic arm. and Representing from the first To the The rotation matrix and translation vector of each, Representing the The rotation axis vector of each robotic arm joint These represent the angular velocity and angular acceleration of the joint rotation, respectively. represent A skew-symmetric matrix of vectors.
[0017] The base itself is stationary; it is only affected by gravity, specifically by acceleration (gravity term), which can be expressed as follows: (7) The forces at each joint are determined using Newton's and Euler's formulas: (8) Among them, force It can be represented as: (9) in Representing the The mass of each robotic arm component Representing the The mass moment at the rotation axis of a robotic arm link Representing the Spatial inertia of each robotic arm link ,at the same time A transformation matrix representing a special structure can be expressed as: (10) By linearly separating the mass, mass moment, and inertia in equation (9), the equation can be transformed into: (11) Since each link is subjected to the superposition of the forces of the following links, the total spatial force of joint i can be expressed as: (12) The matrix in equation (11) is defined as: (13) By superimposing forces from the end to the front, each force is transformed into each joint through spatial force transformation, thereby obtaining the torque of the joint rotation axis. The corresponding link parameters of the robot are separated from the formula through linearization of dynamic parameters. The linearization matrix can be obtained recursively: (14) (15) This leads to the construction of linearized equations for joint torques and parameters: (16) in , This establishes a linear relationship between joint torque and inertial parameters. In system control, the inertial parameters are continuously corrected through joint errors to achieve dynamic adaptive control. The joint errors... sum of error change rate It can be represented as: (17) (18) in Represents the desired joint angle. ,and That is the actual joint angle.
[0018] The dynamic equations of the redundant robotic arm can be expressed as: (19) in The inertial force representing the robotic arm body, Representing forces such as Coriolis force and centripetal force, This represents the weight of the arm itself, while It represents the joint torque.
[0019] Substituting the torque obtained by linearizing the dynamic parameters into equation (19) yields the following equation: (20) Designing the adaptive rate of a redundant robot system using sliding mode control: (twenty one) in ,at the same time It represents The estimated value is initially determined by the inertial parameters of the arm's initial attitude, and then adaptively estimated based on the error generated by trajectory tracking. From this, the torque of the joint can be obtained, which is mainly divided into two parts: one is the torque obtained through PD control, and the other is the torque obtained through the dynamic adaptive part. (twenty two) Considering Lyapunov stability, we can design the Lyapunov function as an energy function: (twenty three) Taking the derivative of this function, we get: (twenty four) Considering the above properties and substituting them into the control law and adaptive law, we obtain... (25) Therefore, we can conclude that: (26) When time t When it approaches positive infinity, the estimated value as well as All converge to 0. Therefore, it can be concluded that when time approaches positive infinity... s It will also tend to 0. Through adaptive control laws, the steady-state closed-loop error of both the system's velocity and position can be reduced to zero simultaneously.
[0020] Since the robotic arm's cable is used for propulsion, it needs to ensure good force distribution and unidirectional force application. The Jacobian of the cable portion is mapped to the torque at the joint through the cable tension: (27) Where the Jacobian matrix is: (28) Using equation (27), the tension of the rope can usually be directly solved by using the Jacobi pseudo-inverse. (29) However, the rope tension obtained by equation (29) is based on the force calculated by treating the rope as a dynamic member model, which contains forces in opposite directions. Due to the property that the rope can only be subjected to force in one direction and the solution obtained by equation (27), This is not a unique solution; a set of forces in all directions must be found within the equations as the solution. Therefore, a quadratic programming function can be used to set the objective as minimizing tension while simultaneously setting upper and lower limits for the rope tension. (30) The minimum warning force of the rope at the set point can be calculated using equation (30). To maximum tension The minimum rope tension that satisfies the condition of equation (27) between them.
[0021] Considering dual-space closed-loop control, with the cable controlling the arm's movement, energy loss occurs during the control of the wire rope's movement. To achieve high-precision control, the parameters of the motor control, as well as its inertia and friction, need to be considered. (31) in , , These represent the motor's inertia matrix, viscous friction coefficient, and Coulomb friction force, respectively. The function represents the switching term function. Based on the rope-driven redundant arm model, we can describe the above equation as: (32) Similarly, by using the linearized expression of the above dynamic parameters, the adaptive synchronization term can be modified as follows: (33) in It estimates the dynamic parameters, and its derivative can be expressed as: (34) Simultaneously define the rope in the rope space The error and its derivative are defined as follows: : (35) (36) To ensure that the error deviation between ropes is not too large and thus affects the coordinated control effect, a synchronization control algorithm is introduced: (37) in Representing the i The synchronization error of the rope root is a combination of the integral of the errors of two adjacent ropes controlled by the same section of the boom and the rope's own error. The proportional coefficient represents the weight of the synchronous control.
[0022] This yields the final torque for rope control. for: (38) (39) Since the inverse kinematics of a redundant robotic arm is highly variable and difficult to solve analytically, the inverse kinematics function is derived by using a nonlinear solution function to find the optimal solution in the solution space based on the forward kinematics equations. The optimal solution is then approximated successively using initial values. As shown in equation (3), the forward kinematics equations can be transformed into: (40) Solve the following constrained optimization problems using nonlinear constrained optimal solution methods: (41) Among them The function can be represented as: (42) After discretizing the trajectory, the inverse kinematics solution is obtained for each point using the algorithm described above. To maintain continuity, the solution from the previous step is used... q The initial solution is used for iterative optimization using nonlinear constraints, and the joint angles and corresponding rope lengths are then provided as inputs. Figure 2 The control torque is calculated in the dual-space closed-loop control shown to achieve closed-loop control.
[0023] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
[0024] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A dual-closed-loop adaptive control method for a rope-driven, highly redundant robot, characterized in that: The steps are as follows: (1) Establish the forward and inverse kinematics models of the redundant robot and calculate the relationship between joint angles and rope lengths; (2) Analyze the joint angles, angular velocities and angular accelerations, solve for the linear velocities, linear accelerations and angular accelerations of the redundant robot arm links, and establish the Newton-Euler equations; (3) Separate the parameters of the equation established in step (2) to obtain the linearized equation; (4) Design an adaptive law to adaptively adjust the linearization parameters and solve for the control torque; (5) Solve for the minimum tension solution within the rope tension range using quadratic programming; (6) Combine the tension calculated by the PD controller controlled by the rope to solve for the final control torque.
2. The dual-closed-loop adaptive control method for a rope-driven, highly redundant robot according to claim 1, characterized in that: According to steps (1)-(4), the specific method is as follows: Suppose the redundant robot starts from the first... i- 1 section to i The forward kinematics of the segment are represented as follows: (1) in This represents the homogeneous rigid body transformation matrix of the redundant robot from one guide rope disk to the next. h This represents the distance from the center of the universal joint to the center of the guide rope disc. L Represents the length of the arm sleeve, of which , as well as The matrix representation is as follows: (2) The transformation matrix of the redundant robot from the base coordinate system to the end effector is expressed as: (3) Since the redundant continuum robot is driven by ropes, it is necessary to map joint angle changes to rope length changes. A mathematical model is established based on the position of the guide cable hole and the arm sleeve structure. (4) In the formula, L represents the length of the arm sleeve. Represents the first layer of guide rope disc j Layer i The spatial coordinates of the root rope, further represented as , among them Represents the corresponding guide rope disc The angle is expressed as: (5) The velocity, angular velocity, linear acceleration, and angular acceleration of each arm link of the redundant robot are expressed by the following recursive formulas: (6) in These are the angular velocity, linear velocity, angular acceleration, and linear acceleration of each robotic arm link. and Representing from the first To the The rotation matrix and translation vector of each, Representing the The rotation axis vector of each robotic arm joint These represent the angular velocity and angular acceleration of the joint rotation, respectively. represent A skew-symmetric matrix of vectors; The redundant robot base itself is stationary; the only force affecting the base is acceleration due to gravity, as shown below: (7) The forces at each joint are determined using Newton's and Euler's formulas: (8) Among them, force Represented as: (9) in Representing the The mass of each robotic arm component Representing the The mass moment at the rotation axis of a robotic arm link Representing the Spatial inertia of each robotic arm link ,at the same time A transformation matrix representing a special structure is expressed as: (10) By linearly separating the mass, mass moment, and inertia in equation (9), equation (9) is transformed into: (11) Since each link is subjected to the superposition of the forces of the following links, the total spatial force of joint i can be expressed as: (12) The matrix in equation (11) is defined as: (13) By superimposing forces from the end effector of the redundant robot forward, each force is transformed into each joint through spatial force transformation, thereby obtaining the torque of the joint rotation axis. The link parameters corresponding to the redundant robot are separated from equation (13) through dynamic parameter linearization, and the linearization matrix is obtained by recursion: (14) (15) This leads to the construction of linearized equations for joint torques and parameters: (16) in , This establishes a linear relationship between joint torque and inertial parameters. In system control, the inertial parameters are continuously corrected through joint errors to achieve dynamic adaptive control. The joint errors... sum of error change rate Represented as: (17) (18) in Represents the desired joint angle. , This refers to the actual joint angle; The dynamic equations of the redundant robotic arm are expressed as follows: (19) in The inertial force representing the robotic arm body, Representing forces such as Coriolis force and centripetal force, This represents the weight of the arm itself, while Represents joint torque; Substituting the torque obtained by linearizing the dynamic parameters into equation (19) yields the following equation: (20) Designing the adaptive rate of a redundant robot system using sliding mode control: (21) in ,at the same time represent The estimated value is initially determined by the inertial parameters of the arm's initial attitude, and then adaptively estimated based on the error generated by trajectory tracking. This yields the torque of the joint, which is mainly divided into two parts: one is the torque obtained through PD control, and the other is the torque obtained through the dynamic adaptive part. (22) Based on Lyapunov stability, the Lyapunov function is designed as an energy function: (23) Taking the derivative of this function, we get: (24) Considering the above properties and substituting them into the control law and adaptive law, we obtain... (25) Therefore, we can conclude that: (26) When time t When it approaches positive infinity, the estimated value as well as They all converge to 0, therefore we know that as time approaches positive infinity... s It will also tend to 0, and through the adaptive control law, the system's velocity and position can both reach zero steady-state closed-loop error.
3. The dual-closed-loop adaptive control method for a rope-driven, highly redundant robot according to claim 2, characterized in that: Based on steps (5) and (6), the specific method is as follows: The Jacobian of the rope section is mapped to the torque of the cable tension at the joint: (27) Where the Jacobian matrix is: (28) The tension of the rope can be directly solved using equation (27) (27) and the Jacobi pseudo-inverse. (29) The quadratic programming function is used to set the objective as minimizing tension while simultaneously setting upper and lower limits for the rope tension: (30) The minimum warning force of the rope at the setting is calculated using equation (30). To maximum tension The minimum rope tension that satisfies the condition of equation (27) at the same time; Considering dual-space closed-loop control, with the cable controlling the arm's movement, energy loss occurs during the control of the wire rope's movement. To achieve high-precision control, parameter separation of the motor control, as well as its inertia and friction factors, must be considered. (31) in , , These represent the motor's inertia matrix, viscous friction coefficient, and Coulomb friction force, respectively. The function represents the switching term function, and the above equation can be described as follows based on the rope-driven redundant arm model: (32) The adaptive synchronization term is modified by using the above linearized expression for the dynamic parameters: (33) in It estimates the dynamic parameters, and its derivative is expressed as: (34) Define rope in rope space The error and its derivative are defined as follows: : (35) (36) To ensure that the error deviation between ropes is within a preset range, a synchronization control algorithm is introduced: (37) in Representing the i The synchronization error of the rope root is composed of the integral of the errors of the two adjacent ropes controlled by the same section of the arm and the rope's own error. The proportional coefficient represents the weight of the synchronous control. This yields the final torque for rope control. for: (38) (39) By using the nonlinear solution function to obtain the optimal solution function in the solution space from the forward kinematics equations, and successively approximating the optimal solution with initial values, the forward kinematics equations are transformed into: (40) Solve the following constrained optimization problems using nonlinear constrained optimal solution methods: (41) Among them The function is represented as: (42) After discretizing the trajectory, the inverse kinematics solution is obtained for each point using the algorithm described above. To maintain continuity, the solution from the previous step is used... q The initial solution is used for optimization iteration using nonlinear constraints. Then, the joint angle and the corresponding rope length are used as inputs to provide the control torque in the dual-space closed-loop control to achieve closed-loop control.