Preset performance self-adaptive joint control method for rope-driven super-redundant snakelike mechanical arm

Abstract

The invention belongs to the technical field of mechanical arm joint control, and particularly discloses a preset performance self-adaptive joint control method for a rope-driven super-redundant snakelike mechanical arm, and the method comprises the following steps: carrying out kinematics modeling on a rope joint link of the rope-driven super-redundant snakelike mechanical arm, determining a relation between a rope speed and a joint angle, and determining a preset performance of the rope-driven super-redundant snakelike mechanical arm; calculating a joint jacobian matrix; designing a joint angle controller, defining an angle error and constraining the angle error in a preset performance range, and obtaining control input through an error transformation and return-to-zero dynamics principle so as to realize joint angle control; according to the method, a joint Jacobian matrix is estimated on line, and the joint Jacobian matrix is dynamically updated according to a rope speed error and a return-to-zero dynamic theory so as to adapt to the flexibility, time-varying characteristics and external disturbance of a rope, and the control precision is ensured. According to the method, it can be guaranteed that the joint angle of the rope-driven super-redundant mechanical arm can be accurately controlled under different working conditions, and it is guaranteed that the mechanical arm completes high-precision operation under the complex working conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical arm joint control, and more particularly relates to a preset performance adaptive joint control method for a rope-driven super-redundant snake-shaped mechanical arm. BACKGROUND

[0002] The rope-driven super-redundant snake-shaped mechanical arm has a wide application prospect in narrow space, complex obstacle environment and high-risk area operation due to its unique structure and motion characteristics. For example, in the tasks of aircraft fuel tank internal pipeline maintenance and aero-engine blade detection, the mechanical arm can easily cope with complex space structures and complete high-precision operation tasks with its high flexibility and redundancy, thereby significantly improving operation efficiency and safety.

[0003] However, the existing rope-driven super-redundant snake-shaped mechanical arm still faces many challenges in actual application. The joint control precision is a core index for measuring the operation ability, and this precision depends not only on the manufacturing quality of the hardware, but also on the control strategy used. Compared with traditional mechanical arms, the rope-driven snake-shaped mechanical arm adopts a rope driving structure, which brings more complex system characteristics and exhibits multi-source nonlinear behavior. The flexible deformation of the motor, ball screw and rope in operation makes the system exhibit significant rigid-flexible coupling characteristics, increases the difficulty of establishing an accurate model, and introduces various disturbance factors. The flexible characteristics of the rope have a particularly prominent influence on the control precision. The rope not only has memory and time-varying characteristics, but also exhibits obvious hysteresis under the action of complex internal and external friction, and its deformation is closely related to the historical force process. In addition, the flexibility of the rope changes in real time with changes in the attitude, load, motion frequency and other working conditions of the snake-shaped mechanical arm, which not only increases the complexity of control, but also may cause system oscillation and instability.

[0004] Therefore, how to ensure that the rope-driven super-redundant mechanical arm can accurately control the joint angle under different working conditions is a problem that needs to be solved at present. SUMMARY

[0005] In view of the defects of the prior art, the purpose of the present application is to provide a preset performance adaptive joint control method for a rope-driven super-redundant snake-shaped mechanical arm, which can ensure that the rope-driven super-redundant mechanical arm can accurately control the joint angle under different working conditions and ensure that the mechanical arm can complete high-precision operation under complex working conditions.

[0006] To achieve the above purpose, in a first aspect, the present application provides a preset performance adaptive joint control method for a rope-driven super-redundant snake-shaped mechanical arm, comprising the following steps: S10, kinematic modeling of the rope joint link of the rope-driven super-redundant snake-shaped mechanical arm, establishing a kinematic model from the joint space to the driving space, determining the relationship between the rope speed and the joint angle, and calculating the joint Jacobian matrix; S20, design a joint angle controller, define the angle error and constrain it within a preset performance range, and obtain the control input through error transformation and zeroing dynamics principle to achieve joint angle control; S30 estimates the joint Jacobian matrix online and dynamically updates it based on the rope speed error and zero-return dynamics theory to adapt to the rope's flexibility, time-varying characteristics, and external disturbances, ensuring control accuracy.

[0007] The pre-set performance adaptive joint control method for a rope-driven, ultra-redundant serpentine robotic arm provided in this application has the following advantages: First, kinematic modeling accurately describes the mapping relationship between rope drive and joint motion, and the established joint Jacobian matrix provides an accurate mathematical basis for subsequent control. Second, the pre-set performance controller ensures that the joint angle error always converges within a preset range by constraining the angle error boundary and employing nonlinear mapping transformation. This control method can adapt to the dynamic performance requirements under different working conditions. Furthermore, the online estimation mechanism updates the joint Jacobian matrix in real time, effectively compensating for model errors caused by rope flexibility deformation and time-varying characteristics, ensuring the system maintains a precise transmission relationship. These three steps work synergistically: kinematic modeling provides the theoretical basis for control, pre-set performance control ensures dynamic response quality, and online estimation maintains model accuracy. Together, they achieve precise control of the joint angle. Through this closed-loop control architecture, the system can automatically adapt to complex working conditions such as load changes and rope creep, ensuring that the robotic arm maintains high-precision motion control performance in various operating environments.

[0008] As a further preferred embodiment, the kinematic modeling step in step S10 specifically includes: Define the coordinate systems of the lower and upper guide vanes, and determine the position vector of the rope in the coordinate systems; The relationship between rope length and joint angle is calculated using a homogeneous transformation matrix. By differentiating the rope length, the relationship between the rope velocity and the joint angular velocity is obtained, and the joint Jacobian matrix is ​​derived.

[0009] As a further preferred option, in step S20, the angle error with inequality constraints is transformed by a smooth, strictly increasing function of a bijective mapping to obtain an angle error with equivalent constraints.

[0010] As a further preferred option, step S30 specifically involves: The rope speed error is defined as the difference between the driving rope speed and the joint angular velocity multiplied by the joint Jacobian matrix; The optimal solution is obtained by using zero-return dynamics theory and the least squares method, and the joint Jacobian matrix is ​​dynamically updated to adapt to the flexibility, time-varying characteristics and external disturbances of the rope, thus ensuring control accuracy.

[0011] As a further preferred embodiment, the method is adapted to the movement of the rope-driven super-redundant snake-like robotic arm under different working conditions, including different postures, loads, and movement frequencies.

[0012] Secondly, this application provides a rope-driven, ultra-redundant snake-like robotic arm, comprising: The robotic arm body has multiple joint modules, each of which is driven by a rope. The control system is used to execute the preset performance adaptive joint control method of the rope-driven super-redundant serpentine robot arm described in any one of the above descriptions, so as to achieve joint angle control.

[0013] As a further preferred embodiment, the control system includes: Sensors are used to measure joint angles and rope lengths; The processor is used to perform calculations for kinematic modeling, joint angle controller design, and joint Jacobian matrix estimation. An actuator is used to drive a rope according to a control input to achieve the movement of a joint.

[0014] As a further preferred embodiment, the joint module of the robotic arm body adopts a universal joint structure, with ropes evenly distributed on the circumference of the joint module, driving the joint to complete the corresponding movement through synchronous stretching and contraction.

[0015] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here. Attached Figure Description

[0016] Figure 1 This is a flowchart of the pre-set performance adaptive joint control method for the rope-driven super-redundant snake-like robotic arm provided in this application; Figure 2 This is a single-joint model diagram provided in the embodiments of this application; Figure 3 This is a step signal joint angle tracking diagram provided in an embodiment of this application; Figure 4 This is a step signal joint angle error diagram provided in an embodiment of this application; Figure 5 This is a sinusoidal signal joint angle tracking diagram provided in an embodiment of this application; Figure 6 This is a sinusoidal signal joint angle error diagram provided in the embodiments of this application; Figure 7 This is a rope speed error diagram provided in an embodiment of this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0018] This application's research found that when designing the control strategy for a rope-driven, super-redundant serpentine robotic arm, the dynamic characteristics of rope flexibility and the influence of complex environmental factors must be fully considered in order to effectively improve the control accuracy and operational stability of the serpentine robotic arm.

[0019] Furthermore, the parameters of the rope-joint transmission link in a rope-driven, ultra-redundant serpentine robotic arm are difficult to measure directly, and the rope undergoes significant flexible deformation during operation, causing its transmission characteristics to change in real time with various factors such as attitude, load, friction conditions, temperature, and usage frequency. This variation not only leads to a shift in the relationship between joint speed and the speed of the driving rope but also causes the statically calibrated system model to gradually become ineffective, thus affecting the positioning accuracy and dynamic response performance of the end effector. Therefore, the control system for a rope-driven, ultra-redundant serpentine robotic arm must introduce an online identification and real-time update mechanism for model parameters to ensure it always reflects the true motion characteristics of the robotic arm. This not only significantly improves disturbance suppression capabilities and end-effector control accuracy but also effectively enhances the system's stability and adaptability under complex working conditions, providing reliable assurance for high-precision operations in narrow, enclosed, or high-risk environments.

[0020] The above analysis shows that designing a reasonable joint angle control strategy is crucial for rope-driven ultra-redundant serpentine robotic arms. Therefore, this application analyzes the structure of the rope-driven ultra-redundant serpentine robotic arm, performs kinematic modeling of the "rope-joint" link, designs a preset performance controller to control joint angles, and estimates the joint Jacobian matrix online. Thus, the design method of this application can ensure that the rope-driven ultra-redundant robotic arm can accurately control joint angles under different working conditions, guaranteeing high-precision operation even in complex situations.

[0021] like Figure 1 As shown, this application provides a preset performance adaptive joint control method for a rope-driven ultra-redundant snake-like manipulator. This method can be adapted to the motion control of the rope-driven ultra-redundant snake-like manipulator under different working conditions such as posture, load, and motion frequency. It includes steps S10 to S30, which are detailed below: Step S10: Perform kinematic modeling on the rope joints of the rope-driven super-redundant serpentine robot arm, establish a kinematic model from joint space to drive space, determine the relationship between rope velocity and joint angle, and calculate the joint Jacobian matrix.

[0022] In step S10, the kinematic modeling steps are as follows: define the coordinate systems of the lower guide vane and the upper guide vane, and determine the position vector of the rope in the coordinate system; calculate the relationship between the rope length and the joint angle through the homogeneous transformation matrix; differentiate the rope length to obtain the relationship between the rope velocity and the joint angular velocity, and derive the joint Jacobian matrix.

[0023] Step S20: Design a joint angle controller, define the angle error and constrain it within a preset performance range, and obtain the control input through error transformation and zeroing dynamics principle to achieve joint angle control.

[0024] In step S20, the angle error with inequality constraints can be transformed by the smooth, strictly increasing function of the bijective mapping to obtain the angle error with equivalent constraints.

[0025] Step S30: Estimate the joint Jacobian matrix online. Based on the rope speed error and zero-return dynamics theory, dynamically update the joint Jacobian matrix to adapt to the rope's flexibility, time-varying characteristics, and external disturbances, ensuring control accuracy.

[0026] In this application, step S30 can be implemented as follows: the rope speed error is defined as the difference between the driving rope speed and the joint angular velocity multiplied by the joint Jacobian matrix; the optimal solution is obtained by using zero-return dynamics theory and the least squares method, and the joint Jacobian matrix is ​​dynamically updated to adapt to the rope's flexibility, time-varying characteristics and external disturbances, thereby ensuring control accuracy.

[0027] The pre-set performance adaptive joint control method for a rope-driven, ultra-redundant serpentine robotic arm provided in this application has the following advantages: First, kinematic modeling accurately describes the mapping relationship between rope drive and joint motion, and the established joint Jacobian matrix provides an accurate mathematical basis for subsequent control. Second, the pre-set performance controller ensures that the joint angle error always converges within a preset range by constraining the angle error boundary and employing nonlinear mapping transformation. This control method can adapt to the dynamic performance requirements under different working conditions. Furthermore, the online estimation mechanism updates the joint Jacobian matrix in real time, effectively compensating for model errors caused by rope flexibility deformation and time-varying characteristics, ensuring the system maintains a precise transmission relationship. These three steps work synergistically: kinematic modeling provides the theoretical basis for control, pre-set performance control ensures dynamic response quality, and online estimation maintains model accuracy. Together, they achieve precise control of the joint angle. Through this closed-loop control architecture, the system can automatically adapt to complex working conditions such as load changes and rope creep, ensuring that the robotic arm maintains high-precision motion control performance in various operating environments.

[0028] Based on the same inventive concept, this application also provides a rope-driven super-redundant snake-like robotic arm, including the robotic arm body and a control system.

[0029] The robotic arm itself has multiple joint modules, each of which is driven by a rope.

[0030] Specifically, the joint module of the robotic arm body can adopt a universal joint structure, with ropes evenly distributed on the circumference of the joint module, driving the joint to complete the corresponding movement through synchronous stretching and contraction.

[0031] The control system is used to execute the preset performance adaptive joint control method of the rope-driven super-redundant snake-like robotic arm provided above, so as to achieve joint angle control.

[0032] Specifically, the control system may include sensors, a processor, and actuators. The sensors are used to measure joint angles and cable lengths. The processor performs kinematic modeling, joint angle controller design, and joint Jacobian matrix estimation calculations. The actuators drive the cables according to control inputs to achieve joint movement.

[0033] In one embodiment, the technical solution to achieve the above objective can be as follows: This embodiment provides a preset performance adaptive joint control method for a rope-driven super-redundant serpentine manipulator, including kinematic modeling of the "rope-joint" link of the rope-driven super-redundant manipulator, joint angle controller design, and joint Jacobian matrix estimation.

[0034] In this embodiment, kinematic modeling of the "rope-joint" link of the rope-driven super-redundant robotic arm is performed as follows: like Figure 2 As shown, for a single-joint module, three ropes evenly distributed on the circumference drive the universal joint to complete the corresponding movement through synchronous stretching and contraction.

[0035] in, These represent the positions of the three rope holes on the lower guide reel. These represent the positions of the three rope holes on the upper guide reel. If the three drive cables of the joint are represented respectively, then the plane... This indicates the end face of the lower rope hole, a plane. Indicates the end face of the upper rope hole, universal joint cross axis rotation coordinate system The origin is the center point of the cross axis. Based on the two rotational directions of the universal joint , Determined according to the right-hand rule Assume the universal joint cross shaft rotates at an angle of... , When all corners are At that time, the upper and lower guide vanes are parallel, and the distance between the origin of the end face coordinate system and the origin of the center block coordinate system is... At this point, the coordinate system Move up ,get The origin of the coordinate system is the origin of the upper guide vane. coordinate axes direction and Parallel, at this time the coordinate system Move down ,get The origin of the coordinate system is the origin of the lower guide vane. coordinate axes direction and parallel. rope hole , Connect the origins of their respective end-face coordinate systems with the coordinate system. The included angle of the axis is The distance from the origin of the upper and lower guide rails to the rope is... .

[0036] The coordinate system of the lower end face can be obtained. To the center block coordinate system homogeneous transformation matrix for:

[0037] in, Representing coordinate system Around Rotation angle, represent Along Translation distance.

[0038] Upper surface coordinate system To the center block coordinate system The homogeneous transformation matrix is:

[0039] in, Representing coordinate system Around Rotation angle, represent Along Translation distance.

[0040] therefore, , Dot at The coordinates in the coordinate system are respectively , :

[0041] exist In the coordinate system, the rope vector is:

[0042] Find the length of the rope for:

[0043] Differentiating the above equation, we obtain the rope velocity as follows: :

[0044] in, It is the rotation angle The derivative of It is the rotation angle The derivative of represent function, represent function.

[0045] Similarly, Replace with +120° and +240° allows us to obtain the velocities of the other two ropes at the same joint, meaning the velocities of all three ropes at the same joint are... , , :

[0046] make The joint Jacobian matrix is ,

[0047] The formula can be rearranged as follows .

[0048] In this embodiment, regarding the design of the joint angle controller: Define the angle error as ,in For the desired angle of the joint, The actual angle of the joint is used to control the preset performance by constraining the angle error. The angle error is constrained as follows:

[0049] in, Indicates a constant parameter. Represents the performance function. :

[0050] in, , , These are defined positive constants used to control the specified performance to be achieved.

[0051] Define a smooth, strictly increasing function for a bijective mapping.

[0052] By transforming the error, the angle error with inequality constraints is transformed. Angle error transformed into equivalent constraint :

[0053] Therefore, the inverse transform can be defined as... ,in .

[0054] in:

[0055] Based on the principle of zero-return dynamics, we can obtain:

[0056] in It is a positive coefficient. It is a monotonically increasing activation function. Substituting the above formula and simplifying, we get:

[0057] in:

[0058]

[0059] The final result is:

[0060] in: .

[0061] In this embodiment, regarding the estimation of the joint Jacobian matrix: Define the rope speed error as ,in It drives the rope speed. It is the joint angular velocity. It is a joint Jacobian matrix.

[0062] According to the theory of zero-return dynamics, we can obtain:

[0063] in It is a positive coefficient. It is a monotonically increasing activation function.

[0064] After sorting, we can obtain:

[0065] in Represents the acceleration of the rope. The derivative of the joint Jacobian matrix, Represents joint angular acceleration. Since is an unknown variable to be solved, and considering that the solution to an underdetermined equation is not unique, the least squares solution is chosen as the optimal solution. Therefore, the above equation is rewritten as:

[0066] in Representative identity matrix and Kronecker's product, This represents the vectorization of a matrix.

[0067]

[0068] Finally, the joint Jacobian matrix is ​​dynamically updated according to the following adaptive law:

[0069] in It is the damping constant.

[0070] The key points of the rope-driven super-redundant snake manipulator preset performance adaptive joint control method provided in this embodiment are: (1) The transmission joint of the rope-driven super-redundant snake manipulator is "motor-rope-joint-end", and in the "rope-joint" link, kinematic modeling from joint space to drive space is required; (2) In the joint control of the rope-driven super-redundant snake manipulator, in order to enable the joint angle to move within the specified performance constraints, the controller design needs to construct a mapping transformation between the error with inequality constraints and the equivalent inequality error; (3) Due to the flexibility, time-varying characteristics of the rope and external disturbances, the joint Jacobian of the "rope-joint" link is time-varying. Therefore, the joint Jacobian needs to be estimated online and updated in real time to ensure control accuracy.

[0071] To verify the effectiveness of the controller designed in this application, simulation experiments were conducted, and the experimental results are as follows: Figures 3 to 7 As shown. Figure 3 This is the actual joint angle transformation value given a desired joint angle [10°; -10°]. As you can see, it can quickly reach the preset value. Figure 4 This is the error diagram of the joint angle, which shows that it can converge within the error boundary set in this embodiment. Figure 5This is a sinusoidal signal joint angle tracking diagram, tracking the desired joint angle [5sin(t); 5cos(t)]. It can be seen that it tracks the error signal very well. Figure 6 The diagram shows the joint angle error of a sinusoidal signal, and it can also be seen that the designed controller can meet the error boundary constraints. Figure 7 The diagram shows the rope velocity error during online estimation of the joint Jacobian. It can be seen that the designed online adaptive law enables the rope velocity error to converge quickly, verifying the effectiveness of the design scheme.

[0072] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for adaptive joint control of a rope-driven, ultra-redundant serpentine robotic arm with preset performance, characterized in that, Includes the following steps: S10, perform kinematic modeling of the rope joints of the rope-driven super-redundant snake-like robot arm, establish a kinematic model from joint space to drive space, determine the relationship between rope velocity and joint angle, and calculate the joint Jacobian matrix. S20, design a joint angle controller, define the angle error and constrain it within a preset performance range, and obtain the control input through error transformation and zeroing dynamics principle to achieve joint angle control; S30 estimates the joint Jacobian matrix online and dynamically updates it based on the rope speed error and zero-return dynamics theory to adapt to the rope's flexibility, time-varying characteristics, and external disturbances, ensuring control accuracy.

2. The pre-set performance adaptive joint control method for a rope-driven, ultra-redundant serpentine robotic arm as described in claim 1, characterized in that, In step S10, the kinematic modeling steps are as follows: Define the coordinate systems of the lower and upper guide vanes, and determine the position vector of the rope in the coordinate systems; The relationship between rope length and joint angle is calculated using a homogeneous transformation matrix. By differentiating the rope length, the relationship between the rope velocity and the joint angular velocity is obtained, and the joint Jacobian matrix is ​​derived.

3. The pre-set performance adaptive joint control method for a rope-driven, super-redundant serpentine robotic arm as described in claim 1, characterized in that, In step S20, the angle error with inequality constraints is transformed by the smooth, strictly increasing function of the bijective mapping to obtain the angle error with equivalent constraints.

4. The pre-set performance adaptive joint control method for a rope-driven, super-redundant serpentine robotic arm as described in claim 1, characterized in that, Step S30 is as follows: The rope speed error is defined as the difference between the driving rope speed and the joint angular velocity multiplied by the joint Jacobian matrix; The optimal solution is obtained by using zero-return dynamics theory and the least squares method, and the joint Jacobian matrix is ​​dynamically updated to adapt to the flexibility, time-varying characteristics and external disturbances of the rope, thus ensuring control accuracy.

5. The pre-set performance adaptive joint control method for a rope-driven, super-redundant serpentine robotic arm as described in claim 1, characterized in that, The method is adapted to the movement of a rope-driven, super-redundant serpentine robotic arm under different working conditions, including different postures, loads, and movement frequencies.

6. A rope-driven, ultra-redundant serpentine robotic arm, characterized in that, include: The robotic arm body has multiple joint modules, each of which is driven by a rope. A control system is used to execute the preset performance adaptive joint control method of the rope-driven super-redundant serpentine manipulator as described in any one of claims 1 to 5, so as to achieve control of the joint angle.

7. The cable-driven, ultra-redundant serpentine robotic arm according to claim 6, characterized in that, The control system includes: Sensors are used to measure joint angles and rope lengths; The processor is used to perform calculations for kinematic modeling, joint angle controller design, and joint Jacobian matrix estimation. An actuator is used to drive a rope according to a control input to achieve the movement of a joint.

8. The cable-driven, ultra-redundant serpentine robotic arm according to claim 6, characterized in that, The joint module of the robotic arm adopts a universal joint structure, with ropes evenly distributed on the circumference of the joint module. The joint is driven to complete the corresponding movement by synchronous stretching and contraction.

Images