Control method of point cloud polishing remote control system based on sliding mode and adaptive control

Abstract

The present application belongs to the technical field of grinding processing, and discloses a control method of a point cloud polishing remote control system based on a sliding mode and adaptive control. The control method comprises the following steps: S1, establishing a dynamic equation of the remote control system to obtain control equations of a master robot and a slave robot; S2, performing point cloud scanning on a weld to be polished to obtain corresponding point cloud data, calculating the depth gradient, dexterity and stiffness of each point in the point cloud data, setting a starting point and an ending point of polishing, and planning an optimal polishing path; and S3, inputting the control equations obtained in step S1 and the optimal polishing path obtained in step S2 into a controller to control the slave robot to polish. Through the present application, the accuracy of the control algorithm and the optimization of the point cloud path search are combined, and the efficiency of remote operation control under polishing conditions is improved.

Description

Technical Field

[0001] This invention belongs to the technical field of grinding processing, and more specifically, relates to a control method for a point cloud grinding remote control system based on sliding mode and adaptive control. Background Technology

[0002] In recent years, the use of collaborative robots has become increasingly widespread. Adopting human-robot collaboration plays a crucial role in improving productivity. Its essence lies in balancing human adaptability and decision-making capabilities in real-world scenarios with the high efficiency, repeatability, and precision of robots. Extensive research into teleoperation has diversified the application scenarios of robots, including surgical procedures, welding and assembly, industrial drilling, and CNC grinding.

[0003] For grinding scenarios, the complexity and danger of the environment place higher demands on processing precision. In practical teleoperation applications, the parameters in the system dynamics model are difficult to obtain accurately, exhibiting varying degrees of uncertainty. Furthermore, the robot itself has friction and dead zones, which affect control processes. In addition, external environmental interference is unpredictable. Such grinding processes involve complex and even dangerous working environments, hindering close-range operation by operators. Therefore, teleoperated robots operating in an interactive manner have received widespread attention and research. Moreover, during robot grinding, the design of control algorithms reduces uncertainties and external environmental interference, and the use of point clouds and other methods for trajectory planning improves the workpiece grinding effect. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a control method for a point cloud grinding remote control system based on sliding mode and adaptive control, solving the control problem of operating the system during the grinding process.

[0005] To achieve the above objectives, according to the present invention, a control method for a point cloud grinding remote control system based on sliding mode and adaptive control is provided, the control method comprising the following steps:

[0006] S1 establishes the dynamic equations of the remote control system, designs a sliding mode controller, and uses the sliding mode controller to construct a four-channel sliding mode-adaptive controller to obtain the control equations of the master robot and the slave robot.

[0007] S2 performs point cloud scanning on the weld to be ground to obtain the corresponding point cloud data, calculates the depth gradient, dexterity and stiffness of each point in the point cloud data, sets the starting point and ending point of grinding, and plans the optimal grinding path using the depth gradient, dexterity and stiffness of each point.

[0008] S3 inputs the control equation obtained in step S1 and the optimal grinding path obtained in step S2 into the controller to control the slave robot to perform grinding.

[0009] More preferably, in step S1, the design of the sliding mode controller is performed according to the following steps:

[0010] S11 sets the delay angle error between the angle signals of the slave robot and the master robot as the control quantity, constructs a continuous non-singular terminal sliding surface of the remote control system with respect to the angle error, and sets the nonlinear sliding mode approach rate of the sliding surface.

[0011] S12 uses the aforementioned dynamic equations to solve for the angular acceleration error;

[0012] S13 substitutes the angle error obtained from the solution into the set nonlinear sliding mode approach rate to obtain the control torque of the remote control system and realize the design of the sliding mode controller.

[0013] More preferably, in step S11, the sliding surface is configured according to the following relationship:

[0014]

[0015]

[0016] Where e s e is the control amount for the end angle error. m Main end angle error control quantity To differentiate from the end angle error, i.e., the angular velocity error, The derivative of the main end angle error is the angular velocity error, s m Main end sliding surface, s s Let ω be the sliding surface at the end, ω be a constant and ω > 0, γ be a constant and 1 < γ < 2, and μ be a constant.

[0017] More preferably, in step S11, the nonlinear sliding mode convergence rate is determined according to the following relationship:

[0018]

[0019]

[0020] Where s m Main end sliding surface, s s To the end sliding surface, The derivative of the main end sliding surface Let K1 be the derivative of the sliding surface at the end, K2 be a constant, and ρ be a constant.

[0021] More preferably, in step S12, the angular acceleration is performed according to the following steps:

[0022]

[0023]

[0024] in, To account for the end-angle acceleration error, Let M be the angular acceleration error at the master end, and M be the inertia matrix. For the master end, q m For angle, For speed, For acceleration, G is the Coriolis / centrifugal force matrix. m (q m Let q be the gravity vector. For the slave end, q s For angle, q s For velocity, q s For acceleration, M s (q s ) is the inertia matrix. G is the Coriolis / centrifugal force matrix. s (q s ) is the gravity vector, and u m and u s It is the input of control force, τ h and τ e T represents the force exerted by the operator on the master robot and by the environment on the slave robot. m The delay between the master and slave ends of the remote operating system is denoted as t, where t is the time interval at each moment.

[0025] More preferably, in step S13, the control torque of the remote control system is performed according to the following steps:

[0026] u s =u1+u2

[0027] u m =u3+u4

[0028] in:

[0029]

[0030] u2 = -M0(K1s) s +K2sig(s s ))

[0031]

[0032] u4=-M0(K1s m +K2sig(s m))

[0033] Where u m The sliding mode control torque at the main end, u s Let u1 and u2 be the sliding mode control torques at the slave end. s The two components, u3 and u4, are u m The two components, To differentiate from the end angle error, i.e., the angular velocity error, The derivative of the angle error at the master end is the angular velocity error. Since the master and slave robots are identical, M0 is the inertia matrix, C0 is the Coriolis / centrifugal force matrix, and G0 is the gravity matrix. For the master end, q... m For angle, For speed, For acceleration, q s For angle, q s For velocity, q s Let ω be the acceleration, ω be a constant and ω > 0, and γ be a constant and 1 < γ < 2, s m Main end sliding surface, s s For the sliding surface at the end, K1 is a constant, K2 is a constant, and T m The delay between the master and slave ends of the remote operating system is denoted as t, where t is the time interval at each moment.

[0034] More preferably, the control equations for the master robot and the slave robot are obtained according to the following steps:

[0035] S14 sets the error vector between the slave robot and the master robot, and uses the error vector and the kinematic equation to obtain the open-loop equation of the remote control system.

[0036] S15 sets the total control torque and dynamic adaptive rate of the sliding mode-adaptive controller, and substitutes the set total control torque and adaptive rate into the open-loop equation to obtain the required control equation.

[0037] More preferably, in step S14, the open-loop equation is performed according to the following relationship:

[0038]

[0039]

[0040] For the master end, q m For angle, For speed, For acceleration, M m (q m ) is the inertia matrix. For the Coriolis / centrifugal force matrix, q s For angle, For speed, For acceleration, M s (q s ) is the inertia matrix. For the Coriolis / centrifugal force matrix, u m and u s It is the input of control force, τ h and τ e It refers to the forces applied by the operator to the master robot and by the environment to the slave robot, e m2 The new error vector for the master end, e s2 For the new error vector from the end, κ m κ is a diagonal positive definite constant matrix. s Hq is a diagonal positive definite constant matrix. m The uncertain parameters of the master-end robot system dynamics, Hq s This refers to the uncertain parameters of the dynamics of the slave robot system.

[0041] More preferably, in step S15, the governing equations are performed according to the following relationship:

[0042]

[0043]

[0044] in For the master end, q m For angle, For speed, For acceleration, M m (q m ) is the inertia matrix. For the Coriolis / centrifugal force matrix, q s For angle, q s For velocity, q s For acceleration, M s (q s ) is the inertia matrix. For the Coriolis / centrifugal force matrix, e m2 The new error vector for the master end, e s2 Let u1 and u2 be the new error vectors from the slave end. s The two components, u3 and u4, are u m The two components, τ h and τ e Hq is the force exerted by the operator on the master robot and by the environment on the slave robot. m The uncertain parameters of the master-end robot system dynamics, Hq s For the uncertain parameters of the end-user robot system dynamics, Ks K is a constant. m C1 is a constant, C2 is a constant, and C3 is a constant.

[0045] More preferably, in step S3, the optimal grinding path is planned and obtained in the stiffness distribution map using the RRT path search algorithm.

[0046] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0047] 1. In this invention, a sliding mode adaptive controller is used to control the robot. Since the robot system is a multi-degree-of-freedom system, it is highly nonlinear and has dynamic uncertainty and force information chatter phenomenon. Therefore, the adaptive controller needs to continuously update and substitute the estimated value of the dynamic uncertainty to solve the torque. In addition, the force chatter phenomenon in the control process will cause system oscillation and instability. The sliding mode controller alleviates force chatter and improves the tracking effect.

[0048] 2. This invention addresses the master-slave tracking control system for multi-degree-of-freedom robots. Based on the transparency of the four-channel architecture, it uses an adaptive controller to adjust the control torque in real time, reducing errors caused by dynamic uncertainties. A sliding mode controller is used to mitigate system instability caused by force chatter and sudden changes during the control process, ultimately achieving good tracking performance between the master and slave robots during the grinding process.

[0049] 3. This invention designs and builds a bilateral teleoperation platform, which combines the accuracy of the control algorithm with the optimization of point cloud path search, thereby improving the efficiency of teleoperation control under grinding conditions. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the structure of a point cloud grinding remote control system based on sliding mode and adaptive control, constructed according to a preferred embodiment of the present invention.

[0051] Figure 2 This is a four-channel adaptive control block diagram constructed according to a preferred embodiment of the present invention;

[0052] Figure 3 It is the point cloud data of the weld seam constructed according to the preferred embodiment of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0054] A point cloud grinding remote control system based on sliding mode and adaptive control includes a controller, a master robot, and a slave robot. The controller is connected to both the master robot and the slave robot. The master robot moves and transmits the torque of the movement to the controller, which controls the slave robot to perform corresponding movements, thereby realizing the remote operation of the slave robot.

[0055] In this embodiment, the robot bilateral teleoperation platform includes a seven-degree-of-freedom robot located at the master end and a slave end, and a corresponding control chassis. Both the master end robot and the slave end robot are seven-degree-of-freedom Franka Emika robots from Germany.

[0056] The end effector of the main robot is equipped with a force sensor, which is fixed to the end effector of the robot via a sensor flange. All connections are made by bolts and nuts, and the sensor is used to measure the user's operating force.

[0057] For the slave robot, since it needs to perform processing in a specific working environment, it is necessary to design and install grinding tools. At the same time, to ensure processing quality, a constant force actuator is installed at it.

[0058] First, a sensor is fixed to the end effector of the robot via a sensor flange to measure force changes during processing. Second, the ACF constant force actuator is fixed to the sensor flange using bolts and nuts. Finally, the constant force actuator is connected to the belt sander via a rectangular flange.

[0059] The ACF constant force actuator is pneumatically driven, and the end effector force is set via software and monitored in real time. A six-dimensional sensor reads the force and torque in the XYZ directions, and the data is acquired in real time via MATLAB.

[0060] The software experimental platform for the remote operation control system mainly includes the Simulink control program, the robot ROS program, the custom node program, the communication link, the experimental module, and the data acquisition module.

[0061] The entire teleoperation system's data transmission is based on ROS and mainly includes a Simulink control program, a robot ROS program, a custom node program, communication components, experimental modules, and a data acquisition module. The master device sends data via a topic named "Datafromfranka," which includes information such as joint angles, joint velocities, joint accelerations, end-effector positions, end-effector velocities, and end-effector accelerations. The slave device also sends data via a topic named "Datafromfranka_1." Throughout the control process, ROS topics transmit robot information, and MATLAB reads sensor information, enabling data transmission between the master and slave devices.

[0062] The control method of the above-mentioned remote control system includes the following steps:

[0063] S1 establishes the dynamic equations of the remote control system, designs a sliding mode controller, and uses the sliding mode controller to construct a four-channel sliding mode-adaptive controller to obtain the control equations of the master robot and the slave robot.

[0064] Specifically, a four-channel adaptive algorithm combining continuous fast sliding mode is designed to adaptively and rapidly track the uncertainties of nonlinear systems. For teleoperated robot control systems, there are many degrees of freedom and strong system nonlinearity. During motion, the angle signal from the slave robot, after a time delay, will have an error compared to the angle signal sent by the master robot.

[0065] Step 1: The dynamic equations of the teleoperated robot system of this invention are as follows:

[0066]

[0067]

[0068] In the above formula, the subscripts m and s represent the master and slave ends of the teleoperated robot system, respectively. For the master end, These are angle, velocity, and acceleration, respectively, M. m (q m ) is the inertia matrix. G is the Coriolis / centrifugal force matrix. m (q m () is the gravity vector. For the slave end, These are angle, velocity, and acceleration, respectively, M. s (q s ) is the inertia matrix. G is the Coriolis / centrifugal force matrix. s (q s ) is the gravity vector. Furthermore, u m and u s It is the input of control force, τ h and τe These are the forces applied by the operator to the master robot and by the environment to the slave robot.

[0069] Step 2: Obtain the control torque of the sliding mode.

[0070] (1) The angle error between the angle signal of the slave robot after time delay and the angle signal sent by the master robot during the motion is used as the control quantity:

[0071] e s =q s -q m (tT m (3)

[0072] The following can be obtained by solving the dynamic equation (1):

[0073]

[0074]

[0075] Similarly, we have:

[0076] e m =q m -q s (t+T m (6)

[0077] The following can be obtained by solving the dynamic equation (2):

[0078]

[0079]

[0080] Where e s and e m These are the angular error control values ​​for the slave end and the master end, respectively. and The derivatives of the angle error are respectively taken, i.e., the angular velocity error. and These are the angular acceleration errors, respectively.

[0081] (2) To avoid chattering and singularities, the angular velocity signal delay error e is utilized. s and e m Design a continuous non-singular terminal sliding surface:

[0082]

[0083] Where s m ,s s Let μ, ω, and γ be the sliding surface, and μ, ω, and γ be constants.

[0084] (3) Utilizing the sliding surface s m ,s s To improve the convergence performance of the system, a fast nonlinear reaching rate is designed, the expression of which is:

[0085]

[0086] Where K1, K2, and ρ are constants.

[0087] Substituting (5) and (8) into the sliding mode approach ratio (10) and combining it with the set sliding surface (9), the control torque of the robot system can be finally obtained as follows:

[0088]

[0089] u2 = -M0(K1s) s +K2sig(s s (12)

[0090] u s =u1+u2 (13)

[0091]

[0092] u4=-M0(K1s m +K2sig(s m (15)

[0093] u m =u3+u4 (16)

[0094] Where u m ,u s The sliding mode control torque for the master and slave ends.

[0095] Step 3: Obtain the four-channel sliding mode and adaptive coupling controller, and solve the control equations. As shown in the previous section, the four-channel structure can achieve good transparency and stability in the teleoperation system. However, due to the complex structures of the master and slave robots, dynamic uncertainties exist, leading to instability and low accuracy in the actual grinding process. A four-channel bilateral adaptive teleoperation control structure is designed. In this control algorithm, the original position controller at the slave robot end is replaced by an adaptive position controller, which can solve the problem of robot dynamic uncertainties.

[0096] (1) The angular error e between the slave robot and the master robot m ,e s Perform the processing and define a new error vector:

[0097]

[0098] in, κ m ,κ s It is a diagonal positive definite constant matrix.

[0099] From equation (17) above, we can obtain:

[0100]

[0101] Substituting equation (18) into equations (1) and (2) and combining this with the error handling and dynamic uncertainty of the robot system described above, we can obtain the open-loop equation of the robot as follows:

[0102]

[0103] Among them, Hq m For the uncertain parameters of the robot system dynamics,

[0104] (2) Combining the previous sliding mode controller design equations (13) and (16), design the total control torque of the sliding mode and adaptive controller:

[0105]

[0106] Among them, K s It is a diagonal positive definite constant matrix. C1 and C2 are estimates of the uncertainties in the dynamics; C3 and C4 are positive constants.

[0107] Adaptive dynamics of robots:

[0108]

[0109] Where, ξ m ,ξ s It is a diagonal positive definite constant matrix. According to the above adaptive law (21), ... It is updated in real time.

[0110] (3) Substituting equation (20) into equation (19), the control equations for the sliding mode and adaptive controller of the slave robot are finally obtained as follows:

[0111]

[0112] in,

[0113] Similarly, the control equations for the sliding mode and adaptive controller of the S4 master robot are as follows:

[0114]

[0115] u4=-M0(K1s m +K2sig(s m)) (twenty four)

[0116]

[0117] in,

[0118] By introducing a sliding mode control law on the basis of a four-channel adaptive architecture, bilateral tracking of the robot under nonlinear conditions can be achieved with the transparency between the master and slave ends.

[0119] like Figure 2 As shown, the four-channel system consists of the operator, the master robot, the communication network, the slave robot, and the external environment. The operator sends signal commands to the master robot and initiates trajectory movements. These commands are transmitted to the slave robot via the communication network. Upon receiving the signal, the slave robot executes the command to complete the required tracking task. Simultaneously, the slave robot receives information from the master robot and senses the environment, providing feedback through the communication network. Ultimately, this allows the operator to control the remote robot as if it were a local robot, creating a more realistic and immersive experience. Where v h and v e T represents the speed of the master and slave ends, and T is the communication delay between the master and slave ends. The position signals of the master end, the position signals of the slave end, the force between the operator and the master end, and the force between the slave end and the environment are transmitted to each other. Each channel controls and adjusts parameters through C1 to C6.

[0120] S2 performs point cloud scanning on the weld seam to be ground to obtain the corresponding point cloud data, such as Figure 3 As shown, the depth gradient, dexterity, and stiffness of each point in the point cloud data are calculated, the starting point and ending point of the grinding are set, and the optimal grinding path is planned using the depth gradient, dexterity, and stiffness of each point.

[0121] Specifically, based on the point cloud features of the weld, a stiffness distribution map of the robotic arm is generated during the grinding process on the weld surface. Based on this distribution map, the optimal grinding posture path is planned using the RRT path search algorithm. During the robotic arm grinding process, it is necessary to maintain a certain angle between the end of the grinding tool and the grinding surface to ensure the grinding effect. The point information and curvature information of the grinding surface determine the grinding posture of the robotic arm. The stiffness of the robotic arm changes under different poses. Grinding under low stiffness conditions will cause significant vibration of the robotic arm, thus affecting the grinding quality. Therefore, it is necessary to optimize the robotic arm posture during grinding based on the surface information of the weld to reduce vibration. This patent proposes a method to generate a robotic arm stiffness point cloud distribution map based on a depth image according to the weld surface, and then use the RRT algorithm to find the optimal grinding posture trajectory based on this distribution map. The details are as follows:

[0122] Furthermore, based on a depth camera, depth point cloud information of the ground weld is acquired, and the normal vector information of the point cloud is calculated using the depth gradient. The specific algorithm is as follows:

[0123]

[0124]

[0125] Here, f is the required depth information, f is the camera focal length (an intrinsic parameter of the camera), and d is the depth information acquired by the depth camera. and It is the depth gradient along the X and Y axes in the coordinate system.

[0126] Furthermore, based on the point information and normal vector information of the weld point cloud, the posture of the robotic arm when grinding this point is calculated, and then the stiffness and dexterity indices of the robotic arm in this posture are calculated. The stiffness of the robotic arm is obtained based on its inherent characteristics combined with posture testing. The formula for calculating dexterity is:

[0127]

[0128] σ1, σ r These are the maximum and minimum singular values ​​of the Jacobian matrix J(q) of the robot's current posture, respectively.

[0129] Repeat the above calculations for each point in the weld seam point cloud until the stiffness index of all weld seam point clouds is obtained, and draw a comprehensive point cloud distribution map of the dexterity and stiffness of the weld grinding robot arm.

[0130] Furthermore, by setting the starting and ending points of grinding on the distribution map, and using the RRT path search algorithm, a grinding path with globally optimal stiffness is planned on the stiffness distribution map. The workpiece can then be ground along this path using a control algorithm.

[0131] A voxel model is constructed based on the point cloud of the weld seam. The comprehensive grinding cost at each point is calculated iteratively. The comprehensive grinding cost is determined by the robot's stiffness, pose singularity, obstacle avoidance distance, and optimal grinding angle when the robot is in that point's pose. Robot stiffness, dexterity, and obstacle avoidance distance are related to the teleoperation algorithm described earlier, while the optimal grinding angle is related to the grinding process. Other factors can be easily added as needed for subsequent weld seam grinding. The grinding path is then generated using the RRT algorithm based on the generated cost voxel map. The equation for calculating the comprehensive grinding cost is as follows:

[0132]

[0133] s i(i = 1, 2, ..., n) represents the polishing cost indicators that need to be considered. The larger the absolute value, the more the indicator will increase the overall polishing cost, and vice versa (for indicators with opposite actual changing patterns, take their reciprocal and substitute them in); σ i (i = 1, 2, ... n) represents the influence index of each indicator. In actual refinement, different influence factors of different sizes will be selected as needed to change the degree of influence of different indicators on the overall cost.

[0134] S3 inputs the control equation obtained in step S1 and the optimal grinding path obtained in step S2 into the controller to control the slave robot to perform grinding.

[0135] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A control method for a point cloud grinding remote control system based on sliding mode and adaptive control, characterized in that, The control method includes the following steps: S1. Establish the dynamic equations of the remote control system, design a sliding mode controller, and use the sliding mode controller to construct a four-channel sliding mode-adaptive controller to obtain the control equations of the master robot and the slave robot. S2 performs point cloud scanning on the weld to be ground to obtain the corresponding point cloud data, calculates the depth gradient, dexterity and stiffness of each point in the point cloud data, sets the starting point and ending point of grinding, and plans the optimal grinding path using the depth gradient, dexterity and stiffness of each point. S3 inputs the control equation obtained in step S1 and the optimal polishing path obtained in step S2 into the controller to control the slave robot to perform polishing. In step S1, the design of the sliding mode controller is carried out according to the following steps: S11 sets the delay angle error between the angle signals of the slave robot and the master robot as the control quantity, constructs a continuous non-singular terminal sliding surface of the remote control system with respect to the angle error, and sets the nonlinear sliding mode approach rate of the sliding surface. S12 uses the aforementioned dynamic equations to solve for the angular acceleration error; S13 Substitute the angle error obtained from the solution into the set nonlinear sliding mode approach rate to obtain the control torque of the remote control system and realize the design of the sliding mode controller. In step S2, the optimal polishing path is planned according to the following steps: Based on a depth camera, depth point cloud information of the ground weld is acquired. The normal vector information of the point cloud is calculated using the depth gradient. The specific algorithm is as follows: This is the required normal vector information. It is the camera's focal length, an intrinsic parameter of the camera. It is depth information acquired by a depth camera. and It is the depth gradient along the X and Y axes in the coordinate system; Based on the point information and normal vector information of the weld seam point cloud, the posture of the robotic arm when grinding this point is calculated, and then the stiffness and dexterity indices of the robotic arm under this posture are calculated. The stiffness of the robotic arm is obtained based on the inherent characteristics of the robotic arm combined with posture testing, and the formula for calculating dexterity is as follows: , These are the Jacobian matrices of the robot's current pose. Maximum and minimum singular values, Repeat the above calculation for each point in the weld point cloud until the stiffness index of all weld point clouds is obtained, and draw a comprehensive point cloud distribution map of the dexterity and stiffness of the weld grinding robot arm. After setting the starting and ending points of the grinding process on the distribution map, a grinding path with optimal global stiffness is planned on the stiffness distribution map based on the RRT path search algorithm.

2. The control method as described in claim 1, characterized in that, In step S11, the sliding surface is determined according to the following relationship: in This is the control amount for the end angle error. Main end angle error control quantity To differentiate from the end angle error, i.e., the angular velocity error, The derivative of the main end angle error is the angular velocity error. Main end sliding surface, To the end sliding surface, is a constant and , is a constant and , It is a constant.

3. The control method as described in claim 1, characterized in that, In step S11, the nonlinear sliding mode approach rate is determined according to the following relationship: in Main end sliding surface, To the end sliding surface, The derivative of the main end sliding surface For the derivative from the end sliding surface, It is a constant. It is a constant. It is a constant.

4. The control method as described in claim 1, characterized in that, In step S12, the angular acceleration is performed according to the following steps: in, To account for the end-angle acceleration error, The main end angular acceleration error, Let the inertia matrix be the matrix for the principal end. For angle, For speed, For acceleration, For the Coriolis / centrifugal force matrix, Let gravitational force be the vector, for the slave end, For angle, For speed, For acceleration, The inertia matrix, For the Coriolis / centrifugal force matrix, It is the gravity vector, in addition, and It is the input of control force. and These are the forces applied by the operator to the master robot and by the environment to the slave robot. To reduce master-slave latency in remote operating systems, This represents the time interval at each instant.

5. The control method as described in claim 1, characterized in that, In step S13, the control torque of the remote control system is performed according to the following steps: in: in The sliding mode control torque at the main end, To control the sliding mode torque at the slave end, for The two components, for The two components, To differentiate from the end angle error, i.e., the angular velocity error, The derivative of the master-end angle error is the angular velocity error. Since the master and slave robots are identical... The inertia matrix, For the Coriolis / centrifugal force matrix, For the gravity matrix, at the principal end, For angle, For speed, For acceleration, for the slave end, For angle, For speed, For acceleration, is a constant and , is a constant and , Main end sliding surface, To the end sliding surface, It is a constant. It is a constant. To reduce master-slave latency in remote operating systems, This represents the time interval at each instant.

6. The control method as described in claim 1 or 2, characterized in that, The control equations for the master robot and the slave robot are obtained according to the following steps: S14. Set the error vector between the slave robot and the master robot, and use the error vector and the kinematic equation to obtain the open-loop equation of the remote control system. S15 sets the total control torque and dynamic adaptive rate of the sliding mode-adaptive controller, and substitutes the set total control torque and adaptive rate into the open-loop equation to obtain the required control equation.

7. The control method as described in claim 6, characterized in that, In step S14, the open-loop equation is performed according to the following relationship: For the master end, For angle, For speed, For acceleration, The inertia matrix, For the Coriolis / centrifugal force matrix, for the slave end, For angle, For speed, For acceleration, The inertia matrix, For the Coriolis / centrifugal force matrix, and It is the input of control force. and These are the forces applied by the operator to the master robot and by the environment to the slave robot. The new error vector for the master end. For the new error vector from the slave end, It is a diagonal positive definite constant matrix. It is a diagonal positive definite constant matrix. For the uncertain parameters of the main-end robot system dynamics, This refers to the uncertain parameters of the dynamics of the slave robot system.

8. The control method as described in claim 6, characterized in that, In step S15, the governing equations are performed according to the following relationship: in , For the master end, For angle, For speed, For acceleration, The inertia matrix, For the Coriolis / centrifugal force matrix, for the slave end, For angle, For speed, For acceleration, The inertia matrix, For the Coriolis / centrifugal force matrix, The new error vector for the master end. For the new error vector from the slave end, for The two components, for The two components, and These are the forces applied by the operator to the master robot and by the environment to the slave robot. For the uncertain parameters of the main-end robot system dynamics, For the uncertain parameters of the end-user robot system dynamics, It is a constant. It is a constant. It is a constant. It is a constant.

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