Mechanical arm path planning method and system based on mixed proportional integral sliding mode control

Abstract

The application discloses a mechanical arm path planning method based on a mixed proportional integral sliding mode control, and comprises a three-link mechanical arm, the length of three links of the three-link mechanical arm and the corresponding joint angle are connected through a forward kinematics equation of the three-link mechanical arm to obtain the coordinates of an end effector of the three-link mechanical arm in a Cartesian coordinate system; an initial state and a target state are set, the initial state is connected with the target state to generate a predefined path of the end effector of the three-link mechanical arm, a proportional integral controller PI is combined with a sliding mode controller SMC to obtain a proportional integral sliding mode controller PI-SMC; a mixed proportional integral sliding mode controller is generated; the mixed proportional integral sliding mode controller is combined with the predefined path to generate a mechanical arm path planning, and the mechanical arm of the robot can accurately repeat the same action in an unstructured scene.

Description

Technical Field

[0001] This invention relates to the field of path planning technology, specifically to a method and system for path planning of a robotic arm based on hybrid proportional-integral sliding mode control. Background Technology

[0002] With the development and progress of social productivity, robots are being widely used in various structured and unstructured scenarios. In structured scenarios, with the help of simple forward and inverse kinematics calculation tools, the robot's robotic arm can accurately repeat the same actions. However, in unstructured scenarios, the smoothness, vibration, and accuracy of the robot's robotic arm movements have become major challenges. To solve this problem, this invention improves and adjusts the point-to-point path planning of the robot's three-bar linkage, ensuring that the robotic arm moves within the optimal working range, reducing the vibration of the robotic arm, and providing excellent working accuracy. Summary of the Invention

[0003] This invention provides a robotic arm path planning method and system based on hybrid proportional-integral sliding mode control, which solves the problems of low smoothness, large jitter, and low accuracy of robotic arm movements in the prior art, and enables the robotic arm to accurately repeat the same movements in unstructured scenarios.

[0004] To solve the above problems, the present invention adopts the following technical solution:

[0005] The first aspect is a robotic arm path planning method based on hybrid proportional-integral sliding mode control, comprising:

[0006] S1. The robotic arm has three links, which are connected by three rotary joints to form a three-link robotic arm.

[0007] S2. The lengths of the three links of the three-bar linkage and the corresponding joint angles are used to obtain the coordinates of the end effector of the three-bar linkage in the Cartesian coordinate system by applying the forward kinematics equation of the three-bar linkage.

[0008] S3. Based on the coordinates of the end effector of the three-bar linkage robot, set an initial state and a target state, connect the initial state and the target state, and generate a predefined path for the end effector of the three-bar linkage robot.

[0009] S4. Based on the noise caused by the PID controller in the control operation, a proportional-integral controller PI is set up, and the proportional-integral controller PI is combined with the sliding mode controller SMC to obtain a proportional-integral sliding mode controller PI-SMC.

[0010] S5. Connect the proportional-integral sliding mode controller PI-SMC to the three-bar linkage robotic arm to generate a hybrid proportional-integral sliding mode controller.

[0011] S6. Combine the hybrid proportional integral sliding mode controller with the predefined path to generate a robotic arm path plan.

[0012] Furthermore, in S3, based on the coordinates of the end effector of the three-bar linkage, an initial state and a target state are set. The initial state and the target state are connected to generate a predefined path for the end effector of the three-bar linkage. The predefined path also includes the initial state as... The target state is Introducing a new situation variable ( , ), and the initial state time and target state time We obtain the following using the third derivative:

[0013] , ,

[0014] Establish initial state With the target state The connection.

[0015] Furthermore, in step S3, based on the coordinates of the end effector of the three-bar linkage robot, an initial state and a target state are set. The initial state and the target state are connected to generate a predefined path for the end effector of the three-bar linkage robot. The predefined path also includes...

[0016] The coefficients are obtained using a seventh-order polynomial. , the coefficient The normalized time λ is expressed by the equation: ,in express The normalized time, i=1,2,3…, yields the seventh-order polynomial path.

[0017] Furthermore, in S4, based on the noise caused by the PID controller during control operation, a proportional-integral (PI) controller is set up. The PI controller is then combined with a sliding mode controller (SMC) to obtain a proportional-integral sliding mode controller (PI-SMC). The PI-SMC further includes...

[0018] S41. Set the initial state in the predefined path. Corresponding initial position The input is fed into the proportional-integral controller (PI), through the equation: , and obtain the data u(t);

[0019] S42. Input the data u(t) into the sliding mode controller SMC, and obtain the time-varying S(t) by reducing all trajectories along the sliding surface.

[0020] S43. Pass the time-varying S(t) through a Lyapunov function: This keeps the time-varying S(t) at zero;

[0021] S44, The time-varying variable that remains at zero is controlled by the control method. and open-loop signal As marginal conditions for the motion parameters of the robotic arm system, a precise predefined path is generated. Among them, Represents sliding gain and , It is a symbolic function.

[0022] Furthermore, in S7, when combining the hybrid proportional-integral sliding mode controller with a predefined path to generate a robotic arm path plan, the robotic arm path plan further includes using the angular velocity generated by the hybrid proportional-integral sliding mode controller. With joint vector Combined, a path plan for the robotic arm is generated.

[0023] Secondly, a robotic arm path planning system based on hybrid proportional-integral sliding mode control includes:

[0024] The three-bar linkage robotic arm module is used to establish connections between three links and three rotary joints;

[0025] The three-bar linkage robotic arm end effector module is used to generate a predefined path from the initial state to the target state;

[0026] The Proportional-Integral Sliding Mode Controller (PI-SMC) module is used to connect the Proportional-Integral Controller (PI) and the Sliding Mode Controller (SMC).

[0027] Hybrid proportional-integral sliding mode controller module, used to connect proportional-integral sliding mode controller (PI-SMC) to three-bar linkage mechanism;

[0028] The robotic arm path planning module is used to connect the hybrid proportional integral sliding mode controller with the predefined path.

[0029] Furthermore, the three-bar linkage robotic arm end effector module also includes a component for the initial state being... The target state is Introducing a new situation variable ( , ), and the initial state time and target state time We obtain the following using the third derivative:

[0030] , ,

[0031] Establish initial state With the target state The connection.

[0032] Furthermore, the three-bar linkage robotic arm end effector module also includes a mechanism for obtaining coefficients from a seventh-order polynomial. , the coefficient The normalized time λ is expressed by the equation: ,in express The normalized time, i=1,2,3…, establishes a seventh-order polynomial path.

[0033] The further proportional-integral sliding mode controller (PI-SMC) module also includes a method for processing the initial state in the predefined path. Corresponding initial position The input is fed into the proportional-integral controller (PI), through the equation: , and obtain the data u(t);

[0034] The data u(t) is input into the sliding mode controller SMC, and the time-varying S(t) is obtained by reducing all trajectories along the sliding surface.

[0035] The time-varying S(t) is passed through a Lyapunov function: This keeps the time-varying S(t) at zero;

[0036] The time-varying variable, kept at zero, is controlled by a control method. and open-loop signal As marginal conditions for the motion parameters of the robotic arm system, a precise predefined path is established. Among these, Represents sliding gain and , It is a symbolic function.

[0037] Furthermore, the robotic arm path planning module also includes,

[0038] Used for generating angular velocities in a hybrid proportional-integral sliding mode controller. With joint vector Combined, a path planning mechanism for the robotic arm is established.

[0039] Beneficial effects: A robotic arm path planning method based on hybrid proportional-integral sliding mode control improves and adjusts the point-to-point path planning of the robot's three-bar linkage to achieve smoother movements, reduced jitter, and increased accuracy of the robot's arm in unstructured scenarios. Attached Figure Description

[0040] Figure 1 The flowchart shows a path planning method for a robotic arm based on hybrid proportional-integral sliding mode control.

[0041] Figure 2 A block diagram of a robotic arm path planning system based on hybrid proportional-integral sliding mode control;

[0042] Figure 3 This is a schematic diagram of the robotic arm path planning method and system using hybrid proportional-integral sliding mode control in an embodiment of the present invention. Detailed Implementation

[0043] The following will provide a more detailed description of the technical solution of the robotic arm path planning method and system based on hybrid proportional-integral sliding mode control, which is based on the present invention, with reference to the embodiments.

[0044] By providing a path planning method and system for robotic arms based on hybrid proportional-integral sliding mode control, the problems of low smoothness, large jitter, and low accuracy of robotic arm movements in the prior art are solved, enabling the robotic arm to accurately repeat the same movements even in unstructured scenarios.

[0045] See Figure 1 The first aspect is a path planning method for a robotic arm based on hybrid proportional-integral sliding mode control, comprising:

[0046] S1. The robotic arm has three links, which are connected by three rotating joints to form a three-link robotic arm.

[0047] S2. The lengths L1, L2, L3 of the three links of the three-bar linkage robot arm and the corresponding joint angles q1, q2, q3 are expressed by the forward kinematics equations of the three-bar linkage robot arm:

[0048]

[0049] Obtain the coordinates of the end effector of the three-bar linkage robotic arm in the Cartesian coordinate system. , ), where L1, L2, and L3 are the lengths of the first, second, and third links in the robotic arm, respectively, and q1, q2, and q3 are the joint angles of the first, second, and third links in the robotic arm, respectively.

[0050] S3, Based on the coordinates of the end effector of the three-bar linkage robot ( , Set an initial time. initial state And a final time target state ,in It is the initial position of the last connecting link in the Cartesian coordinate system. It is the final position of the last connecting link in the Cartesian coordinate system. Joint vector (radians, rad); Angular velocity (rad / s); It is angular acceleration (rad / s²) 2 ), introducing a new situation variable ( , ), and the initial state time and target state time We obtain the following using the third derivative:

[0051] , ,

[0052] Establish initial state With the target state The connection generates a predefined path for the end effector of the three-bar linkage robotic arm.

[0053] Through a seventh-order polynomial:

[0054]

[0055] Obtain the coefficient , the coefficient The normalized time λ is expressed by the equation: ,in express The normalized time, i=1,2,3…, yields a seventh-order polynomial path, which solves the numerical interpolation problem of the predefined path.

[0056] See Figure 3 A path planning method and system diagram for a robotic arm based on hybrid proportional-integral sliding mode control.

[0057] S4. The derivative coefficient in PID unit control based on the PID controller is incompatible with certain operations, and this coefficient introduces noise in the control operation. Therefore, a proportional-integral (PI) controller is used to replace the PID controller. The PI controller algorithm includes two parameters: proportional value and integral value. The proportional and integral values ​​are based on the analysis of the current error e(t), the integration of past errors, and the prediction of future errors, and are applied to the initial state in the predefined path. Corresponding initial position The input is fed into the proportional-integral controller (PI), through the equation: ,

[0058] We obtain the data u(t), where It is proportional gain. It is integral gain. It is an error, the output of the controller Input into the sliding mode controller (SMC), first specify the time-varying parameters. The sliding surface, through the equation: Time-varying ,in Positive steady-state constant, which will be the time-varying constant. Through Lyapunov functions: To keep the time-varying S(t) at zero, the time-varying value kept at zero is controlled by a control method.

[0059] and open-loop signal As marginal conditions for the motion parameters of the robotic arm system, a proportional-integral sliding mode controller (PI-SMC) is generated. Represents sliding gain and , It is a symbolic function.

[0060] S5. Connect the proportional-integral sliding mode controller (PI-SMC) to the three-bar linkage robotic arm to generate a hybrid proportional-integral sliding mode controller.

[0061] S6. Output a new angular velocity via a hybrid proportional-integral sliding mode controller. angular acceleration The initial position and target position are used to obtain the path planning for the robotic arm.

[0062] Secondly, a robotic arm path planning system based on hybrid proportional-integral sliding mode control includes:

[0063] The three-bar linkage robotic arm module is used to establish connections between three links and three rotary joints;

[0064] The three-bar linkage robotic arm end effector module is used to generate a predefined path from the initial state to the target state;

[0065] The Proportional-Integral Sliding Mode Controller (PI-SMC) module is used to connect the Proportional-Integral Controller (PI) and the Sliding Mode Controller (SMC).

[0066] Hybrid proportional-integral sliding mode controller module, used to connect proportional-integral sliding mode controller (PI-SMC) to three-bar linkage mechanism;

[0067] The robotic arm path planning module is used to connect the hybrid proportional integral sliding mode controller with the predefined path.

[0068] Furthermore, the three-bar linkage robotic arm end effector module also includes a component for the initial state being... The target state is Introduce a new situation variable ( , ), and the initial state time and target state time We obtain the following using the third derivative:

[0069] Establish initial state With the target state The connection.

[0070] Furthermore, the three-bar linkage robotic arm end effector module also includes a mechanism for obtaining coefficients from a seventh-order polynomial. , the coefficient The normalized time λ is expressed by the equation: ,in express The normalized time, i=1,2,3…, establishes a seventh-order polynomial path.

[0071] The further proportional-integral sliding mode controller (PI-SMC) module also includes a method for processing the initial state in the predefined path. Corresponding initial position The input is fed into the proportional-integral controller (PI), through the equation: , and obtain the data u(t);

[0072] The data u(t) is input into the sliding mode controller SMC, and the time-varying S(t) is obtained by reducing it along all trajectories of the sliding surface.

[0073] The time-varying S(t) is passed through a Lyapunov function: This keeps the time-varying S(t) at zero;

[0074] The time-varying variable, kept at zero, is controlled by a control method. and open-loop signal As marginal conditions for the motion parameters of the robotic arm system, a precise predefined path is generated. Among them, Represents sliding gain and It is a symbolic function.

[0075] Furthermore, the robotic arm path planning module also includes a mechanism for generating angular velocities using a hybrid proportional-integral sliding mode controller. With joint vector Combined, a path planning mechanism for the robotic arm is established.

[0076] Beneficial effects: A robotic arm path planning method based on hybrid proportional-integral sliding mode control improves and adjusts the point-to-point path planning of the robot's three-bar linkage to achieve smoother movements, reduced jitter, and increased accuracy of the robot's arm in unstructured scenarios.

Claims

1. A path planning method for a robotic arm based on hybrid proportional-integral sliding mode control, characterized in that, include, S1. The robotic arm has three links, which are connected by three rotary joints to form a three-link robotic arm. S2. The lengths of the three links of the three-bar linkage and the corresponding joint angles are used to obtain the coordinates of the end effector of the three-bar linkage in the Cartesian coordinate system by applying the forward kinematics equation of the three-bar linkage. S3. Based on the coordinates of the end effector of the three-bar linkage robot, set an initial state and a target state, connect the initial state and the target state to generate a predefined path for the end effector of the three-bar linkage robot, and obtain the coefficients using a seventh-order polynomial. , the coefficient With normalized time Through the equation: ,in express The normalized time, i=1,2,3…, yields the seventh-order polynomial path; S4. Based on the noise caused by the PID controller in the control operation, a proportional-integral controller PI is set up, and the proportional-integral controller PI is combined with the sliding mode controller SMC to obtain a proportional-integral sliding mode controller PI-SMC. The initial position corresponding to the initial state in the predefined path is input into the proportional-integral controller (PI), through the equation: , obtain data ; in, It is proportional gain. It is integral gain. It is an error; The data The input is fed into the sliding mode controller (SMC), and the time-varying parameters are obtained by reducing the input along all trajectories of the sliding surface. ; The time-varying Through Lyapunov functions: , making time change Keep it at zero; The time-varying variable, kept at zero, is controlled by a control method. And the open-loop signal serves as the marginal condition for the motion parameters of the robotic arm system, generating a precise predefined path, wherein, Represents sliding gain and , It is a symbolic function; S5. Connect the proportional-integral sliding mode controller PI-SMC to the three-bar linkage robotic arm to generate a hybrid proportional-integral sliding mode controller. S6. Combine the hybrid proportional-integral sliding mode controller with a predefined path to generate a robotic arm path plan, and use the angular velocity generated by the hybrid proportional-integral sliding mode controller... With joint vector Combined, a path plan for the robotic arm is generated.

2. A robotic arm path planning system based on hybrid proportional-integral sliding mode control, characterized in that, include, The three-bar linkage robotic arm module is used to establish connections between three links and three rotary joints; The three-bar linkage robotic arm end effector module is used to generate a predefined path from the initial state to the target state, and to obtain the coefficients of a seventh-order polynomial. , the coefficient With normalized time Through the equation: ,in express Normalized time, i=1,2,3…, establish a seventh-order polynomial path; The Proportional-Integral Sliding Mode Controller (PI-SMC) module connects the Proportional-Integral Controller (PI) and the Sliding Mode Controller (SMC). It inputs the initial position corresponding to the initial state in the predefined path into the Proportional-Integral Controller (PI) via the equation: , Obtain data ;in, It is proportional gain. It is integral gain. It is an error; The data The input is fed into the sliding mode controller (SMC), and the time-varying parameters are obtained by reducing the input along all trajectories of the sliding surface. ; The time-varying Through Lyapunov functions: , making time change Keep it at zero; The time-varying variable, kept at zero, is controlled by a control method. and open-loop signal As a marginal condition for the motion parameters of the robotic arm system, a precise predefined path is established; among which, Represents sliding gain and , It is a symbolic function; Hybrid proportional-integral sliding mode controller module, used to connect proportional-integral sliding mode controller (PI-SMC) to three-bar linkage mechanism; The robotic arm path planning module connects the hybrid proportional-integral sliding mode controller (HIMSC) to a predefined path, and is used by the HIMSC to generate angular velocities. With joint vector Combined, a path planning mechanism for the robotic arm is established.

Images