A mechanical arm trajectory tracking method based on improved super-spiral sliding mode control

Abstract

The patent relates to a kind of trajectory tracking control of mechanical arm based on improved super-helix sliding mode control, belongs to the adjacent of mechanical arm trajectory tracking technology.The method comprises the following steps: S1, constructing the dynamics model of mechanical arm according to the related parameters of mechanical arm, DH parameter method and Lagrange method;S2, based on the dynamics system model of mechanical arm, construct super-helix sliding surface;S3, design improved super-helix sliding mode control approach law;S4, use Cartesian interpolation method to carry out trajectory planning of mechanical arm;S5, based on super-helix sliding surface and its approach law, combined with the dynamics model of mechanical arm, determine trajectory tracking control law;S6, build the control model of improved super-helix sliding mode control and mechanical arm combination;S7, select control parameter, carry out trajectory tracking control.The controller proposed in the application can effectively suppress chattering under the premise that the system can reach state stability, has strong robustness to external disturbance, and ensures the trajectory tracking of mechanical arm end effector.

Description

Technical Field

[0001] This invention relates to the field of robotic arm trajectory tracking technology, specifically to a robotic arm trajectory tracking method based on improved super-helical sliding mode control. Background Technology

[0002] The main research content of robotic arm trajectory control is to design appropriate control methods to control the movement of the robotic arm, enabling it to complete tasks according to a predetermined trajectory or path. The main goal of robotic arm trajectory control is to enable the robotic arm to accurately reach the target position from the starting position and execute movements along the predetermined trajectory, ensuring accuracy, smoothness, and dynamic performance during the movement process. In the early stages of robotics technology, due to the simplicity of robotic arm tasks and the relatively limited application scenarios, PID control was widely used because of its simple structure and ease of implementation. PID control can meet the accuracy requirements to a certain extent, but as the complexity of tasks increases, traditional PID control begins to face problems of insufficient accuracy and slow response. Therefore, researchers have begun to explore more advanced control methods.

[0003] Sliding mode control, due to its strong anti-interference capability, good robustness, high reliability, and ability to effectively solve nonlinear problems in systems, has become a widely used control strategy in engineering applications. First-order sliding mode controllers have relatively few design parameters and simple structures, making parameter tuning very convenient. Mature controller design schemes and stability analysis methods are already available, and they are widely used in robotic arm control. However, the discontinuous switching characteristics of sliding mode control can lead to high-frequency chattering in the system. This is because when the system's state trajectory approaches the sliding mode, it cannot accurately move to the equilibrium point along the sliding surface. Its actual motion involves continuously crossing both sides of the sliding surface until finally reaching the equilibrium point, causing the robotic arm system to tremble. To mitigate this chattering phenomenon, a robotic arm trajectory tracking control method based on improved super-helical sliding mode control is proposed to address the aforementioned problem. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] To address the shortcomings of existing technologies, this invention provides a robotic arm trajectory tracking method based on improved super-helical sliding mode control, which solves the problems mentioned in the background art.

[0006] (II) Technical Solution

[0007] To achieve the above objectives, the present invention specifically adopts the following technical solution:

[0008] A robotic arm trajectory tracking control method based on improved active disturbance rejection includes the following steps:

[0009] S1. Construct a dynamic model of the robotic arm based on relevant parameters of the robotic arm, the DH parameter method, and the Lagrange method;

[0010] S2. Based on the dynamic system model of the robotic arm, construct a super-helical sliding surface;

[0011] S3. Design and improve the approach law of super-spiral sliding mode control;

[0012] S4. Use Cartesian interpolation to plan the trajectory of the robotic arm;

[0013] S5. Based on the super-helical sliding surface and its approach law, the trajectory tracking control law is determined by combining the dynamic model of the robotic arm.

[0014] S6. Build an improved control model that combines super-helical sliding mode control with a robotic arm;

[0015] S7. Select control parameters and perform trajectory tracking control.

[0016] Furthermore, in S1, the following constraints are imposed on the multi-degree-of-freedom robotic arm: all mechanical structures of the robotic arm are rigid; frictional forces generated in all mechanical structures are not considered; the configuration of the n-degree-of-freedom robot is determined, a specific DH parameter table is obtained, and a dynamic model is established using the Lagrange method.

[0017]

[0018] in , respectively represent the positively defined moment of inertia, Coriolis centripetal force, and gravitational force. , and These represent the joint angular position, angular velocity, and angular acceleration of the robotic arm, respectively. It controls the input torque.

[0019] Furthermore, in S2, the super-helical sliding surface is constructed as follows:

[0020]

[0021] in, These are the parameters of the sliding surface. It is the error between the expected angle and the actual angle of the robotic arm. It is the error between the expected angular velocity and the actual angular velocity of the robotic arm.

[0022] Furthermore, in S3, the trajectory tracking control method for a robotic arm based on improved superspiral sliding mode control according to claim 1 is characterized in that, in order to reduce chattering in the system, a boundary layer is introduced and defined in the control law, and a sliding mode controller based on the saturation function *sat* is proposed. The improved superspiral sliding mode control reaching law is designed as follows:

[0023]

[0024]

[0025] In the formula, , For the parameters to be designed, The boundary layer thickness is a saturation function that satisfies... .

[0026] Furthermore, in S4, during the Cartesian space trajectory planning of the robotic arm, an interpolation method is used to parameterize the position and attitude changes of the end effector in three-dimensional space from the starting point to the ending point. Then, an inverse kinematics algorithm is used to map each trajectory point of the end effector in Cartesian space to the joint space of the robotic arm, so that the end effector of the robotic arm can move according to the pre-planned trajectory.

[0027] Furthermore, in S5, based on the super-helical sliding surface and its approach law, combined with the robotic arm dynamics model, the trajectory tracking control law is determined as follows:

[0028]

[0029] in, This is the actual angle of the robotic arm. This is the actual angular acceleration of the robotic arm. The desired angular acceleration of the robotic arm, This represents the actual angular velocity of the robotic arm. Let be the desired angular velocity of the robotic arm.

[0030] Furthermore, in S6, an improved super-helical sliding mode controller is built to perform trajectory tracking control on the controlled object, the robotic arm. The input desired trajectory position information is converted into a desired angle signal through inverse kinematics solution. By controlling the improved super-helical sliding mode controller, the robotic arm can better track the input signal and run the desired trajectory.

[0031] (III) Beneficial Effects

[0032] Compared with the prior art, the present invention provides a robotic arm trajectory tracking control method based on improved super-helical sliding mode control, which has the following beneficial effects:

[0033] This invention employs a novel boundary layer superspiral sliding mode algorithm. The difference between this algorithm and traditional sliding mode algorithms lies in the presence of a saturation function. By replacing the sign function Sign(s) in the traditional superspiral algorithm with a saturation function Sat(s), the chattering problem present in traditional sliding mode control is mitigated while achieving more accurate trajectory tracking of the robotic arm. Attached Figure Description

[0034] Figure 1 This is a flowchart of a robotic arm trajectory tracking method based on improved superhelical sliding mode control according to an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of the improved super-helical sliding mode control robotic arm trajectory tracking method of the present invention;

[0036] Figure 3 A comparison diagram of the improved super-spiral sliding mode control surface provided by this invention and the ordinary sliding mode;

[0037] Figure 4 The graph shows a comparison of the improved super-helical sliding mode control and the robotic arm trajectory tracking without control, as provided by this invention.

[0038] Figure 5 This is a graph showing the effect of the improved super-helical sliding mode control provided by this invention on the trajectory tracking of a robotic arm.

[0039] Figure 6 This is a comparison curve of the tracking error of the robotic arm trajectory between the improved super-helical sliding mode control provided by this invention and ordinary sliding mode control; Detailed Implementation

[0040] 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.

[0041] Example

[0042] An embodiment of the present invention proposes a robotic arm trajectory tracking method based on improved superhelical sliding mode control, comprising the following steps:

[0043] S1. Establish the dynamics and kinematics model of the robotic arm;

[0044] The following constraints are imposed on the multi-degree-of-freedom robotic arm: all mechanical structures of the robotic arm are rigid; frictional forces generated in all mechanical structures are not considered; the configuration of the n-degree-of-freedom robot is determined, a specific DH parameter table is obtained, and a dynamic model is established using the Lagrange method.

[0045]

[0046] in , respectively represent the positively defined moment of inertia, Coriolis centripetal force, and gravitational force. , and These represent the joint angular position, angular velocity, and angular acceleration of the robotic arm, respectively. It controls the input torque.

[0047] S2. Based on the dynamic system model of the robotic arm, construct a super-helical sliding surface;

[0048] Take the desired angle of the robotic arm From a practical perspective difference Its derivative is the desired angular velocity of the robotic arm. Compared with actual angular velocity difference The superspiral sliding surface is constructed as follows:

[0049]

[0050] in, These are the parameters of the sliding surface. It is the error between the expected angle and the actual angle of the robotic arm. It is the error between the expected angular velocity and the actual angular velocity of the robotic arm.

[0051] S3. Design and improve the approach law of super-spiral sliding mode control;

[0052] An improved superhelical sliding mode control reaching law is designed by replacing the sign function Sign(s) in the traditional superhelical algorithm with the saturation function Sat(s):

[0053]

[0054]

[0055] By introducing and defining boundary layers in the control law The existence of the sign function Sign(s) was still caused by the slip surface not being able to switch in time, which was optimized by using the saturation function Sat(s). This further weakened the chattering problem and enabled each joint to track the desired trajectory quickly and with high precision.

[0056] S4. Use Cartesian interpolation to plan the trajectory of the robotic arm;

[0057] In the Cartesian space trajectory planning of a robotic arm, the coordinates of the intermediate point, i.e., the interpolation point, can be obtained through an interpolation algorithm. After obtaining the intermediate point, the pose of the robotic arm's end effector at the intermediate point is converted into the corresponding joint angles of each robotic arm. Then, by controlling the joint angles, the end effector of the robotic arm can move according to the pre-planned trajectory.

[0058] Interpolation methods include linear interpolation and circular interpolation. The Cartesian linear interpolation method calculates the pose of each trajectory interpolation point based on the known positions and orientations of the beginning and end points of a straight line.

[0059] Assume a straight line has two points M and N at its beginning and end, and their coordinate orientations relative to the base coordinate system. Let v be the desired velocity along the line, and t be the interpolation time interval. We can calculate the line length L, the distance d within the t interval, and the number of interpolations N as follows:

[0060]

[0061]

[0062]

[0063] The increments of each axis and the coordinate values ​​of each interpolation point for adjacent interpolation points are as follows:

[0064] Increment of adjacent interpolation points:

[0065]

[0066]

[0067]

[0068] Where: i = 0,1,2…N

[0069] Coordinates of the interpolation point:

[0070]

[0071]

[0072]

[0073] In the trajectory planning of a circular arc in Cartesian space, coordinate system transformation must be used for ease of calculation. That is, a new rectangular coordinate system must first be established in the plane where the arc is located. The values ​​of each interpolation point of the arc in the new coordinate system are calculated in the new coordinate system. Finally, the intermediate interpolation points are transformed into Cartesian space through a transformation matrix.

[0074] Three points define an arc. Suppose a robot's end effector starts at position P1(x1,y1,z1), passes through midpoint P2(x2,y2,z2), and finally reaches endpoint P3(x3,y3,z3). If these three points are not collinear, then an arc must exist from the starting point P1 through midpoint P2 to the endpoint P3. The algorithm steps for arc trajectory planning are as follows:

[0075] (1) First, find the center P0(X0,Y0,Z0) and its radius:

[0076] (2) Establish a new spatial coordinate system in the plane containing the arc, and find the mapping relationship between the coordinate system and the base coordinate system.

[0077] (3) Determine the trajectory of the arc and calculate the total angle of the arc.

[0078] (4) Using the trigonometric relationships, find the coordinates of each interpolation point and map them to the base coordinate system.

[0079] S5. Based on the super-helical sliding surface and its approach law, the trajectory tracking control law is determined by combining the dynamic model of the robotic arm.

[0080] Given that the variables controlling the trajectory of the robotic arm are the angular velocities and angular accelerations of its joints, the trajectory tracking control law is determined based on the robotic arm's dynamics model as follows:

[0081]

[0082] in, This is the actual angle of the robotic arm. This is the actual angular acceleration of the robotic arm. The desired angular acceleration of the robotic arm, This represents the actual angular velocity of the robotic arm. Let be the desired angular velocity of the robotic arm.

[0083] S6. Build an improved control model that combines a super-helical sliding mode controller with a robotic arm to achieve trajectory tracking control;

[0084] An improved super-helical sliding mode controller with an improved control law was built to perform trajectory tracking control on the controlled object, a robotic arm. The input position information of the desired trajectory is converted into the desired angle signal through inverse kinematics. By controlling the improved super-helical sliding mode controller, the robotic arm can better track the input signal and run the desired trajectory.

[0085] S7. Select control parameters and perform trajectory tracking control;

[0086] The sliding surface parameters in steps S2 and S3 were determined through engineering experiments. Parameters of the reaching law for superspiral sliding mode control , Boundary layer thickness of saturation function Estimates of key system parameters, etc. , All values ​​are greater than zero. The selection principle is to ensure that the system state point has a relatively fast approach speed when it is far away from the switching surface. It avoids that the approach speed is too slow if it is too small, and that it is too large if it causes violent chattering. By comparing and observing the experimental data, an appropriate value is selected so that the system approaches the switching surface at an appropriate speed.

[0087] satisfy It can be equivalent to a slope with the following characteristics: The diagonal line. The selection of [value] directly affects the system's chattering phenomenon. When [value] is selected, it will directly affect the system's chattering phenomenon. When the slope is smaller, the slope will be steeper, resulting in more noticeable system chattering. Conversely, when When the value is larger, the slope is gentler, and the chattering phenomenon is weaker. To balance accuracy and chattering, an appropriate value needs to be selected based on experimental data. The value is adjusted.

[0088] This invention provides a robotic arm trajectory tracking control method based on improved superhelical sliding mode control. The method includes acquiring the desired trajectory input, transitioning the input signal through a tracking differentiator to obtain the transitioned angular velocity, comparing it with the actual angular velocity signal output by the robotic arm to obtain an error signal, and performing trajectory tracking control of the robotic arm through a superhelical sliding mode controller. The trajectory planning uses Cartesian interpolation.

[0089] This invention improves the super-helical sliding mode controller, enabling trajectory tracking control of a robotic arm even with modeling errors. Compared to ordinary sliding mode control, it reduces system chattering and improves trajectory tracking accuracy.

[0090] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robotic arm trajectory tracking method based on improved superspiral sliding mode control, characterized in that, Includes the following steps: S1. Construct a dynamic model of the robotic arm based on relevant parameters of the robotic arm, the DH parameter method, and the Lagrange method; S2. Based on the dynamic system model of the robotic arm, construct a super-helical sliding surface; S3. Design and improve the approach law of super-spiral sliding mode control; S4. Use Cartesian interpolation to plan the trajectory of the robotic arm; S5. Based on the super-helical sliding surface and its approach law, the trajectory tracking control law is determined by combining the dynamic model of the robotic arm. S6. Build an improved control model that combines super-helical sliding mode control with a robotic arm; S7. Select control parameters and perform trajectory tracking control; To mitigate chattering in the system, a boundary layer is introduced and defined in the control law. A sliding mode controller based on the saturation function *sat* is proposed, and an improved super-spiral sliding mode control reaching law is designed. ; ; In the formula, , For the parameters to be designed, The boundary layer thickness is a saturation function that satisfies... ; Based on the superspiral sliding surface and its reaching law, the trajectory tracking control law is determined by combining the dynamic model of the robotic arm as follows: ; in, This is the actual angular acceleration of the robotic arm. The desired angular acceleration of the robotic arm, This represents the actual angular velocity of the robotic arm. Let be the desired angular velocity of the robotic arm.

2. The robotic arm trajectory tracking method based on improved super-helical sliding mode control according to claim 1, characterized in that, include: In S1, the following constraints are imposed on the multi-degree-of-freedom robotic arm: all mechanical structures of the robotic arm are rigid, and the frictional forces generated in all mechanical structures are not considered. The model of the n-degree-of-freedom robot is determined, the specific DH parameter table is obtained, and the dynamic model is established by the Lagrange method. ; in , respectively represent the positively defined moment of inertia, Coriolis centripetal force, and gravitational force; , and These represent joint angular position, angular velocity, and angular acceleration, respectively. It controls the input torque.

3. The robotic arm trajectory tracking method based on improved super-helical sliding mode control according to claim 1, characterized in that, Based on the dynamic system model of the robotic arm, a super-helical sliding surface is constructed, specifically including: Based on the dynamic system model of the robotic arm, the joint angle tracking error and angular velocity tracking error in the robotic arm tracking control process are determined to generate the joint angle tracking error set and the angular velocity tracking error set; The super-helical sliding surface is constructed based on the joint angle tracking error set and the angular velocity tracking error set, and the sliding surface is as follows: ; in, These are the parameters of the sliding surface. It is the error between the expected angle and the actual angle of the robotic arm. It is the error between the expected angular velocity and the actual angular velocity of the robotic arm.

4. The robotic arm trajectory tracking method based on improved superspiral sliding mode control according to claim 1, characterized in that, In the Cartesian space trajectory planning of a robotic arm, the position and posture changes of the end effector in three-dimensional space from the starting point to the ending point are described parametrically using interpolation. Then, the inverse kinematics algorithm is used to map each trajectory point of the end effector in Cartesian space to the joint space of the robotic arm, so that the end effector of the robotic arm can move according to the pre-planned trajectory.

5. The robotic arm trajectory tracking method based on improved super-helical sliding mode control according to claim 1, characterized in that: An improved super-helical sliding mode controller with an improved control law was built to perform trajectory tracking control on the controlled object, a robotic arm. The input position information of the desired trajectory is converted into the desired angle signal through inverse kinematics. By controlling the improved super-helical sliding mode controller, the robotic arm can better track the input signal and run the desired trajectory.

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