A redundant robot arm motion planning method based on wave transmission artificial potential field

Abstract

This invention discloses a motion planning method for a redundant robotic arm based on a wave-transmitted artificial potential field. First, a repulsive potential field is established based on the obstacle environment. Then, a wave-transmitted attractive potential field is established based on the target configuration of the redundant robotic arm. Finally, the repulsive and attractive potential fields work together to form a wave-transmitted artificial potential field, which guides the robotic arm to the target position, thus realizing the motion planning of the redundant robotic arm. This application, by constructing a wave-transmitted attractive potential field to achieve motion planning for the redundant robotic arm, can effectively suppress the occurrence of local minima in traditional artificial potential field methods, improving computational efficiency while reducing the probability of local minima.

Description

Technical Field

[0001] This invention relates to the field of motion planning technology. Specifically, it is a method for motion planning of a redundant robotic arm based on a wave-transmitted artificial potential field. Background Technology

[0002] Redundant degrees of freedom robotic arms are characterized by high motion flexibility and strong environmental adaptability, and are widely used in scenarios such as operation in confined spaces, human-robot collaboration, and unstructured environment work. While redundancy brings high flexibility, it also increases the complexity of robotic arm motion planning. Especially in complex obstacle environments, the real-time requirements for motion planning methods are even higher. Robotic arm motion planning methods can be broadly divided into global planning methods and local planning methods.

[0003] Global planning methods mainly fall into two categories: sampling-based algorithms, such as fast-exploration random trees and probabilistic route maps; and intelligent optimization-based algorithms, such as particle swarm optimization and genetic algorithms. Global planning algorithms search for paths in joint space according to a predetermined strategy, theoretically guaranteeing probabilistic completeness. However, their computational cost increases rapidly with the degrees of freedom and environmental complexity, making it difficult to meet real-time requirements. In contrast, local planning methods, represented by artificial potential field planning, have advantages such as simple computational structure and good real-time performance, and are widely used in online obstacle avoidance and local planning. The artificial potential field method constructs an attractive potential field for the target and a repulsive potential field for the obstacle, transforming the motion planning problem into a gradient descent process guided by the potential field. It has a clear physical model and mathematical relationships, and its computational speed can meet real-time requirements. However, the artificial potential field method also suffers from the local minimum problem, where the attractive and repulsive potential fields reach equilibrium in a local region, leading to motion stagnation.

[0004] With the widespread application of redundant robotic arms across various industries, the real-time requirements for robotic arm motion planning are becoming increasingly stringent, especially in complex scenarios requiring rapid response, such as harvesting operations and dynamic environment operations. The artificial potential field method, characterized by high computational efficiency and good real-time performance, is widely used in online obstacle avoidance. However, the local minimum problem is a key constraint on its planning efficiency. Existing methods update the virtual target position and recalculate the robot's next position when the robot gets stuck in a local minimum, thus incentivizing the robot to escape the local minimum. While this method can solve the local minimum problem to some extent, its passive escape process is computationally intensive and time-consuming, making it difficult to guarantee the efficiency of robotic arm motion planning. Therefore, there is an urgent need for a motion planning method that can solve the local minimum problem while ensuring planning efficiency. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to provide a redundant robotic arm motion planning method based on a wave-transfer artificial potential field. By combining a repulsive potential field and a wave-transfer attractive potential field to form a wave-transfer artificial potential field, the robotic arm is guided to move to the target position through the wave-transfer artificial potential field while avoiding obstacles. This method can improve computational efficiency while reducing the probability of local minima.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] A redundant robotic arm motion planning method based on a wave-transmitted artificial potential field includes the following steps:

[0008] Step P1: Establish a repulsive potential field based on the obstacle environment;

[0009] Step P2: Establish the wave propagation attractive potential field based on the target configuration of the redundant robotic arm;

[0010] The repulsive potential field in step P3 and step P1, together with the wave-transfer attraction potential field in step P2, work together to form a wave-transfer artificial potential field. This artificial potential field guides the robotic arm to move to the target position, thus realizing the motion planning of the redundant robotic arm.

[0011] In the aforementioned redundant robotic arm motion planning method based on a wave-transmitted artificial potential field, step P1 involves establishing a repulsive potential field on the surface of each obstacle. When the distance between the robotic arm and the obstacle is outside a preset range, the repulsive force is zero. When the distance between the robotic arm and the obstacle is within the preset range, the repulsive force increases as the distance between the robotic arm and the obstacle decreases. The repulsive potential field U... rep and repulsive force F rep The expression is:

[0012]

[0013] Where η represents the repulsive potential field influence factor, ρ min ρ represents the minimum distance between the robotic arm and the obstacle. c V represents the switching distance of the repulsive potential field. dir It indicates the direction of the repulsive force.

[0014] The aforementioned method for planning the motion of a redundant robotic arm based on a wave-transmitted artificial potential field requires repulsive force calculation and collision detection for each step of the planning process; wherein, the repulsive force calculation is performed by ρ min Substituting into expression (1) for calculation, collision detection is performed using ρ min The size is used to determine;

[0015] When ρ min When ρ ≤ safety threshold, a collision is determined to have occurred in the robotic arm; when ρmin When the safety threshold is reached, it is determined that the robotic arm has not collided.

[0016] In the above-mentioned redundant robotic arm motion planning method based on wave-transmitted artificial potential field, in step P1, a capsule is used to enclose the robotic arm and obstacles, and the distance between the robotic arm and the obstacles is transformed into the distance between the geometric envelope, thereby simplifying the calculation process of repulsive force and collision detection.

[0017] The above-mentioned redundant robotic arm motion planning method based on wave-transfer artificial potential field includes the following steps in step P2:

[0018] Step P2-1: Determine the location of the subpotential field;

[0019] Step P2-2: Classify all sub-potential fields according to their different positions, and divide all sub-potential fields into joint sub-potential fields and link sub-potential fields;

[0020] Steps P2-3 involve sorting all sub-potential fields and constructing a wave-transfer attraction potential field from the root to the end of the robotic arm. The expression for the wave-transfer attraction potential field is:

[0021]

[0022] Among them, F att Indicating attraction, o i Let ξ represent the origin of the i-th subpotential field. i ξ represents the weighting factor of the i-th subpotential. n ξ represents the weighting factor of the terminal subpotential field. j s represents the weighting factor of the joint subpotential field adjacent to the end. i S represents the position of the i-th reference point. n S indicates the position of the end reference point. j Indicates the position of the joint reference point adjacent to the end reference point, d e o represents the critical distance for activation of the subpotential field. n The potential field at the end of the robotic arm is represented by ε, which represents the maximum permissible error. j This represents the potential field of the joint adjacent to the end.

[0023] In the aforementioned redundant robotic arm motion planning method based on wave-transmitted artificial potential fields, the specific process for determining the position of the sub-potential field in step P2-1 is as follows:

[0024] First, select multiple reference points S1-S on the robotic arm. nAs a reference point for setting the sub-potential field and the point of application of the attraction force, the reference point includes joint reference points on the origin of each link coordinate system and link reference points selected on the links of the robotic arm. The distance between adjacent reference points is determined according to the size of the obstacle. The sub-potential field is set on the reference points of the robotic arm in the target configuration state.

[0025] The specific process of steps P2-3 in the above-mentioned redundant robotic arm motion planning method based on wave-transmitted artificial potential field is as follows:

[0026] All sub-potential fields are activated sequentially from the root of the robotic arm in order, attracting the reference point on the robotic arm corresponding to the activated sub-potential field. Only one sub-potential field is activated at a time. When the reference point moves to a distance less than a set value from the origin of the current sub-potential field, the current sub-potential field stops working and the next sub-potential field is activated. This process continues until the sub-potential field at the end of the robotic arm is activated.

[0027] While the current subpotential field attracts the corresponding reference point to move, the remaining joints between the reference point and the end of the robotic arm are adaptively adjusted so that the direction of the end of the robotic arm remains the same as the initial direction.

[0028] When the sub-potential field at the end of the robotic arm is activated, the sub-potential fields of the adjacent joints are activated simultaneously. Under the combined action of the end-effector sub-potential field and the adjacent joint sub-potential fields, the pose of the robotic arm is adjusted, ensuring that the end of the robotic arm moves smoothly to the target position.

[0029] The above-mentioned redundant robotic arm motion planning method based on wave-transfer artificial potential field, in step P3, the specific process of redundant robotic arm motion planning using the wave-transfer artificial potential field includes the following steps:

[0030] Step P3-1: All links of the robotic arm will be subjected to an attractive force F. att and repulsive force F rep The effect is that, according to the law of translation of force, the attractive and repulsive forces on the connecting rod are equivalent to the force-torque vector at the origin of the connecting rod coordinate system;

[0031] Step P3-2: Convert the force-torque vectors on all links into joint torque vectors using the Jacobi matrix, and add all joint torque vectors to obtain the overall joint torque vector of the robotic arm;

[0032] If we consider the joints of the robotic arm as dampers, the ratio of joint torque to damping is the angular velocity of the joint. The joint torque is the total joint torque vector obtained by adding all the joint torque vectors mentioned above. Therefore, the formulas for calculating joint torque and joint angular velocity are as follows:

[0033] (3);

[0034] Where τ represents the n-dimensional joint torque vector, n represents the total degrees of freedom of the robotic arm, and J i J represents the Jacobian matrix of the i-th link's coordinate system relative to the base coordinate system. i It is a 6×n matrix, where columns i+1 to n are 0; and These represent the attractive and repulsive forces acting on the i-th link, respectively. denoted by angular velocity, and B represents joint damping.

[0035] Step P3-4: Each joint of the robotic arm rotates according to the calculated angular velocity. Based on the position of the robotic arm, the steps P3-1 to P3-3 are iteratively repeated until the robotic arm reaches the target position, thus realizing the motion planning of the redundant robotic arm.

[0036] The aforementioned redundant robotic arm motion planning method based on a wave-transmitted artificial potential field further includes:

[0037] Step P4: Design and conduct simulation experiments to verify the efficiency and stability of redundant robotic arm motion planning achieved by transmitting an artificial potential field through waves.

[0038] The above-mentioned redundant robotic arm motion planning method based on wave-transmitted artificial potential field includes the following steps in step P4 of the simulation experiment:

[0039] Step P4-1: Using a redundant robotic arm to pick fruit as a simulation experiment scenario, three obstacle environments are set up, including low-density environment, medium-density environment and high-density environment. The number of obstacles in the low-density environment is <5, the number of obstacles in the medium-density environment is 5 to 15, and the number of obstacles in the high-density environment is >15.

[0040] Step P4-2: Complete the writing of the motion planning program for the artificial potential field of wave propagation in MATLAB, and add the digital model of the redundant robotic arm and the obstacle environment to the motion planning program;

[0041] Step P4-3: Conduct 100 motion planning simulation experiments in three obstacle environments respectively. At the same time, use the Bi-RRT planning algorithm for comparative simulation experiments. Finally, compare and analyze the efficiency and stability of redundant robotic arm motion planning by using wave-transmitted artificial potential field based on the simulation results.

[0042] The technical solution of the present invention achieves the following beneficial technical effects:

[0043] This application addresses the technical problems of traditional artificial potential field methods, such as being prone to getting trapped in local minima and having high computational costs for passive escape, leading to low planning efficiency. It provides a redundant robotic arm motion planning method based on a wave-transfer artificial potential field. First, a repulsive potential field is constructed based on the robotic arm's link capsule envelope model and the obstacle environment. Then, a wave-transfer attractive potential field is constructed using the desired target configuration of the redundant robotic arm as the wave source. Next, the repulsive and wave-transfer attractive potential fields are combined to form a wave-transfer artificial potential field. Finally, the wave-transfer artificial potential field guides the robotic arm to the target position, realizing the motion planning of the redundant robotic arm. This method effectively suppresses the occurrence of local minima in traditional artificial potential field methods, improving computational efficiency while reducing the probability of local minima. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the enveloping and repulsive potential field between the robotic arm and the obstacle in this invention;

[0045] Figure 2 A schematic diagram of an existing structure that gets stuck in a local minimum problem when performing motion planning using an artificial potential field;

[0046] Figure 3 A structural diagram showing the flexion and extension movements of the human arm and its corresponding projection;

[0047] Figure 4 This is a schematic diagram of the wave propagation attractive potential field of the present invention;

[0048] Figure 5 This is a schematic diagram of the structure of the robotic arm motion planning process using the artificial potential field for wave propagation according to the present invention.

[0049] Figure 6 This is a schematic diagram of the structure of the simulation experiment results of motion planning in a low-density obstacle environment according to the present invention;

[0050] Figure 7 This is a schematic diagram of the structure of the simulation experiment results of motion planning in a density obstacle environment in this invention;

[0051] Figure 8 This is a schematic diagram of the structure of the simulation experiment results of motion planning in a high-density obstacle environment according to the present invention;

[0052] Figure 9 This is a schematic diagram of the dispersion analysis of the simulation experimental results of this invention;

[0053] Figure 10 This is a flowchart of a redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to the present invention. Detailed Implementation

[0054] This embodiment discloses a redundant robotic arm motion planning method based on a wave-transmitted artificial potential field, such as... Figure 10As shown, it includes the following steps:

[0055] Step P1: Establish a repulsive potential field based on the obstacle environment and determine the collision detection method between the robotic arm and the obstacle;

[0056] First, a repulsive potential field is set on each obstacle. This field is typically placed on the obstacle surface and exerts a repulsive force on the robotic arm, causing it to move away from the obstacle. When the distance between the robotic arm and the obstacle is outside a preset range (10–50 mm), the repulsive force is zero. When the distance is within the preset range, the repulsive force increases as the distance decreases. The repulsive potential field U... rep and repulsive force F rep The expression is:

[0057]

[0058] Where η represents the repulsive potential field influence factor, ρ min ρ represents the minimum distance between the robotic arm and the obstacle. c V represents the switching distance of the repulsive potential field. dir It indicates the direction of the repulsive force.

[0059] During the planning process, each step of the movement requires repulsive force calculation and collision detection; among them, the repulsive force calculation is performed by ρ min Substituting into expression (1) for calculation, collision detection is performed using ρ min The size is used to determine;

[0060] When ρ min When the distance is ≤ the safety threshold (generally 2-5mm), a collision is considered to have occurred in the robotic arm; when ρ min When the safety threshold is reached, it is determined that the robotic arm has not collided.

[0061] Furthermore, the robotic arm is composed of multiple links connected sequentially via joints. During motion planning, the distance between each link and environmental obstacles needs to be calculated individually. To reduce the complexity of the solution and simplify the calculation, regular geometric shapes are used to envelop the robotic arm links and obstacles, transforming the problem of calculating the actual distance between the robotic arm and obstacles into the problem of calculating the distance between each geometric envelope. By geometrically enveloping the robotic arm and obstacles, the calculation process for repulsive potential field modeling and collision detection can be effectively simplified, reducing computational overhead and improving the overall efficiency of motion planning. Since the robotic arm links are mostly cylindrical or polygonal prism structures, conventional sphere and cube envelopment methods have low fitting accuracy and large redundancy. This application uses capsules to tightly envelop the robotic arm links, with a geometric shape that closely matches the actual shape of the links, more closely resembling the actual spatial volume occupied by the links. This further ensures the accuracy of distance calculation and obstacle avoidance potential field modeling, and simplifies the calculation process of repulsive force and collision detection. Taking a seven-DOF robotic arm and an obstacle as an example, the robotic arm enclosed by a capsule and the obstacle, along with the set repulsive potential field, are shown below. Figure 1 As shown.

[0062] Step P2: Establish the wave propagation attractive potential field based on the target configuration of the redundant robotic arm;

[0063] Traditional artificial potential field methods for motion planning of redundant robotic arms typically employ a composite attractive potential field. This composite attractive potential field consists of multiple sub-attractive potential fields, each exerting an attractive force on a specific point of action on the robotic arm. Each sub-attractive potential field uses a unified expression, and its characteristics are divided into two intervals: when the distance between the robotic arm and the attractive potential field is large, the attractive potential field exhibits a conical potential field that varies linearly with distance; when the distance is small, the attractive potential field exhibits parabolic potential field characteristics that vary with the square of the distance. Attractive potential field U att and attraction F att The expression is:

[0064] ;

[0065] Where ξ represents the attraction potential field influence factor, P goal P represents the location of the attractive potential field. n d represents the position of the point of application of the attractive force on the robotic arm. c This represents the switching distance of the attractive potential field.

[0066] Traditional artificial potential field methods plan motion based on repulsive and attractive forces, which easily leads to local minima. At locations where attractive and repulsive forces cancel each other out, the net force approaches zero, causing the robotic arm to malfunction. For example... Figure 2As shown, the obstacle avoidance motion planning problem for redundant robotic arms is more complex and more prone to local minima. This application addresses the problem of traditional artificial potential field methods easily getting trapped in local minima by proposing a wave-transmitted attracting potential field. This reduces the probability of local minima by adjusting the spatial distribution and interaction sequence of the attractor potential field.

[0067] The construction of the wave-transfer attracting potential field draws inspiration from the movement of the human arm. The human arm possesses excellent continuous movement and autonomous obstacle avoidance capabilities in complex environments, and the robotic arm is highly similar to the human arm in terms of structural configuration and movement patterns. Therefore, by constructing a wave-transfer attracting potential field to enable the robotic arm to achieve human-arm-like movement, the probability of local minima occurring in motion planning can be effectively reduced from a mechanistic perspective.

[0068] During the grasping and moving of objects, the human arm can flexibly avoid surrounding obstacles by adjusting its natural flexion and extension posture. Projecting the movement of the human arm onto a characteristic two-dimensional plane clearly reveals its inherent movement patterns and rules of change. Figure 3 It can be seen that the movement of the human arm can be equivalent to the dynamic migration of a broken line in a plane, and the broken line is accompanied by bending from the root to the end during the movement. The projection characteristics of the flexion and extension movement of the human arm can be further abstracted as a whip-like movement: the bending control command is transmitted from the proximal end of the arm to the end in the form of waves, and finally drives the end of the arm to smoothly reach the desired position.

[0069] Inspired by the continuous transmission motion mechanism, this application incorporates the bending transmission motion mode into the artificial potential field, and establishes a wave transmission attractive potential field that can improve the local minimum problem of the artificial potential field. Specifically, the process of establishing the wave transmission attractive potential field includes the following steps:

[0070] Step P2-1: The wave-transfer attraction potential field consists of multiple sub-potential fields. Generating these sub-potential fields requires determining their locations. Specifically, firstly, multiple reference points S1-Sn are selected on the robotic arm as reference points for setting the sub-potential fields and as points of application of the attraction force. These reference points include joint reference points at the origin of each link's coordinate system and link reference points selected on the robotic arm links. The distance between adjacent reference points is determined based on the size of the obstacle; the distance between adjacent reference points is less than the sum of the minimum diameter of the obstacle and the diameter of the robotic arm link. Because the wave-transfer attraction potential field aims to attract the robotic arm to the target configuration, the sub-potential fields are set at each reference point of the robotic arm within the target configuration. The selection of reference points is as follows: Figure 4 As shown.

[0071] Step P2-2: Classify all subpotential fields according to their different positions, and divide all subpotential fields into joint subpotential fields and link subpotential fields. The purpose of classification is to facilitate subsequent activation of subpotential fields by category.

[0072] Steps P2-3, as follows Figure 4 As shown, all sub-potential fields are sorted to construct a wave-transfer attraction potential field from the root to the end of the robotic arm. The expression for the wave-transfer attraction potential field is:

[0073]

[0074] Among them, F att Indicating attraction, o i Let ξ represent the origin of the i-th subpotential field. i ξ represents the weighting factor of the i-th subpotential. n ξ represents the weighting factor of the terminal subpotential field. j s represents the weighting factor of the joint subpotential field adjacent to the end. i S represents the position of the i-th reference point. n S indicates the position of the end reference point. j The position d of the joint reference point adjacent to the end reference point. e o represents the critical distance for activation of the subpotential field. n The potential field at the end of the robotic arm is represented by ε, which represents the maximum permissible error. j This represents the potential field of the joint adjacent to the end.

[0075] The specific process of constructing the wave-transfer attractive potential field from the root to the end of the robotic arm is as follows:

[0076] All sub-potential fields are activated sequentially from the root of the robotic arm in order, attracting the reference point on the robotic arm corresponding to the activated sub-potential field. Only one sub-potential field is activated at a time. When the reference point moves to a distance of less than a set value (5-10mm) from the origin of the current sub-potential field, the current sub-potential field stops working and the next sub-potential field is activated. This process continues until the sub-potential field at the end of the robotic arm is activated.

[0077] While the current subpotential field attracts the corresponding reference point to move, the remaining joints between the reference point and the end of the robotic arm are adaptively adjusted to keep the direction of the end of the robotic arm the same as the initial direction, reducing the probability of these joints being subjected to repulsive forces, thereby improving the efficiency of the subpotential field in attracting the movement of the robotic arm.

[0078] When the sub-potential field at the end of the robotic arm is activated, the sub-potential fields of the adjacent joints are activated simultaneously. Under the combined action of the end-effector sub-potential field and the adjacent joint sub-potential fields, the pose of the robotic arm is adjusted, ensuring that the end of the robotic arm moves smoothly to the target position.

[0079] The repulsive potential fields in steps P3 and P1, together with the wave-transfer attracting potential field in step P2, work together to form a wave-transfer artificial potential field. This artificial potential field guides the robotic arm to the target position, achieving motion planning for the redundant robotic arm. The wave-transfer attracting potential field and the repulsive potential field on the obstacle together constitute the wave-transfer artificial potential field (WP-APF). The wave-transfer artificial potential field is a three-dimensional potential field, enabling the robotic arm to freely bend and transfer motion in three-dimensional space. When planning the robotic arm's motion, the planning speed is fast and it is less prone to getting trapped in local minima.

[0080] The specific process of using an artificial potential field to perform redundant robotic arm motion planning includes the following steps:

[0081] Step P3-1: All links of the robotic arm will be subjected to an attractive force F. att and repulsive force F rep The effect is that, according to the law of translation of force, the attractive and repulsive forces on the connecting rod are equivalent to a 6×1 force-torque vector at the origin of the connecting rod coordinate system;

[0082] Step P3-2: Convert the force-torque vectors on all links into joint torque vectors using the Jacobi matrix, and add all joint torque vectors to obtain the overall joint torque vector of the robotic arm;

[0083] If we consider the joints of the robotic arm as dampers, the ratio of joint torque to damping is the angular velocity of the joint. The joint torque is the total joint torque vector obtained by adding all the joint torque vectors mentioned above. Therefore, the formulas for calculating joint torque and joint angular velocity are as follows:

[0084] (3);

[0085] Where τ represents the n-dimensional joint torque vector, n represents the total degrees of freedom of the robotic arm, and J i J represents the Jacobian matrix of the i-th link's coordinate system relative to the base coordinate system. i It is a 6×n matrix, where columns i+1 to n are 0; and These represent the attractive and repulsive forces acting on the i-th link, respectively. denoted by angular velocity, and B represents joint damping.

[0086] Step P3-4: Each joint of the robotic arm rotates according to the calculated angular velocity. Based on the position of the robotic arm, the steps P3-1 to P3-3 are iteratively repeated until the robotic arm reaches the target position, thus realizing the motion planning of the redundant robotic arm.

[0087] Taking the motion planning of a seven-degree-of-freedom redundant robotic arm as an example, the process of wave-transmitted artificial potential field motion planning is as follows: Figure 5As shown. First, based on the reference point on the target configuration, set up each sub-potential field of the wave propagation attractive potential field, that is... Figure 5 The diagram shows sub-potential fields O1 to O6. Starting from the root of the robotic arm, each sub-potential field sequentially attracts the corresponding reference points S1 to S6 on the robotic arm. Sub-potential field O2 attracts reference point S2, and the robotic arm moves under the combined action of the attracting and repulsive potential fields. When the distance between the reference point S2 of the robotic arm and the origin of sub-potential field O2 is less than a critical value (5-10 mm), sub-potential field O2 stops attracting, and sub-potential field O3 begins to attract reference point S3, and so on. Finally, when the sub-potential field O6 at the end of the arm is activated, the adjacent joint sub-potential field O4 is activated simultaneously, adjusting the robotic arm to the target configuration.

[0088] Step P4: Design and conduct simulation experiments to verify the efficiency and stability of redundant robotic arm motion planning achieved by transmitting an artificial potential field via waves.

[0089] The specific process of the simulation experiment includes the following steps:

[0090] Step P4-1: Using a 7-DOF redundant robotic arm to harvest fruit as a simulation experiment scenario, three obstacle environments are set up, including low-density environment, medium-density environment and high-density environment. The number of obstacles in the low-density environment is <5, the number of obstacles in the medium-density environment is 5 to 15, and the number of obstacles in the high-density environment is >15.

[0091] Step P4-2: Complete the writing of the motion planning program for the artificial potential field of wave propagation in MATLAB, and add the digital model of the redundant robotic arm and the obstacle environment to the motion planning program;

[0092] Step P4-3: Conduct 100 motion planning simulation experiments in three obstacle environments respectively. Simultaneously, use the Bi-RRT planning algorithm for comparative simulation experiments. Finally, analyze the efficiency and stability of redundant robotic arm motion planning achieved through wave-transmitted artificial potential fields based on the simulation results. Simulation results are as follows: Figures 6 to 9 As shown in the simulation results, in low-density environments, the planning time of the artificial potential field method for wave propagation is reduced to a small extent compared with the traditional method, while in medium- and high-density environments, the average planning time of the artificial potential field method for wave propagation is reduced by more than 75% compared with the traditional method. Furthermore, from... Figure 9 As can be seen, the planning time of the wave propagation artificial potential field method has low dispersion and higher stability and reliability.

[0093] The above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of the claims of this patent application.

Claims

1. A redundant robotic arm motion planning method based on a wave-transmitted artificial potential field, characterized in that, Includes the following steps: Step P1: Establish a repulsive potential field based on the obstacle environment; Step P2: Establish the wave propagation attractive potential field based on the target configuration of the redundant robotic arm; The repulsive potential field in step P3 and step P1, together with the wave-transfer attraction potential field in step P2, work together to form a wave-transfer artificial potential field. This artificial potential field guides the robotic arm to move to the target position, thus realizing the motion planning of the redundant robotic arm.

2. The redundant robotic arm motion planning method based on wave-transmitted artificial potential field according to claim 1, characterized in that, In step P1, a repulsive potential field is established on the surface of each obstacle. When the distance between the robotic arm and the obstacle is outside a preset range, the repulsive force is 0. When the distance between the robotic arm and the obstacle is within the preset range, the repulsive force increases as the distance between the robotic arm and the obstacle decreases, and the repulsive potential field U... rep and repulsive force F rep The expression is: ； Where η represents the repulsive potential field influence factor, ρ min ρ represents the minimum distance between the robotic arm and the obstacle. c V represents the switching distance of the repulsive potential field. dir It indicates the direction of the repulsive force.

3. The redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to claim 2, characterized in that, During the planning process, each step of the movement requires repulsive force calculation and collision detection; among them, the repulsive force calculation is performed by ρ min Substituting into expression (1) for calculation, collision detection is performed using ρ min The size is used to determine; When ρ min When ρ ≤ safety threshold, a collision is determined to have occurred in the robotic arm; when ρ min When the safety threshold is reached, it is determined that the robotic arm has not collided.

4. The redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to claim 3, characterized in that, In step P1, a capsule is used to enclose the robotic arm and the obstacle in shape, transforming the distance between the robotic arm and the obstacle into the distance between the geometric envelope, thereby simplifying the calculation process of repulsion force and collision detection.

5. The redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to claim 4, characterized in that, In step P2, the process of establishing the wave propagation attractive potential field includes the following steps: Step P2-1: Determine the location of the subpotential field; Step P2-2: Classify all sub-potential fields according to their different positions, and divide all sub-potential fields into joint sub-potential fields and link sub-potential fields; Steps P2-3 involve sorting all sub-potential fields and constructing a wave-transfer attraction potential field from the root to the end of the robotic arm. The expression for the wave-transfer attraction potential field is: ； Among them, F att Indicating attraction, o i Let ξ represent the origin of the i-th subpotential field. i ξ represents the weighting factor of the i-th subpotential. n ξ represents the weighting factor of the terminal subpotential field. j s represents the weighting factor of the joint subpotential field adjacent to the end. i S represents the position of the i-th reference point. n S indicates the position of the end reference point. j Indicates the position of the joint reference point adjacent to the end reference point, d e o represents the critical distance for activation of the subpotential field. n The potential field at the end of the robotic arm is represented by ε, which represents the maximum permissible error. j This represents the potential field of the joint adjacent to the end.

6. The redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to claim 5, characterized in that, In step P2-1, the specific process of determining the position of the subpotential field is as follows: First, select multiple reference points S1-S on the robotic arm. n As a reference point for setting the sub-potential field and the point of application of the attraction force, the reference point includes joint reference points on the origin of each link coordinate system and link reference points selected on the links of the robotic arm. The distance between adjacent reference points is determined according to the size of the obstacle. The sub-potential field is set on the reference points of the robotic arm in the target configuration state.

7. The redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to claim 5, characterized in that, The specific process of step P2-3 is as follows: All sub-potential fields are activated sequentially from the root of the robotic arm in order, attracting the reference point on the robotic arm corresponding to the activated sub-potential field. Only one sub-potential field is activated at a time. When the reference point moves to a distance less than a set value from the origin of the current sub-potential field, the current sub-potential field stops working and the next sub-potential field is activated. This process continues until the sub-potential field at the end of the robotic arm is activated. While the current subpotential field attracts the corresponding reference point to move, the remaining joints between the reference point and the end of the robotic arm are adaptively adjusted so that the direction of the end of the robotic arm remains the same as the initial direction. When the sub-potential field at the end of the robotic arm is activated, the sub-potential fields of the adjacent joints are activated simultaneously. Under the combined action of the end-effector sub-potential field and the adjacent joint sub-potential fields, the pose of the robotic arm is adjusted, ensuring that the end of the robotic arm moves smoothly to the target position.

8. The redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to claim 7, characterized in that, In step P3, the specific process of using the artificial potential field for wave propagation to perform redundant robotic arm motion planning includes the following steps: Step P3-1: All links of the robotic arm will be subjected to an attractive force F. att and repulsive force F rep The effect is that, according to the law of translation of force, the attractive and repulsive forces on the connecting rod are equivalent to the force-torque vector at the origin of the connecting rod coordinate system; Step P3-2: Convert the force-torque vectors on all links into joint torque vectors using the Jacobi matrix, and add all joint torque vectors to obtain the overall joint torque vector of the robotic arm; If we consider the joints of the robotic arm as dampers, the ratio of joint torque to damping is the angular velocity of the joint. The joint torque is the total joint torque vector obtained by adding all the joint torque vectors mentioned above. Therefore, the formulas for calculating joint torque and joint angular velocity are as follows: （3）； Where τ represents the n-dimensional joint torque vector, n represents the total degrees of freedom of the robotic arm, and J i J represents the Jacobian matrix of the i-th link's coordinate system relative to the base coordinate system. i It is a 6×n matrix, where columns i+1 to n are 0; and These represent the attractive and repulsive forces acting on the i-th link, respectively. denoted by angular velocity, and B represents joint damping. Step P3-4: Each joint of the robotic arm rotates according to the calculated angular velocity. Based on the position of the robotic arm, the steps P3-1 to P3-3 are iteratively repeated until the robotic arm reaches the target position, thus realizing the motion planning of the redundant robotic arm.

9. A redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to any one of claims 1-8, characterized in that, Also includes: Step P4: Design and conduct simulation experiments to verify the efficiency and stability of redundant robotic arm motion planning achieved by transmitting an artificial potential field through waves.

10. The redundant robotic arm motion planning method based on a wave-transmitted artificial potential field according to claim 9, characterized in that, In step P4, the specific process of the simulation experiment includes the following steps: Step P4-1: Using a redundant robotic arm to pick fruit as a simulation experiment scenario, three obstacle environments are set up, including low-density environment, medium-density environment and high-density environment. The number of obstacles in the low-density environment is <5, the number of obstacles in the medium-density environment is 5 to 15, and the number of obstacles in the high-density environment is >15. Step P4-2: Complete the writing of the motion planning program for the artificial potential field of wave propagation in MATLAB, and add the digital model of the redundant robotic arm and the obstacle environment to the motion planning program; Step P4-3: Conduct 100 motion planning simulation experiments in three obstacle environments respectively. At the same time, use the Bi-RRT planning algorithm for comparative simulation experiments. Finally, compare and analyze the efficiency and stability of redundant robotic arm motion planning by using wave-transmitted artificial potential field based on the simulation results.

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