Mechanical arm path planning method based on improved RRT*- Connect algorithm

Abstract

The invention discloses a mechanical arm path planning method based on an improved RRT *-Connect algorithm, and the method comprises the steps: firstly employing a target sampling bias strategy, and improving the sampling efficiency and convergence speed; then, a dynamic target point selection strategy is adopted, and the convergence speed between the two trees is increased; an improved artificial potential field method is adopted to solve a local optimum problem and a target unreachable problem; and finally, through path pruning and path smoothing processing, redundant points are removed, the path length is reduced, and the path smoothness is increased. According to the method, the search efficiency is improved, the calculation cost is reduced, the overall convergence time is shortened, the global exploration capability is enhanced, the local minimum problem and the target unreachable problem are solved, the path length is reduced, the path smoothness is improved, and the method has remarkable advantages in the aspects of planning time, path length and stability; good path planning efficiency is shown, and the method is suitable for actual operation and operation of the mechanical arm.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to a robotic arm path planning method based on an improved RRT*-Connect algorithm. Background Technology

[0002] With the rapid development of automation technology, robotic arms have been widely applied in various industries, such as metal processing, medical procedures, and space exploration. Path planning is the most crucial aspect of robotic arm operations, aiming to find a collision-free path from a specified starting point to a specified ending point within a space containing obstacles. Continuously finding and optimizing this path through algorithms to enable the robotic arm to complete tasks more efficiently is currently a hot research topic.

[0003] Scholars have conducted extensive research on the hot topic of path planning. Path planning algorithms can be divided into traditional algorithms and sampling-based algorithms. Traditional algorithms include the A* algorithm, the artificial potential field method, and Dijkstra's algorithm. Sampling-based algorithms include the Probabilistic Roadmap (PRM) algorithm and the Rapid-exploration Random Tree (RRT) algorithm.

[0004] The A* algorithm can find the optimal solution, but in high-dimensional environments, it generates too many nodes, leading to low computational efficiency. While the artificial potential field method is simple to implement, it is prone to getting trapped in local minima. Dijkstra's algorithm has a large search range, resulting in low convergence efficiency.

[0005] Sampling-based algorithms can effectively reduce computation and time in high-dimensional spaces, and the RRT algorithm is even more efficient in high-dimensional spaces and environments with obstacles, thus it has been widely used in robotic arm path planning problems. However, the RRT algorithm suffers from slow convergence, excessive path redundancy, and suboptimal planned paths due to its overly random sampling. To address these issues, many researchers have improved the RRT algorithm. KRRAMAN et al. proposed the RRT* algorithm, which adds parent node reselection and rewiring strategies to the RRT algorithm, making the path asymptotically optimal, but it has a long search time and consumes a lot of memory. Gammell et al. proposed the Informed RRT* algorithm, which uses heuristic information to focus the search on relevant regions in the configuration space, thereby reducing exploration time and improving the efficiency of finding the optimal path, but it suffers from high computational cost, strong parameter sensitivity, and slow convergence. Building upon this, Yin Xiong et al. proposed the GI-RRT* algorithm, introducing an adaptive sampling function and employing a direct sampling method based on elliptic subsets to optimize path generation, reducing path length and computation time. However, path quality and efficiency are significantly affected by random sample distribution, potentially leading to insufficient local search. Jia Haoduo et al. combined the Informed RRT* algorithm with the artificial potential field method, limiting the randomness of path direction, adjusting the step size based on potential field information to increase convergence efficiency, and proposing a position function to guide iteration point generation, thus optimizing iteration efficiency. However, this approach suffers from high computational complexity and overhead. Qi et al. proposed an improved algorithm based on RRT*FN, employing a heuristic sampling method to prioritize deleting leaf nodes outside the ellipsoid, addressing the node deletion problem. It then uses a greedy bisection method for node expansion and triangular inequality path optimization to obtain a better search path and faster search speed. However, this approach suffers from path non-optimality, low node utilization, and insufficient environmental adaptability. To address the slow convergence speed of the RRT* algorithm, Zhang Yanjun et al. proposed the KNN-RRT* algorithm. This algorithm introduces the AdaGrad method to dynamically adjust the expansion step size based on the gravity function and uses KDTree to store nodes, reducing the risk of getting trapped in local minima and improving algorithm efficiency. However, it suffers from insufficient real-time performance and path quality being significantly affected by parameters. Wu Fei et al., building upon the APF and RRT* algorithm, introduced the DP algorithm and improved the gravity function, employing an adaptive step size adjustment strategy. This improved path planning efficiency and reduced path planning cost, but it also suffers from insufficient real-time performance and limited applicability. Summary of the Invention

[0006] The purpose of this invention is to provide a robotic arm path planning method and approach that features high search efficiency, low computational cost, fast convergence speed, short path length, high path smoothness, strong environmental adaptability, and high practical application value.

[0007] The technical solution to achieve the purpose of this invention is: a robotic arm path planning method based on the improved RRT*-Connect algorithm, comprising the following steps:

[0008] Step 1: Obtain relevant parameters and predicted parameters of the area to be detected, and determine the starting position and target position of the robotic arm;

[0009] Step 2: Based on the relative positions of the target point and the starting point in the current space, guide the process to obtain a random target point;

[0010] Step 3: Use the target bias strategy to select sampling points, enhance the guidance of sampling, and optimize the convergence speed of the path;

[0011] Step 4: Employ a dynamic target point selection strategy to accelerate the convergence speed between the two trees;

[0012] Step 5: Obtain new nodes using the improved artificial potential field method;

[0013] Step 6: Determine if the target point has been reached. If yes, proceed to Step 7; otherwise, return to Step 2.

[0014] Step 7: Remove redundant points and reduce path length through path pruning;

[0015] Step 8: Smooth the path using a cubic B-spline curve.

[0016] Furthermore, the acquisition of relevant parameters and predicted parameters of the area to be detected in step 1, and the determination of the starting position and target position of the robotic arm, are as follows:

[0017] First, obtain the relevant parameters and prediction parameters of the area to be detected. Based on the pre-set reference information of the area, obtain the initial extension target point of the robotic arm. Then, based on the position of the target point, determine the starting position and target position of the robotic arm.

[0018] Furthermore, the target position information of the robotic arm mentioned in step 1 includes obstacle data, two-dimensional image information, and three-dimensional image information.

[0019] Furthermore, step 2, which involves guiding the user based on the relative positions of the target point and the starting point in the current space to obtain a random target point, is detailed as follows:

[0020] Step 2.1: Find the distance to the random sampling point in tree T. The nearest node Along from arrive Expand forward in a fixed step size in the direction of the node and generate new nodes. ,if Without colliding with obstacles, Add to the tree;

[0021] Step 2.2: After sampling a new node At that time, with this node Define a neighborhood circle centered at the new node, and connect the new node to it. When adding a node, the node within the circle that minimizes the path cost generated when adding the new node to the tree will be selected as the parent node.

[0022] Furthermore, the path cost function described in step 2.2 is:

[0023] (1)

[0024] Represents the current node. Represents the starting point. Represents the most recent node.

[0025] Furthermore, step 3, which uses a target bias strategy to select sampling points, enhances the guidance of sampling and optimizes the convergence speed of the path, is detailed as follows:

[0026] The target sampling bias strategy formula is:

[0027] (2)

[0028] in, Represents the sampling point. Represents the target point; generate a random number rand, and determine the sampling point using the above formula.

[0029] Furthermore, the dynamic target point selection strategy described in step 4 accelerates the convergence speed between the two trees, as detailed below:

[0030] When two trees are close enough to each other, each sampling has a certain probability of selecting the nearest neighbor pair in the two trees as the sampling target point in the other tree:

[0031] (3)

[0032] (4)

[0033] In the formula, i and j represent the index numbers of the two nodes closest to the starting tree and the ending tree in this iteration, respectively. This represents the minimum distance between two trees in this iteration; and Represents two nodes;

[0034] The dynamic target selection strategy is as follows:

[0035] (5)

[0036] (6)

[0037] Equation (5) represents the selection of the initial tree sampling target point, and Equation (6) represents the selection of the target tree sampling target point. Indicates the minimum distance threshold; Represents the target point. This represents the minimum distance between two trees in this iteration; and It represents two nodes.

[0038] Furthermore, the new node obtained in step 5 using the improved artificial potential field method is as follows:

[0039] The improved artificial potential field method is shown below:

[0040] (7)

[0041] (8)

[0042] in, Represents the target point. Represents the current node. and These represent the distance from the obstacle to the current node and the Euclidean distance from the current node to the destination, respectively. Represents the gravitational potential field function. This represents the repulsive potential field function, where the magnitudes of the attractive and repulsive forces are:

[0043] (9)

[0044] (10)

[0045] (11)

[0046] (12)

[0047] In the formula, and These represent the gravitational field coefficient and the repulsive field coefficient, respectively. This represents the range of influence of the repulsive field. This represents the distance between the current node and the obstacle; Represents gravity. Represents repulsive force. This represents the repulsive force exerted by the obstacle on the current point. This represents the repulsive force of the target point on the current point; The vector representing the obstacle and the current point. This represents the vector from the current point to the target point.

[0048] Furthermore, step 7 involves path pruning to remove redundant points and reduce path length, as detailed below:

[0049] Starting from the starting point, check if there are any obstacles between the starting point and the path points. If there are no obstacles, update the parent node of the path point to the starting point and delete the node between the two points. If there are obstacles, keep the current parent node of the target point unchanged and continue to use the parent node to replace the starting point for detection until the target point is reached.

[0050] Furthermore, step 8 involves smoothing the path using a cubic B-spline curve, as detailed below:

[0051] The path planned by the algorithm is smoothed using a cubic B-spline curve. The equation of the Kth-order B-spline curve is:

[0052] (13)

[0053] In the formula, This indicates that the B-spline curve has the following parameters. The coordinates of the location Let k be the basis function, and k represent the k-th degree B-spline. Representing the i-th control point; the recursive formula for the basis function of the k-th B-spline is:

[0054] (14)

[0055] in, Indicates the first Each node value Indicates the first k-th degree B-spline basis functions.

[0056] Compared with the prior art, the present invention has the following significant advantages: (1) The present invention adopts a target bias strategy, which guides the algorithm to expand towards the target point by adjusting the path search direction, thereby reducing unnecessary search areas, improving search efficiency, and reducing computational costs; (2) The present invention adopts a dynamic target point selection strategy, which accelerates the convergence speed between two trees and shortens the overall convergence time, thereby enhancing the global exploration capability; (3) By randomly selecting the sampling target point in each sampling iteration, the algorithm can explore a wider search space and increase the possibility of finding the global optimal path; (4) The improved artificial potential field method solves the local minimum problem and the target unreachability problem and accelerates the search speed; (5) By path pruning and path smoothing, redundant points are removed, the path length is reduced, and the path smoothness is increased; (6) It has significant advantages in planning time, path length, and stability, and demonstrates good path planning efficiency, which is suitable for the actual operation and operation of robotic arms. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the robotic arm path planning method based on the improved RRT*-Connect algorithm of this invention. Detailed Implementation

[0058] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0059] like Figure 1 As shown, the present invention provides a robotic arm path planning method based on an improved RRT*-Connect algorithm, comprising the following steps:

[0060] Step 1: Obtain relevant and predicted parameters of the area to be detected, and determine the starting position and target position of the robotic arm, as follows:

[0061] First, relevant parameters and prediction parameters of the area to be detected are obtained. Based on the pre-set reference information of the area, the initial extension target point of the robotic arm is obtained. Then, based on the position of the target point, the starting position and target position of the robotic arm are determined. The target position information of the robotic arm includes obstacle data, two-dimensional image information, and three-dimensional image information.

[0062] Step 2: Based on the relative positions of the target point and the starting point in the current space, guide the process to obtain a random target point, as follows:

[0063] Step 2.1: Find the distance to the random sampling point in tree T. The nearest node Along from arrive Expand forward in a fixed step size in the direction of the node and generate new nodes. ,if Add it to the tree without it colliding with obstacles;

[0064] Step 2.2: After sampling a new node When a new node is connected to a neighborhood circle centered on that node, a neighborhood circle is defined. When adding a node, the node within the circle that minimizes the path cost generated when adding the new node to the tree will be selected as the parent node.

[0065] The path cost function is as follows:

[0066] (1)

[0067] Represents the current node. Represents the starting point. Represents the most recent node.

[0068] Step 3: Use a target bias strategy to select sampling points, enhance the guidance of sampling, and accelerate the convergence speed of the path, as follows:

[0069] The target sampling bias strategy formula is:

[0070] (2)

[0071] in, Represents the sampling point. Represents the target point; generate a random number rand, and determine the sampling point using the above formula.

[0072] Step 4: Employ a dynamic target point selection strategy to accelerate the convergence speed between the two trees, as detailed below:

[0073] When two trees are close enough to each other, each sampling has a certain probability of selecting the nearest neighbor pair in the two trees as the sampling target point in the other tree:

[0074] (3)

[0075] (4)

[0076] In the formula, i and j represent the index numbers of the two nodes closest to the starting tree and the ending tree in this iteration, respectively. This represents the minimum distance between two trees in this iteration; and Represents two nodes;

[0077] The dynamic target selection strategy is as follows:

[0078] (5)

[0079] (6)

[0080] Equation (5) represents the selection of the initial tree sampling target point, and Equation (6) represents the selection of the target tree sampling target point. Indicates the minimum distance threshold; Represents the target point. This represents the minimum distance between two trees in this iteration; and It represents two nodes.

[0081] Step 5: Obtain new nodes using the improved artificial potential field method, as detailed below:

[0082] The improved artificial potential field method is shown below:

[0083] (7)

[0084] (8)

[0085] in, Represents the target point. Represents the current node. and These represent the distance from the obstacle to the current node and the Euclidean distance from the current node to the destination, respectively. Represents the gravitational potential field function. This represents the repulsive potential field function, where the magnitudes of the attractive and repulsive forces are:

[0086] (9)

[0087] (10)

[0088] (11)

[0089] (12)

[0090] In the formula, and These represent the gravitational field coefficient and the repulsive field coefficient, respectively. This represents the range of influence of the repulsive field. This represents the distance between the current node and the obstacle; Represents gravity. Represents repulsive force. This represents the repulsive force exerted by the obstacle on the current point. This represents the repulsive force of the target point on the current point; The vector representing the obstacle and the current point. This represents the vector from the current point to the target point.

[0091] Step 6: Determine if the target point has been reached. If yes, proceed to Step 7; otherwise, return to Step 2.

[0092] Step 7: Remove redundant points and reduce path length through path pruning, as follows:

[0093] After the algorithm finds a feasible path, the continuous sampling and connection of nodes can lead to the generation of paths with curves and redundant points. This can result in paths that are too long and not smooth. Path pruning can remove redundant points, reduce path length, and increase path smoothness. The steps are as follows:

[0094] Starting from the starting point, check if there are any obstacles between the starting point and the path points. If there are no obstacles, update the parent node of the path point to the starting point and delete the node between the two points. If there are obstacles, keep the current parent node of the target point unchanged and continue to use the parent node to replace the starting point for detection until the target point is reached.

[0095] Step 8: Smooth the path using a cubic B-spline curve, as follows:

[0096] After pruning the path, the number of turning and bending points is reduced. However, since the path is composed of discrete points, it can lead to abrupt changes in direction, which can cause wear and tear on the robotic arm. Therefore, further smoothing of the path is necessary to generate a smooth curve that meets the robotic arm's motion characteristics. Using B-spline basis functions with respect to the position in space, a smooth interpolation can be performed between control points, generating a continuous and smooth trajectory. The influence of each control point on the curve is calculated and adjusted step-by-step to ensure the robotic arm moves smoothly along the predetermined path, avoiding sharp turns and oscillations. The steps are as follows:

[0097] The path planned by the algorithm is smoothed using a cubic B-spline curve. The equation of the Kth-order B-spline curve is:

[0098] (13)

[0099] In the formula, This indicates that the B-spline curve has the following parameters. The coordinates of the location Let k be the basis function, and k represent the k-th degree B-spline. Representing the i-th control point; the recursive formula for the basis function of the k-th B-spline is:

[0100] (14)

[0101] in, Indicates the first Each node value Indicates the first k-th degree B-spline basis functions.

[0102] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A robotic arm path planning method based on an improved RRT*-Connect algorithm, characterized in that, Includes the following steps: Step 1: Obtain relevant parameters and predicted parameters of the area to be detected, and determine the starting position and target position of the robotic arm; Step 2: Based on the relative positions of the target point and the starting point in the current space, guide the process to obtain a random target point; Step 3: Use the target bias strategy to select sampling points, enhance the guidance of sampling, and optimize the convergence speed of the path; Step 4: Employ a dynamic target point selection strategy to accelerate the convergence speed between the two trees; Step 5: Obtain new nodes using the improved artificial potential field method; Step 6: Determine if the target point has been reached. If yes, proceed to Step 7; otherwise, return to Step 2. Step 7: Remove redundant points and reduce path length through path pruning; Step 8: Smooth the path using a cubic B-spline curve.

2. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 1, characterized in that, Step 1, which involves acquiring relevant and predicted parameters of the area to be detected and determining the starting and target positions of the robotic arm, is detailed below: First, obtain the relevant parameters and prediction parameters of the area to be detected. Based on the pre-set reference information of the area, obtain the initial extension target point of the robotic arm. Then, based on the position of the target point, determine the starting position and target position of the robotic arm.

3. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 2, characterized in that, The target position information of the robotic arm mentioned in step 1 includes obstacle data, two-dimensional image information, and three-dimensional image information.

4. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 1, characterized in that, Step 2, which involves guiding the user based on the relative positions of the target point and the starting point in the current space to obtain a random target point, is detailed below: Step 2.1: Find the distance to the random sampling point in tree T. The nearest node Along from arrive Expand forward in a fixed step size in the direction of the node and generate new nodes. ,if Without colliding with obstacles, Add to the tree; Step 2.2: After sampling a new node At that time, with this node Define a neighborhood circle centered at the new node, and connect the new node to it. When adding a node, the node within the circle that minimizes the path cost generated when adding the new node to the tree will be selected as the parent node.

5. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 4, characterized in that, The path cost function described in step 2.2 is: （1） Represents the current node. Represents the starting point. Represents the most recent node.

6. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 1, characterized in that, Step 3 describes using a target bias strategy to select sampling points, enhancing the guidance of sampling and optimizing the path convergence speed, as follows: The target sampling bias strategy formula is: （2） in, Represents the sampling point. Represents the target point; generate a random number rand, and determine the sampling point using the above formula.

7. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 1, characterized in that, Step 4 describes a dynamic target point selection strategy to accelerate the convergence speed between the two trees, as detailed below: When two trees are close enough to each other, each sampling has a certain probability of selecting the nearest neighbor pair in the two trees as the sampling target point in the other tree: （3） （4） In the formula, i and j represent the index numbers of the two nodes closest to the starting tree and the ending tree in this iteration, respectively. This represents the minimum distance between two trees in this iteration; and Represents two nodes; The dynamic target selection strategy is as follows: （5） （6） Equation (5) represents the selection of the initial tree sampling target point, and Equation (6) represents the selection of the target tree sampling target point. Indicates the minimum distance threshold; Represents the target point. This represents the minimum distance between two trees in this iteration; and It represents two nodes.

8. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 1, characterized in that, Step 5 describes the use of an improved artificial potential field method to obtain new nodes, as detailed below: The improved artificial potential field method is shown below: （7） （8） in, Represents the target point. Represents the current node. and These represent the distance from the obstacle to the current node and the Euclidean distance from the current node to the destination, respectively. Represents the gravitational potential field function. This represents the repulsive potential field function, where the magnitudes of the attractive and repulsive forces are: （9） （10） （11） （12） In the formula, and These represent the gravitational field coefficient and the repulsive field coefficient, respectively. This represents the range of influence of the repulsive field. This represents the distance between the current node and the obstacle; Represents gravity. Represents repulsive force. This represents the repulsive force exerted by the obstacle on the current point. This represents the repulsive force of the target point on the current point; The vector representing the obstacle and the current point. This represents the vector from the current point to the target point.

9. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 1, characterized in that, Step 7 describes the process of removing redundant points and reducing path length through path pruning, as follows: Starting from the starting point, check if there are any obstacles between the starting point and the path points. If there are no obstacles, update the parent node of the path point to the starting point and delete the node between the two points. If there is an obstacle, keep the current parent node of the target point unchanged and continue to use that parent node instead of the starting point for detection until the target point is reached.

10. The robotic arm path planning method based on the improved RRT*-Connect algorithm according to claim 1, characterized in that, Step 8 involves smoothing the path using a cubic B-spline curve, as detailed below: The path planned by the algorithm is smoothed using a cubic B-spline curve. The equation of the Kth-order B-spline curve is: （13） In the formula, This indicates that the B-spline curve has the following parameters. The coordinates of the location Let k be the basis function, and k represent the k-th degree B-spline. Representing the i-th control point; the recursive formula for the basis function of the k-th B-spline is: （14） in, Indicates the first Each node value Indicates the first k-th degree B-spline basis functions.

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