A meta-heuristic method for fast path search and obstacle avoidance of robotic arms

Abstract

The present invention belongs to the field of artificial intelligence, and discloses a meta-heuristic method for rapid search and obstacle avoidance of a robot path, in order to solve the problems of slow convergence and long planning time caused by the random sampling strategy of the existing robot obstacle avoidance algorithm. The present invention integrates the improved Gaussian mixture distribution sampling strategy and the map complexity constraint strategy to implement a hybrid sampling strategy. The present invention reduces the random sampling points in the obstacle-free area and increases the random sampling points in the area close to the obstacle, thereby improving the generation speed and sampling efficiency of the planned path, and the obstacle avoidance search process requires the joint space to be fully controllable, without breaking the physical limits of the joint control position and speed, thereby ensuring the safe operation of the robot arm.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence, and in particular relates to a meta-heuristic method for rapid search and obstacle avoidance of a robot arm path. Background Art

[0002] Traditional robot path obstacle avoidance algorithms use a global area and explore completely random areas. When the target offset point is blocked by an obstacle, random sampling of the global area is still performed, lacking target orientation. This traditional obstacle avoidance search method has the following drawbacks:

[0003] 1. Failure to select the sampling point closest to the target point, performing invalid obstacle avoidance exploration in unnecessary space, and generating invalid obstacle avoidance search directions;

[0004] 2. Traditional obstacle avoidance search uses a fixed step size expansion, which cannot adaptively adjust the search speed and has a slow iterative update speed;

[0005] 3. There is a lack of angle restriction constraint strategy, and the angle between the line connecting the current sampling point and the current point and the line connecting the starting point and the end point is not used to limit the path search, which can easily cause the robot arm to overshoot and exceed the physical limits of the joints.

[0006] Therefore, the target obstacle sampling points are concentrated near the target center, resulting in the best path sampling results and quality. However, when the target obstacle sampling points are located far from the target center, the path sampling results are reduced. Therefore, ensuring that the robot's search direction quickly approaches the target center is crucial to achieving optimal obstacle avoidance efficiency. This requires avoiding ineffective and irrelevant spatial searches and selecting the optimal search direction. It is also necessary to appropriately accelerate the search process and use a variable step-size search method to adjust the obstacle avoidance search speed. Furthermore, the joint space must be fully controllable during the obstacle avoidance search process, and the physical limits of joint control position and speed must not be exceeded to ensure the safe operation of the robot. Summary of the Invention

[0007] This paper provides a meta-heuristic method for rapid path search and obstacle avoidance for robotic arms. This method addresses the slow convergence and long planning times associated with existing random sampling strategies for robotic arm obstacle avoidance. Based on an improved Gaussian mixture distribution sampling strategy, this method applies interval constraints to random tree generation, reducing the number of random points sampled in obstacle-free areas and increasing the number of random points sampled near obstacles, thereby speeding up the generation of planned paths.

[0008] In order to solve the technical problem, the technical solution adopted by the present invention is:

[0009] A meta-heuristic method for rapid path search and obstacle avoidance for a robotic arm, characterized by comprising:

[0010] (1) During the path planning process, the robot arm uses an improved Gaussian mixture distribution sampling strategy to impose interval constraints on the generation of random trees to improve the generation speed of the planned path;

[0011] (2) The robot arm introduces a map complexity evaluation strategy during the sampling process to reduce the time of finding the optimal path point;

[0012] (3) A hybrid sampling strategy is implemented by integrating the improved Gaussian mixture distribution sampling strategy and the map complexity constraint strategy.

[0013] In some embodiments, in the improved Gaussian mixture distribution sampling strategy, the n-dimensional function expression of the Gaussian function is as follows:

[0014]

[0015] σ is the standard deviation of the Gaussian distribution function, representing the distance between the sampling point and the obstacle, and μ is the expected value.

[0016] The probability distribution function of the sampling point in the obstacle area is:

[0017]

[0018] From the above probability distribution function, we can see that the closer to the obstacle, the greater the sampling probability. To avoid collision between the sampling point and the obstacle, the obstacle function obs(x) is set and the probability distribution function is improved. The improved probability distribution function expression is as follows:

[0019] g(x;μ,σ)=max(0,φ(x;μ,σ)-obs(x)); (3)

[0020] Where obs(x) is the obstacle function. When the generated sampling point collides with an obstacle, obs(x) = 1; otherwise, it is 0. If the sampling point falls in the obstacle-free area, g(x; μ, σ) = φ(x; μ, σ); otherwise, g(x; μ, σ) = 0.

[0021] In some embodiments, the robotic arm introduces a map complexity evaluation strategy during the sampling process to reduce the time spent on finding the optimal path point; and at the same time sets a suitable constraint threshold p.

[0022] Among them, the map complexity coefficient C1 is expressed as:

[0023] 0.5 represents the weight ratio, S obc Indicates the obstacle area, S map Indicates the map area, D obc Indicates the distribution of obstacles.

[0024] In some embodiments, the hybrid sampling strategy that integrates the improved Gaussian mixture distribution sampling strategy and the map complexity constraint strategy is specifically implemented as follows:

[0025] (1) Set the constraint threshold p. If the probability of generating a sampling point is less than the constraint threshold p, a point Q is randomly generated. rand1 Add random trees;

[0026] (2) If Q rand1 If a collision occurs with an obstacle, a point Q is regenerated through the improved probability distribution function (i.e., the formula (3) described above) rand2 ; If no collision occurs, return Q rand1 ;

[0027] (3) If Q rand2 If it collides with an obstacle, select Q rand1 and Q rand2 The midpoint Q in space rand3 If no collision occurs, return Q rand2 ;

[0028] (4) If Q rand3 If there is no collision with the obstacle, then Q rand3 is the sampling point of the random tree, otherwise, return to the first step and resample.

[0029] In some embodiments, the robotic arm introduces a sampling constraint strategy during path planning based on a hybrid sampling strategy. The sampling constraint strategy specifically includes:

[0030] The angle θ between the line connecting the previous sampling point and the current point and the line connecting the starting point and the end point is used as the criterion for judging the positive growth of the sampling point; when the angle θ∈[-π / 2,π / 2], it is judged that the random sampling point belongs to positive growth; when the angle θ is not in the range of [-π / 2,π / 2], the random sampling point does not meet the sampling constraint requirements (i.e., it belongs to reverse growth) and should be eliminated.

[0031] In some embodiments, the present invention introduces an adaptive step size strategy during the sampling process to generate a new node Q new , reducing the probability of collision between the new extended node and the obstacle. new Determined by the following formula:

[0032]

[0033] Where ρ1 is Q new The step size coefficient towards the random sampling point, ρ2 is Q new Step coefficient towards the target point. When ρ1>ρ2, the new node Q newGrow towards the random sampling point position and direction; when ρ1<ρ2, the new node Q new Grow towards the target point position and direction.

[0034] Therefore, in some embodiments, the robot adopts a hybrid sampling strategy and a sampling constraint strategy during the path planning process, and adopts an adaptive step size strategy to generate a new node Q new , to reduce the probability of collision between the newly expanded node and obstacles.

[0035] In some embodiments, the robot generates a reference trajectory x during the path planning process. r (t), when the robot moves along the reference trajectory x r (t) During motion, the following relationship should be satisfied:

[0036] x r (t) = f(θ r (t)); (6)

[0037] Among them, θ r (t) is the reference trajectory x r (t) Corresponding joint motion trajectory.

[0038] During the actual operation of the robotic arm, there are certain limitations on its joint angles. That is, the generated joint angles should not exceed their physical limits, and corresponding constraints should be set:

[0039]

[0040] Among them, g(x r (t),θ(t)) represents the objective function, m represents the number of joints of the robot arm, Indicates the minimum and maximum limit angles of the kth joint of the robot arm. At this time, a tracking error e is defined, and its value is e=x r (t)-f(θ(t)), which is brought into equation (7), so that equation (7) is transformed into:

[0041]

[0042] In some embodiments, after the joint of the robotic arm moves to a position, the direction vector, antenna coordinates, and objective function value are updated, and the process is repeated until the path planning is completed.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The meta-heuristic robot path fast search and obstacle avoidance method of the present invention adopts Gaussian mixture distribution and dynamic target bias probability strategy to sample random points and guide the random tree to expand toward the target point.

[0045] The sampling point closest to the target point is selected through multiple sampling, which reduces the algorithm's exploration of unnecessary space and avoids the expansion and generation of invalid directions.

[0046] The variable step size expansion method allows the search tree to quickly find paths with fewer nodes and iterations.

[0047] An angle restriction constraint strategy is introduced. When the angle between the line connecting the previous sampling point and the current point is equal to the angle between the line connecting the starting point and the end point, the current point is used as a new sampling point and added to the random tree.

[0048] In summary, the present invention can improve the generation speed and sampling efficiency of the planned path, and the obstacle avoidance search process requires that the joint space be fully controllable without breaking the physical limits of the joint control position and speed, thereby ensuring the safe operation of the robotic arm. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of equivalent interactive detection between the robotic arm and a rectangular obstacle; Figure 1 It includes 1(a) and 1(b). In 1(a), the line segment and the plane are parallel to each other, and in 1(b), the line segment and the plane intersect.

[0050] Figure 2 Schematic diagram of equivalent interactive detection between the robotic arm and a cylindrical obstacle;

[0051] Figure 3 Schematic diagram of equivalent interaction detection between the robotic arm and the spherical obstacle;

[0052] Figure 4 Schematic diagram of the sampling constraint strategy of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be further described below with reference to the embodiments. The embodiments described are only a part of the embodiments of the present invention and are not all embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative work are all within the scope of protection of the present invention.

[0054] In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or components referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention; the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance; in addition, unless otherwise expressly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection or an indirect connection through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0055] The present invention takes into account the efficiency of the robot algorithm's obstacle avoidance and the computational efficiency of collision detection, and adopts the idea of ​​bounding boxes and spatial superposition. The arm base is modeled as a rectangular bounding box. The robot arm, arm support structure, operating space, positioning device, etc. are modeled as a cylindrical bounding box. The connecting device, anchor positioning clip, double-ear sleeve, etc. are modeled as a spherical bounding box. The maximized bounding box of the robot arm's connecting rod is used as an obstacle. At this time, the collision detection between the robot arm and the obstacle is converted into an intersection detection between the bounding box line segment and the cuboid, cylinder, and sphere. Although the above strategy will waste part of the robot arm's working space, it greatly simplifies the calculation process of collision detection and improves the efficiency and reliability of planning.

[0056] like Figure 1 As shown in Figure 1, when the robot arm interacts with a rectangular obstacle, there are two different positional relationships: one in which the line segment is parallel to a plane and one in which the line segment intersects a plane. The distance between the robot arm's link and the obstacle is determined by the following two formulas.

[0057]

[0058] In the formula In the equation, d1 is the distance between the line segment and the cuboid when they are parallel to each other, M is the coordinate of the starting point of the line segment (x1, y1, z1), and P is the coordinate of the center point of the parallel surface of the cuboid (x0, y0, z0). is the direction vector of the line segment (m,n,p). When the sum of the distance d1 and the maximum bounding box radius r1 of the manipulator link is greater than 0, the manipulator link does not collide with the obstacle.

[0059] In the formula In the equation, G is the intersection of the line segment and a plane (Gx Gy Gz), and A, B, C, and D are the coefficients of the plane equation Ax+By+Cz+D=0. This value is determined by the coordinates of the three vertices of the cuboid plane.

[0060] When (G.x+r1)>x max ||(G.y+r1)>y max ||(G.z+r1)>z max When the line segment intersects a plane, the robot arm link does not collide with the obstacle.

[0061] like Figure 2 As shown in , when the robot arm interacts with the cylindrical obstacle, it is transformed into the interaction detection between the equivalent line segment of the robot arm link and the equivalent line segment of the cylindrical obstacle. Figure 2 It can be seen that if we take a point E on the line segment MN and slide it back and forth on MN, the coordinates of point E are:

[0062]

[0063] Where a is a sliding parameter. When 0≤a≤1, E is on MN. When 1<a, E is on When a<0, E is on the extension line of Similarly, take a point F on the line segment UV and slide it back and forth on UV. The coordinates of point F are:

[0064]

[0065] Where b is the sliding parameter. When 0≤b≤1, F is on UV. When 1<b, F is on When b<0, F is on the extension line of At this time, the distance d2 between the line segments is:

[0066]

[0067] Substitute the coordinates of point E and point F into the above formula to find the minimum value of d2, and 2min Compare this to the sum of the link maximizing the bounding box radius r1 and the maximum bounding box distance r2 from the obstacle. 2min >(r1+r2), the robot arm link will not collide with obstacles.

[0068] like Figure 3 As shown in Figure 2, when the robot arm interacts with the spherical obstacle, it can be transformed into an interaction detection between the sphere center point O and the equivalent line segment MN of the robot arm link. Figure 3 As shown, the shortest distance between the center point O and the equivalent line segment MN is:

[0069]

[0070] Where O is the center of the spherical obstacle and MN is the equivalent connecting rod. Figure 3 , the sphere radius is defined as the sum of the sphere obstacle radius R and the connecting rod radius r1. When d3>R+r1, the robot arm connecting rod will not collide with the obstacle.

[0071] Based on the above strategies, the meta-heuristic robot path rapid search and obstacle avoidance method of the present invention includes:

[0072] (1) During the path planning process, the robot arm uses an improved Gaussian mixture distribution sampling strategy to impose interval constraints on the generation of random trees to improve the generation speed of the planned path;

[0073] (2) The robot arm introduces a map complexity evaluation strategy during the sampling process to reduce the time of finding the optimal path point;

[0074] (3) A hybrid sampling strategy is implemented by integrating the improved Gaussian mixture distribution sampling strategy and the map complexity constraint strategy.

[0075] In the improved Gaussian mixture distribution sampling strategy, the n-dimensional function expression of the Gaussian function is as follows:

[0076]

[0077] σ is the standard deviation of the Gaussian distribution function, representing the distance between the sampling point and the obstacle, and μ is the expected value.

[0078] The probability distribution function of the sampling point in the obstacle area is:

[0079] φ(x;μ,σ)=∫f(x;μ,σ)dx; (2)

[0080] From the above probability distribution function, we can see that the closer to the obstacle, the greater the sampling probability. To avoid collisions between the sampling point and the obstacle, the obstacle function obs(x) is set and the probability distribution function is improved; the improved probability distribution function expression is as follows:

[0081] g(x;μ,σ)=max(0,φ(x;μ,σ)-obs(x)); (3)

[0082] Where obs(x) is the obstacle function. When a sample point collides with an obstacle, obs(x) = 1; otherwise, it is 0. If the sample point falls within an obstacle-free area, g(x; μ, σ) = φ(x; μ, σ); otherwise, g(x; μ, σ) = 0. In other words, if the collected points do not meet the path planning requirements, resampling is necessary to find a suitable sampling point.

[0083] Based on the improved Gaussian mixture distribution sampling strategy, interval constraints are imposed on the generation of random trees, which reduces the sampling random points in the obstacle-free area and increases the sampling random points in the area close to obstacles, thereby improving the generation speed of the planned path.

[0084] However, in situations with numerous obstacles or complex environments, random points on the search tree (i.e., sampled random points) can fall into local minima, resulting in increased time spent searching for the optimal path. To address this, a map complexity assessment strategy is introduced to calculate the most appropriate map complexity coefficient C1 and obtain the most appropriate constraint threshold p.

[0085] In some embodiments, the robotic arm introduces a map complexity assessment strategy during the sampling process to reduce the time spent on finding the optimal path point.

[0086] The map complexity coefficient C1 is expressed as:

[0087] 0.5 represents the weight ratio, S obc Indicates the obstacle area, S map Indicates the map area, D obc Indicates the distribution of obstacles. The map is divided into 100 equal grids. The ratio of the number of grids occupied by obstacles to 100 is the distribution of obstacles. When the map complexity coefficient C1 is closer to 1, the higher the complexity of the map is, the smaller the value of the constraint threshold p is. According to the calculation, the constraint threshold p is set to p = (1-C1) 3 , and its path planning has the lowest time cost.

[0088] The specific implementation steps of the hybrid sampling strategy that integrates the improved Gaussian mixture distribution sampling strategy and the map complexity constraint strategy are as follows:

[0089] (1) Set the constraint threshold p. If the probability of generating a sampling point is less than the constraint threshold p, a point Q is randomly generated. rand1 Add random trees;

[0090] (2) If Q rand1 If a collision occurs with an obstacle, a point Q is regenerated through the improved probability distribution function (i.e., the formula (3) described above) rand2 ; If no collision occurs, return Qrand1 ;

[0091] (3) If Q rand2 If it collides with an obstacle, select Q rand1 and Q rand2 The midpoint Q in space rand3 If no collision occurs, return Q rand2 ;

[0092] (4) If Q rand3 If there is no collision with the obstacle, then Q rand3 is the sampling point of the random tree, otherwise, return to the first step and resample.

[0093] While a hybrid strategy that combines an improved Gaussian mixture distribution sampling strategy with a map complexity constraint strategy can ensure that sampling points are evenly distributed across obstacle areas, the generation of sampling points lacks directionality, making it prone to reverse growth, increasing both the time and path cost of path planning. To avoid this, this paper proposes a sampling path strategy that constrains the sampling points of the hybrid sampling strategy.

[0094] Therefore, in some embodiments, the robotic arm introduces a sampling constraint strategy during the path planning process based on the hybrid sampling strategy. The sampling constraint strategy specifically includes:

[0095] The angle θ between the line connecting the previous sampling point and the current point and the line connecting the starting point and the end point is used as the criterion for judging the positive growth of the sampling point; when the angle θ∈[-π / 2,π / 2], it is judged that the random sampling point belongs to positive growth; when the angle θ is not in the range of [-π / 2,π / 2], the random sampling point does not meet the sampling constraint requirements (i.e., it belongs to reverse growth) and should be eliminated.

[0096] Combined with attachment Figure 4 , as attached Figure 4 As shown, Q init is the initial point, Q goal is the target point, θ1, θ2, θ3, θ4, θ5, θ6 are the angles between the line connecting the previous sampling point and the current point and the line connecting the starting point and the end point. rand1 , Q rand2 , Q rand3 、、Q rand4 , Q rand6 , Q rand7 Randomly generated by the constraint threshold strategy, Q rand5 Generated by the mixed Gaussian distribution function (i.e., generated by the previous probability distribution function formula (3)). When the sampling point is in the non-obstacle area, it can be directly used as an effective sampling node. When the sampling point is in the obstacle area, according to formula (3), the center point Q between the two obstacles is setrand5 As sampling point. Figure 4 It can be seen that when the sampling constraint strategy is used, the values ​​of θ1 and θ6 are not in the range of [-π / 2,π / 2], which corresponds to the random sampling point Q rand2 and Q rand7 It does not meet the sampling constraint requirements and should be eliminated.

[0097] In the specific implementation process, although the hybrid sampling strategy and sampling constraint strategy solve the interval point generation and forward expansion problems of the random tree, the expansion of the standard RRT algorithm sampling points still has a large degree of randomness. The generation of new nodes is carried out along the direction of the sampling points, rather than always growing towards the target node. In addition, there is still a certain probability that the sampling points are generated near the obstacle area, which increases the probability of the newly expanded nodes colliding with obstacles. Figure 4 Q shown rand4 Therefore, based on the fixed step-size expansion strategy of the standard RRT algorithm, the present invention provides an adaptive step-size strategy to generate a new node Q new , reducing the probability of collision between the new extended node and the obstacle. new Determined by the following formula:

[0098]

[0099] Where ρ1 is Q new The step size coefficient towards the random sampling point, ρ2 is Q new Step coefficient towards the target point. When ρ1>ρ2, the new node Q new Grow towards the random sampling point position and direction; when ρ1<ρ2, the new node Q new Grow towards the target point position and direction.

[0100] In some embodiments, the robot adopts a hybrid sampling strategy and a sampling constraint strategy during the path planning process, and adopts an adaptive step size strategy to generate a new node Q new , to reduce the probability of collision between the newly expanded node and obstacles.

[0101] In some embodiments, the robot generates a reference trajectory x during the path planning process. r (t), when the robot moves along the reference trajectory x r (t) During motion, the following relationship should be satisfied:

[0102] x r (t) = f(θ r (t)); (6)

[0103] Among them, θ r (t) is the reference trajectory x r (t) Corresponding joint motion trajectory.

[0104] During the actual operation of the robotic arm, there are certain limitations on its joint angles. That is, the generated joint angles should not exceed their physical limits, and corresponding constraints should be set:

[0105]

[0106] Among them, g(x r (t),θ(t)) represents the objective function, m represents the number of joints of the robot arm, Indicates the minimum and maximum limit angles of the kth joint of the robot arm. At this time, a tracking error e is defined, and its value is e=x r (t)-f(θ(t)), which is brought into equation (7), so that equation (7) is transformed into:

[0107]

[0108] After the joint of the robotic arm moves to the next position, the direction vector, antenna coordinates and objective function value are updated, and the process is repeated until the path planning is completed.

[0109] As mentioned above, the robot arm can obtain the path trajectory through the position and orientation data of the end effector. Therefore, the tracking error e is defined as:

[0110] In formula (9), is the real Cartesian coordinate of the end effector. Substituting formula (9) into formula (7), we can get the objective function:

[0111]

[0112] During the movement of the robotic arm, an instantaneous time value t is defined k The joint coordinates at this time are θ k , simulates the beetle antenna to generate a normally distributed random direction vector According to the direction vector The endpoint coordinates of the two antennas are calculated as:

[0113]

[0114] In the above formula (11), θ L and θ R The beetle is at time t k The projection positions of the left and right antennas below. k is a hyperparameter representing the length of the beetle’s antenna. Γ(.) is a projection function that projects these points into the constraint space defined by the objective function and applies it to each joint angle in turn. Its value is:

[0115]

[0116] The robot moves the joints to θ in sequence L and θ R The coordinates are located at the bottom of the image, and the value of the objective function is calculated using the following formula:

[0117]

[0118] At this time, x r (t) is t k The coordinates of the points on the reference trajectory at time , t k The position coordinates of the end effector at the moment, so that the objective function value g of the beetle's left and right antennas can be calculated L and g R Then, the objective function value is used to obtain the forward direction of the robot arm and update the joint position θ for the next step. new , and its update strategy is:

[0119]

[0120] in, Indicates that the joint update position of the manipulator moves towards the direction of the antenna with the smaller objective function value, δ k (λ k ) represents the updated θ new and the current joint position θ k The Euclidean distance between them, k is the sample index, which affects the convergence speed of the entire algorithm. k and δ k (λ k ) takes the value of:

[0121]

[0122] δ k (λ k )=c2λ k ; (16)

[0123] At this point, the algorithm converges at a moderate speed and achieves good results. In formulas (15) and (16), c1 and c2 are constants used to dynamically adjust the step size between the end effector and the target position. When the end effector is far from the target position, the algorithm step size is larger, and when the end effector is close to the target position, the step size is smaller. For the values ​​of c1 and c2, the present invention proposes the following fast convergence strategy:

[0124] c1∝T s ,c2∈[1,3];(17)

[0125] Among them, T sis the sampling time of the control loop. When the robot reaches θ new After that, update the value of the objective function:

[0126]

[0127] Will g new Compare with the objective function value at the initial position. If g new The value of is smaller, then the robot moves to θ new position, otherwise, return θ k .

[0128]

[0129] When the robot arm's θ k Move to θ k+1 After that, the direction vector, antenna coordinates, and objective function value are updated again, and the above process is repeated.

[0130] The meta-heuristic robot path fast search and obstacle avoidance method of the present invention adopts Gaussian mixture distribution and dynamic target bias probability strategy to sample random points and guide the random tree to expand toward the target point.

[0131] The sampling point closest to the target point is selected through multiple sampling, which reduces the algorithm's exploration of unnecessary space and avoids the expansion and generation of invalid directions.

[0132] The variable step size expansion method allows the search tree to quickly find paths with fewer nodes and iterations.

[0133] An angle restriction constraint strategy is introduced. When the angle between the line connecting the previous sampling point and the current point is equal to the angle between the line connecting the starting point and the end point, the current point is used as a new sampling point and added to the random tree.

[0134] In summary, the present invention can improve the generation speed and sampling efficiency of the planned path, and the obstacle avoidance search process requires that the joint space be fully controllable without breaking the physical limits of the joint control position and speed, thereby ensuring the safe operation of the robotic arm.

Claims

1. A meta-heuristic method for rapid path search and obstacle avoidance for a robotic arm, characterized in that: include: (1) During the path planning process, the robot arm uses an improved Gaussian mixture distribution sampling strategy to impose interval constraints on the generation of random trees to improve the generation speed of the planned path; In the improved Gaussian mixture distribution sampling strategy, the n-dimensional function expression of the Gaussian function is as follows: σ is the standard deviation of the Gaussian distribution function, representing the distance between the sampling point and the obstacle, and μ is the expected value; The probability distribution function of the sampling point in the obstacle area is: φ(x;μ,σ)=∫f(x;μ,σ)dx; (2) From the above probability distribution function, we can see that the closer to the obstacle, the greater the sampling probability. To avoid collision between the sampling point and the obstacle, the obstacle function obs(x) is set and the probability distribution function is improved. The improved probability distribution function expression is as follows: g(x;μ,σ)=max(0,φ(x;μ,σ)-obs(x)); (3) Where obs(x) is the obstacle function. When the generated sampling point collides with an obstacle, obs(x) = 1, otherwise it is 0. If the sampling point falls in the obstacle-free area, g(x; μ, σ) = φ(x; μ, σ), otherwise g(x; μ, σ) = 0. (2) The robot arm introduces a map complexity evaluation strategy during the sampling process to reduce the time of finding the optimal path point; at the same time, an appropriate constraint threshold p is set; Among them, the map complexity coefficient C1 is expressed as: 0.5 represents the weight ratio, S obc Indicates the obstacle area, S map Indicates the map area, D obc Indicates the distribution of obstacles; (3) The improved Gaussian mixture distribution sampling strategy and the map complexity constraint strategy are integrated to implement the hybrid sampling strategy. The specific implementation steps are as follows: (1) Set the constraint threshold p. If the probability of generating a sampling point is less than the constraint threshold p, a point Q is randomly generated. rand1 Add random trees; (2) If Q rand1 If a collision occurs with an obstacle, a point Q is regenerated through the improved probability distribution function rand2 ; If no collision occurs, return Q rand1 ; (3) If Q rand2 If it collides with an obstacle, select Q rand1 and Q rand2 The midpoint Q in space rand3 If no collision occurs, return Q rand2 ; (4) If Q rand3 If there is no collision with the obstacle, then Q rand3 is the sampling point of the random tree, otherwise, return to the first step and resample.

2. The meta-heuristic robot path rapid search and obstacle avoidance method according to claim 1 is characterized in that: The robot arm introduces a sampling constraint strategy during path planning using a hybrid sampling strategy. The sampling constraint strategy specifically includes: The angle θ between the line connecting the previous sampling point and the current point and the line connecting the starting point and the end point is used as the criterion for judging the positive growth of the sampling point. When the angle θ∈[-π / 2,π / 2], the sampling point is judged to be in positive growth. When the angle θ is not in the range of [-π / 2,π / 2], the sampling point does not meet the sampling constraint requirements and should be eliminated.

3. The meta-heuristic robot path rapid search and obstacle avoidance method according to claim 2 is characterized in that: The robot adopts a hybrid sampling strategy and a sampling constraint strategy in the path planning process, and adopts an adaptive step size strategy to generate a new node Q new , to reduce the probability of collision between the newly expanded node and obstacles.

4. The meta-heuristic robot path rapid search and obstacle avoidance method according to claim 3 is characterized in that: The new node Q new Determined by the following formula: Where ρ1 is Q new The step size coefficient towards the random sampling point, ρ2 is Q new Step coefficient towards the target point; when ρ1>ρ2, the new node Q new Grow towards the random sampling point position and direction; when ρ1<ρ2, the new node Q new Grow towards the target point position and direction.

5. The meta-heuristic robot path rapid search and obstacle avoidance method according to claim 4 is characterized in that: The robotic arm generates a reference trajectory x during the path planning process r (t), when the robot moves along the reference trajectory x r (t) During motion, the following relationship should be satisfied: x r (t)=f(θ r (t)); (6) Among them, θ r (t) is the reference trajectory x r (t) Corresponding joint motion trajectory.

6. The meta-heuristic robot path rapid search and obstacle avoidance method according to claim 5, characterized in that: The robot moves along the reference trajectory x r (t) During motion, the generated joint angles should not exceed their physical limits, and corresponding constraints should be set: Among them, g(x r (t),θ(t)) represents the objective function, m represents the number of joints of the robot arm, Indicates the minimum and maximum limit angles of the kth joint of the robot arm; at this time, a tracking error e is defined, whose value is e = x r (t)-f(θ(t)), which is brought into formula (7), so that formula (7) is transformed into: stθ - <θ<θ + (8)。 7. The meta-heuristic robot path rapid search and obstacle avoidance method according to claim 5, characterized in that: After the joint of the robotic arm moves to the next position, the direction vector, antenna coordinates and objective function value are updated, and the process is repeated until the path planning is completed.

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