CN116852367A - Six-axis mechanical arm obstacle avoidance path planning method based on improved RRTstar - Google Patents
Six-axis mechanical arm obstacle avoidance path planning method based on improved RRTstar Download PDFInfo
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
- B25J9/1666—Avoiding collision or forbidden zones
Abstract
The invention discloses a six-axis mechanical arm obstacle avoidance path planning method based on improved RRTstar, and belongs to the technical field of mechanical arm path planning. Aiming at the defects that the RRTstar algorithm has large search space, long search time and high calculation complexity, and the generated path with too many folded angles is not smooth and is not beneficial to the operation of a mechanical arm, the method firstly introduces a target bias strategy, combines a double-tree expansion strategy to expand from a starting point and a target point simultaneously, adds a path shortening strategy and a redundant node removing strategy, and finally performs B spline fitting optimization on a search path.
Description
Technical Field
The invention belongs to the technical field of path planning of mechanical arms, and particularly relates to a six-axis mechanical arm obstacle avoidance path planning method based on improved RRTstar.
Background
Robot obstacle avoidance path planning is an important field of robot control, and relates to how to enable a robot to avoid various obstacles independently in a complex environment. Common robot obstacle avoidance path planning algorithms include graph search based algorithms and sampling based algorithms. Algorithms based on graph search, such as Dijkstra algorithm and Astar algorithm, abstract robots and obstacles as nodes in the graph by building an environment map, and search the shortest path by using the graph search algorithm. The algorithm has high calculation efficiency, can find the shortest path, but under the conditions of high-dimensional space and complex constraint environment, the search space becomes very large, so that the calculation complexity is increased, and the calculation time is prolonged.
Sampling-based algorithms such as RRT (Rapidly-exploring Random Tree) and PRM (Probabilistic Roadmap), a sampling map of the robot motion space is created by randomly sampling the robot pose and environmental data, and a feasible path is searched using a map search algorithm. The algorithm has quick exploration capability and random property, and can obtain better performance in a complex environment. Therefore, in the path planning of the mechanical arm, a sampling-based algorithm is adopted, so that the mechanical arm can be helped to find a feasible and efficient path and avoid obstacles.
The rapid random expansion tree algorithm is a common mechanical arm path planning algorithm, and a feasible solution can be searched in a large range through a random sampling strategy, so that a globally optimal solution is more likely to be found. However, there may be a situation that the sampling points are unevenly distributed, so that the planned path is not smooth enough, and the mechanical arm may vibrate during movement. However, random sampling may have uneven distribution of sampling points, so that a planned path is not smooth enough, and the quality of the generated path is low, so that the mechanical arm may vibrate during movement.
Disclosure of Invention
Aiming at the defects of the prior art, the mechanical arm obstacle avoidance path planning method with short search time, short path and smoothness is provided.
In order to solve the technical problems, the technical scheme of the invention is as follows: the six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of:
step 1, acquiring the distribution situation of the obstacle in the working space of the mechanical arm, establishing a mechanical arm collision model and a kinematic model, and initializing two random trees: tree1 and Tree2 comprise a starting point X_start and an ending point X_gold, a threshold value Thr, a maximum iteration number MaxItemerations, a step size, a search range search size and a map environment.
Step 2, alternately sampling the random trees Tree1 and Tree2 through a target bias strategy to generate a random point x_rand;
step 3, searching for adjacent nodes x_near, then expanding the adjacent nodes x_near along the direction of the connecting line with the x_rand by a step size stepsize to generate a new node newPoint, performing collision detection after expansion, adding the new node into random trees Tree1 and Tree2 if collision does not occur, and resampling if collision occurs;
and 4, taking the expanded new node newPoint as a circle center, searching a neighbor node set q_near with the newPoint distance smaller than the radius r in the existing tree, taking the node x_min with the smallest distance as a new father node of the newPoint, then performing pruning rewire operation, and reconnecting the new node newPoint to the node with the shortest path except for x_min in the q_near.
Step 5, calculating the distance between the new node newPoint and the existing nodes in the random trees Tree1 and Tree2, and comparing the distance with a distance threshold d; if the distance between the new node and the existing node is greater than or equal to a threshold d, the new node is reserved, and if the distance between the new node and the existing node is smaller than the threshold d, the node which coincides with newPoint in the random tree is removed, and the distance function is as follows:
a and b are node coordinates, a (1), a (2) and a (3) respectively represent xyz coordinates of a node a in a three-dimensional space, and b (1), b (2) and b (3) respectively represent xyz coordinates of a node b in the three-dimensional space;
and 6, after the random trees Tree1 and Tree2 are successfully connected, continuing to alternately sample, outputting a path if the maximum iteration times MaxItems are reached, shortening the path according to a path shortening strategy, and smoothing the path by using a cubic B spline curve.
Further, in the step 1, a start point x_start, an end point x_gold, a search range search size and a map environment required by the operation of the mechanical arm are determined according to the actual operation scene of the mechanical arm and the related parameters of the mechanical arm, and the map environment contains the distribution situation of the obstacle.
Further, in the step 2, the target bias strategy considers the influence of the target point by introducing the target bias probability p1, so that a certain probability of generating a new random point faces the target point. The sampling mode for generating new random points x_rand1 and x_rand2 by the random trees Tree1 and Tree2 is as follows:
wherein P is a random number within a randomly generated (0, 1) range, for the random Tree1, if the random number P is greater than the target bias probability P1, x_rand1 will generate a new random point towards the target point x_gol; if the random number P is less than or equal to the target bias probability P1, then x_rand1 will be a randomly sampled point Sample. For the random Tree2, if P is greater than the target bias probability P1, then x_rand2 will generate a new random point towards the starting point x_start; if the random number P is less than or equal to the target bias probability P1, then x_rand2 will be a randomly sampled point Sample.
Further, the pruning rewire operation in the step 4 finds, for the new node newPoint, a set q_near of all nodes from which it is less than or equal to r.
For each node xi in q_near, it is checked whether there is a path from newPoint to xi such that the cost of the path is less than the current cost value of xi. If such a path exists, the parent node of xi is set to newPoint, and the cost value of xi and the cost values of all child nodes of xi are updated.
Further, the conditions for successful connection of the random trees Tree1 and Tree2 in the step 6 are as follows: the newly added node newPoint (the node extending from Tree1 and Tree 2) is less than the threshold Thr in node distance from the other Tree and passes collision detection.
Further, the path shortening strategy in the step 6 is to shorten the path when the maximum iteration number is reached, and the basic idea is to check three consecutive points in the path to determine whether there is a collision or a point to be deleted. The path formed by the original three points is then replaced by a straight line segment between the first and last points, and the first and last points are added to the path.
Further, the cubic B-spline curve in the step 6 smoothes the path obtained by the path shortening strategy, and adopts a fitting mode, wherein the related formula is as follows:
B 0,3 (t)＝(1-t) 3 /6
B 1,3 (t)＝1/6(3t 3 -6t 2 +4)
B 2,3 (t)＝1/6(-3t 3 +3t 2 +3t+1)
B 3,3 (t)＝t 3 /6
wherein t is a node vector and represents the position on the curve, and the value range is [0,1 ]]Real number B in interval 0,3 (t)、B 1,3 (t)、B 2,3 (t) and B 3,3 (t) are all B-spline basis functions for constructing cubic B-spline curves.
The cubic B-spline curve equation is a linear combination of the four basis functions, and the equation is as follows:
P(t)＝P 0 B 0,3 (t)+P 1 B 1,3 (t)+P 2 B 2,3 (t)+P 3 B 3,3 (t)
wherein P (t) is the total curve equation, P 0 ,P 1 ,P 2 ,P 3 Is the coordinate value of the four control points.
And transmitting the smoothed final path point to the mechanical arm, and executing a work task by the mechanical arm according to the obtained path point.
The beneficial effects of the invention are as follows: the six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar can effectively reduce search time, reduce search complexity, shorten paths and simultaneously realize path smoothing, so that the tail end of the mechanical arm can avoid obstacles smoothly in the working process, and efficient and safe path planning is realized.
Drawings
FIG. 1 is a flow chart of the improved RRTstar algorithm of the invention;
FIG. 2 is a schematic diagram of a path shortening strategy of the present invention;
FIG. 3 is a path search process diagram of an improved RRTstar algorithm in three-dimensional space in accordance with an embodiment of the invention;
FIG. 4 is a diagram of an initial obstacle avoidance path that is not optimized in accordance with an embodiment of the present invention;
FIG. 5 is a diagram of a B-spline smoothed obstacle avoidance path in an embodiment of the present invention;
FIG. 6 is a graph comparing the effects of an initial obstacle avoidance path and a smoothed obstacle avoidance path according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings and specific examples:
example 1: as shown in fig. 1 to 6, the six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar provided by the invention comprises the following steps:
step 1, acquiring the distribution situation of the obstacle in the working space of the mechanical arm, establishing a mechanical arm collision model and a kinematic model, and initializing two random trees: tree1 and Tree2 comprise a starting point X_start and an ending point X_gold, a threshold value Thr, a maximum iteration number MaxItemerations, a step size, a search range search size and a map environment.
In this step, the starting point x_start, the ending point x_gold, the search range search size and the map environment required by the operation of the mechanical arm are determined according to the actual operation scene of the mechanical arm and the related parameters of the mechanical arm, and the map environment contains the distribution situation of the obstacle.
In this example, the method of the present invention was used on a six axis robotic arm model HW700, with a 3kg payload.
Firstly initializing a mechanical arm, then moving an end effector of the mechanical arm to an end point, acquiring a starting point and an end point of a working path of the mechanical arm and distribution conditions of obstacles in space through a sensor, simultaneously constructing a three-dimensional space map model, marking a starting point X_start and an end point X_gold, initializing two random trees, and transmitting the starting point X_start and the end point X_gold, a threshold Thr, the maximum iteration times MaxItemerations, step size, search range search size and map environment to an improved RRTstar algorithm.
Step 2, alternately sampling the random trees Tree1 and Tree2 through a target bias strategy to generate a random point x_rand
The target bias strategy in the step is to consider the influence of the target point by introducing the target bias probability p1, so that a certain probability of generating a new random point faces the target point. The sampling mode for generating new random points x_rand1 and x_rand2 by the random trees Tree1 and Tree2 is as follows:
wherein P is a random number within a randomly generated (0, 1) range, for the random Tree1, if the random number P is greater than the target bias probability P1, x_rand1 will generate a new random point towards the target point x_gol; if the random number P is less than or equal to the target bias probability P1, then x_rand1 will be a randomly sampled point Sample. For the random Tree2, if P is greater than the target bias probability P1, then x_rand2 will generate a new random point towards the starting point x_start; if the random number P is less than or equal to the target bias probability P1, then x_rand2 will be a randomly sampled point Sample.
In this step, before generating the random point, it is first determined whether the maximum iteration number maxItems is exceeded, if yes, sampling is ended, the result is output, if not, the iteration number is increased by one, and sampling is continued to generate a new random point x_rand.
And 3, searching for a neighboring node x_near, expanding the x_near along the direction of the connecting line with the x_rand by a step size stepsize to generate a new node newPoint, performing collision detection after expansion, adding the new node into a random tree if collision does not occur, and resampling if collision occurs.
And 4, taking the expanded new node newPoint as a circle center, searching a neighbor node set q_near with the newPoint distance smaller than the radius r in the existing tree, taking the node x_min with the smallest distance as a new father node of the newPoint, then performing pruning rewire operation, and reconnecting the new node newPoint to the node with the shortest path except for x_min in the q_near.
Pruning rewire operation in the step, aiming at a new node newPoint, a set q_near of all nodes with the distance less than or equal to r is found.
For each node xi in q_near, it is checked whether there is a path from newPoint to xi such that the cost of the path is less than the current cost value of xi. If such a path exists, the parent node of xi is set to newPoint, and the cost value of xi and the cost values of all child nodes of xi are updated.
Step 5, calculating the distance between the new node and the existing node in the random tree, and comparing the distance with a distance threshold d; if the distance between the new node and the nearest node is smaller than the threshold d, the node which coincides with newPoint in the random tree is removed, and the distance function is as follows:
where x and y are the coordinates of two nodes.
And 6, outputting a path if the maximum iteration times MaxItems are reached, shortening the path according to a path shortening strategy, and smoothing the path by using a cubic B spline curve.
The condition of successful connection of the random Tree Tree1 and Tree2 in the step is that: the newly added node newPoint (the node expanded from Tree1 and Tree 2) in the current Tree is less than the threshold Thr in node distance from the other Tree and passes collision detection.
The path shortening strategy in the step shortens the path when the maximum iteration number is reached, and the basic idea is to check three continuous points in the path and judge whether collision exists or not and whether points need to be deleted exist. The path formed by the original three points is then replaced by a straight line segment between the first and last points, and the first and last points are added to the path.
The cubic B spline curve in the step smoothes the path obtained by the path shortening strategy, and adopts a fitting mode, wherein the related formula is as follows:
B 0,3 (t)＝(1-t) 3 /6
B 1,3 (t)＝1/6(3t 3 -6t 2 +4)
B 2,3 (t)＝1/6(-3t 3 +3t 2 +3t+1)
B 3,3 (t)＝t 3 /6
wherein t is a node vector and represents the position on the curve, and the value range is [0,1 ]]Real number B in interval 0,3 (t)、B 1,3 (t)、B 2,3 (t) and B 3,3 (t) are all B-spline basis functions for constructing cubic B-spline curves.
The cubic B-spline curve equation is a linear combination of the four basis functions, and the equation is as follows:
P(t)＝P 0 B 0,3 (t)+P 1 B 1,3 (t)+P 2 B 2,3 (t)+P 3 B 3,3 (t)
wherein P (t) is the total curve equation, P 0 ,P 1 ,P 2 ,P 3 Is the coordinate value of four control points
And transmitting the smoothed final path point to the mechanical arm, and executing a work task by the mechanical arm according to the obtained path point.
The experimental simulation is performed in Matlab2022b, the simulation is performed in a three-dimensional space map provided with five spherical obstacles, the coordinates of a starting point X_start are (15, 15), the coordinates of an ending point X_gold are (160,160,160), and the coordinates of the sphere centers of the spherical obstacles are respectively: (100,100,105), (50,54,50), (100,47,64), (143,100,108), (55,137,53); the radius is 14.5; the search range searchSize is [250 250 250], the step size is 13, and the threshold Thr is 10.
FIG. 3 is a path search process diagram of an improved RRTstar algorithm in three-dimensional space, wherein a target bias strategy, double-tree alternate expansion, path shortening strategy, pruning rewire operation and a search effect diagram after redundant nodes are removed are added.
As can be seen by comparing fig. 4 with fig. 5, the curvature and the length of the path are obviously reduced, the smoothness of the path is improved, no folding angle exists in the path, the planned path is more concise, and the path after the smoothness is also a collision-free path, so that the mechanical arm is not collided with an obstacle in the working space.
In fig. 6, the solid line represents the fitted optimized path of the original obstacle avoidance path planned by the improved RRTstar algorithm after three times of B-spline smoothing, and the line with star represents the initial path, so that the path planned by the algorithm in the invention is shorter and smoother.
It will be apparent to those skilled in the art that the disclosed embodiments are intended to assist the reader in understanding the principles and implementations of the invention and are not intended to limit the scope of the invention. Accordingly, various modifications and combinations of the embodiments disclosed herein can be made by those skilled in the art, and are within the scope of the invention as long as the modifications and combinations do not depart from the spirit of the invention.
Claims (7)
1. The six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of:
step 1, acquiring the distribution situation of the obstacle in the working space of the mechanical arm, establishing a mechanical arm collision model and a kinematic model, and initializing two random trees: tree1 and Tree2 comprise a starting point X_start and an ending point X_gold, a threshold value Thr, a maximum iteration number MaxItems, a step size, a search range search size and a map environment;
step 2, alternately sampling the random trees Tree1 and Tree2 through a target bias strategy to generate a random point x_rand;
step 3, searching for adjacent nodes x_near, then expanding the adjacent nodes x_near along the direction of the connecting line with the x_rand by a step size stepsize to generate a new node newPoint, performing collision detection after expansion, adding the new node into random trees Tree1 and Tree2 if collision does not occur, and resampling if collision occurs;
step 4, taking the expanded new node newPoint as a circle center, searching a neighbor node set q_near with the newPoint distance smaller than the radius r in the existing tree, taking a node x_min with the smallest distance as a new father node of the newPoint, then performing pruning rewire operation, and reconnecting the new node newPoint to a node with the shortest path except for x_min in the q_near;
step 5, calculating the distance between the new node newPoint and the existing nodes in the random trees Tree1 and Tree2, and comparing the distance with a distance threshold d; if the distance between the new node and the existing node is greater than or equal to a threshold d, the new node is reserved, and if the distance between the new node and the existing node is smaller than the threshold d, the node which coincides with newPoint in the random tree is removed, and the distance function is as follows:
a and b are node coordinates, a (1), a (2) and a (3) respectively represent xyz coordinates of a node a in a three-dimensional space, and b (1), b (2) and b (3) respectively represent xyz coordinates of a node b in the three-dimensional space;
and 6, after the random trees Tree1 and Tree2 are successfully connected, continuing to alternately sample, outputting a path if the maximum iteration times MaxItems are reached, shortening the path according to a path shortening strategy, and smoothing the path by using a cubic B spline curve.
2. The six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of: in the step 1, a starting point x_start, an ending point x_gold, a search range search size and a map environment which contain obstacle distribution conditions required by the operation of the mechanical arm are determined according to the actual operation scene of the mechanical arm and related parameters of the mechanical arm.
3. The six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of: in the target bias strategy in the step 2, the influence of the target point is considered by introducing the target bias probability p1, so that a certain probability faces the target point when a new random point is generated, and the sampling mode of generating the new random points x_rand1 and x_rand2 by the random trees Tree1 and Tree2 is as follows:
wherein P is a random number within a randomly generated (0, 1) range, for the random Tree1, if the random number P is greater than the target bias probability P1, x_rand1 will generate a new random point towards the target point x_gol; if the random number P is less than or equal to the target bias probability P1, x_rand1 will be a randomly sampled point Sample, and for the random Tree2, if P is greater than the target bias probability P1, x_rand2 will generate a new random point towards the starting point x_start; if the random number P is less than or equal to the target bias probability P1, then x_rand2 will be a randomly sampled point Sample.
4. The six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of: the pruning rewire operation in the step 4 finds a set q_near of all nodes with the distance r smaller than or equal to the new node newPoint;
for each node xi in q_near, checking whether there is a path from newPoint to xi such that the cost of the path is less than the current cost value of xi, if so, setting the parent node of xi to newPoint, and updating the cost value of xi and the cost values of all child nodes of xi.
5. The six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of: the conditions for successful connection of the random trees Tree1 and Tree2 in the step 6 are as follows: the newly added node newPoint is less than the threshold Thr in node distance from another tree and passes collision detection.
6. The six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of: the path shortening strategy in the step 6 is to shorten the path when the maximum iteration times are reached, check three continuous points in the path, judge whether there are collision and points to be deleted, then replace the path formed by the three points with the straight line segment between the first and last points, and add the first and last points into the path.
7. The six-axis mechanical arm obstacle avoidance path planning method based on the improved RRTstar is characterized by comprising the following steps of: and (3) smoothing the path obtained by the path shortening strategy by using a cubic B spline curve in the step (6), and adopting a fitting mode, wherein the related formula is as follows:
B 0，3 (t)＝(1-t)3/6
B 1，3 (t)＝1/6(3t3-6t2+4)
B 2，3 (t)＝1/6(-3t3+3t2+3t+1)
B 3，3 (t)＝t3/6
wherein t is a node vector and represents the position on the curve, and the value range is [0,1 ]]Real number B in interval 0 ， 3 (t)、B 1 ， 3 (t)、B 2 ， 3 (t) and B 3 ， 3 (t) are B-spline basis functions for constructing cubic B-spline curves;
the cubic B-spline curve equation is a linear combination of the four basis functions, and the equation is as follows:
P(t)＝P0B 0 ， 3 (t)+P1B 1 ， 3 (t)+P2B 2 ， 3 (t)+P3B 3 ， 3 (t)
wherein, P (t) is the total curve equation, P0, P1, P2, P3 are the coordinate values of four control points;
and transmitting the smoothed final path point to the mechanical arm, and executing a work task by the mechanical arm according to the obtained path point.
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| CN117464693A (en) * | 2023-12-27 | 2024-01-30 | 成都电科星拓科技有限公司 | Three-dimensional mechanical arm particle swarm path planning method based on cubic spline interpolation |
| CN117464693B (en) * | 2023-12-27 | 2024-03-19 | 成都电科星拓科技有限公司 | Three-dimensional mechanical arm particle swarm path planning method based on cubic spline interpolation |
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