CN113485369A - Indoor mobile robot path planning and path optimization method for improving A-x algorithm - Google Patents
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Abstract
The invention discloses an improved A-x algorithm indoor mobile robot path planning and path optimization method, which comprises the following steps: s1, acquiring a global static grid map of an indoor scene, wherein each node of the grid map represents that the current position is an obstacle or a passable area, and confirming a starting point and a target point; s2, preprocessing the grid map, and respectively calculating the nearest jumping point distance of each passable node; s3, carrying out route searching based on the improved A-global path planning algorithm of the jumping point search, and obtaining search nodes in the corresponding direction according to the current route searching direction and the obtained jumping point distance, thereby obtaining a planned path, S4, and optimizing the path based on the Bezier curve. By adopting the method for planning the indoor mobile robot path and optimizing the path by improving the A-x algorithm, the planned path meets the turning requirement of the robot, the calculation redundancy and the memory load are reduced, and the global track which is more in line with the actual movement can be obtained.
Description
Technical Field
The invention relates to the field of mobile robot navigation and path planning, in particular to an indoor mobile robot path planning and path optimization method for improving A-x algorithm
Background
Path planning is one of the core problems in mobile robot control research, and generally means that a mobile robot refers to a certain parameter index (e.g., shortest selected path, shortest running time, etc.), and a feasible path from a starting point to an end point is calculated by a path planning algorithm, so that the mobile robot can move to a target position along the path. Currently, commonly used path planning algorithms include a traditional path planning algorithm and an intelligent bionic algorithm: the traditional path planning algorithms include Dijkstra algorithm, Floyd algorithm, A-star algorithm and the like, and the intelligent bionic algorithms include genetic algorithm, ant colony algorithm, artificial intelligence algorithm and the like.
The Dijkstra algorithm and the ant colony algorithm are slow in search speed, the genetic algorithm and the ant colony algorithm can be trapped in local convergence and cannot ensure global optimum, the A-algorithm is best in comprehensiveness, and the A-algorithm is widely applied to robot global path planning. However, the a-x algorithm searches all the adjacent nodes of the node, which results in a large number of unnecessary nodes being searched, resulting in an increase in the amount of calculation and memory consumption, and the real-time performance cannot be guaranteed in a scene requiring a fast response indoors.
Aiming at the defect of large calculation redundancy of the A-star algorithm, Daniel Harabor et al provides a Jump Point Search (JPS) algorithm, and only necessary directions are searched according to the current moving direction during path search, so that the calculation redundancy is reduced, and the calculation efficiency is improved. The calculation bottleneck of the jump point search algorithm is in the judgment of jump points, and the judgment of the jump points in a large-scale map takes a long time to influence the path-finding speed.
For an indoor static scene, an original path obtained by global path planning is a broken line type, the turning angle is too mechanical, an indoor mobile robot often has the turning radius and curvature of the indoor mobile robot, and the mechanical broken line path is not suitable for the mobile robot to move, so that the problem that the globally planned path is invalid in the actual scene is caused.
Disclosure of Invention
Aiming at the problems that the existing path planning method is low in calculation efficiency and high in memory requirement, and the planned path is difficult to meet the kinematics and dynamics model of the actual indoor mobile robot, the invention provides an indoor mobile robot path planning and path optimization method for improving the A-x algorithm in order to overcome the defects of the technology, and the method carries out grid division by referring to the turning radius and the curvature of the robot when a grid map is calculated and obtained so that the planned path meets the turning requirement of the robot; preprocessing the grid map, calculating jumping point distances in the directions of straight lines and diagonal lines, and reducing calculation redundancy and memory load; and obtaining a global track which is more consistent with actual movement based on the Bezier curve optimization path.
The technical scheme adopted by the invention for overcoming the technical problems is as follows: the invention provides an improved A-x algorithm indoor mobile robot path planning and path optimization method, which specifically comprises the steps of S1, obtaining a global static grid map of an indoor scene, wherein each node of the grid map represents that the current position is an obstacle or a passable area, and confirming a starting point and a target point; s2, preprocessing the grid map, and respectively calculating the nearest jumping point distance of each passable node; and S3, carrying out route searching based on the improved A-global path planning algorithm of the jumping point search, and obtaining search nodes in the corresponding direction according to the current route searching direction and the obtained jumping point distance so as to obtain a planned path.
Further, step S1 specifically includes: dividing the grid granularity based on the turning radius of the robot to form a R-C grid map, wherein R is the grid line number of the grid map, and C is the grid column number of the grid map; determining that each node of the grid map represents that the current location is an obstacle or a passable area based on the probability that the grid is free; the start point and target point coordinates are converted to coordinates on the grid map.
The idle probability refers to the probability that no obstacle exists on each grid according to the scale of the divided grids when the three-dimensional point cloud map is mapped to the two-dimensional grid map, and the probability that the grid is idle is obtained.
Further, the preprocessing of the grid map in step S2 at least includes a skip point judgment and a skip point distance backtracking, and the skip point judgment specifically includes: and judging whether the straight line of each passable point moves in 4 directions to be a jumping point.
The jumping point refers to a passable node with a forced neighbor, and is a node which really needs to calculate cost in the path process.
Further, the backtracking of the skip point distance specifically includes: based on the jump points obtained by judgment, calculating the nearest jump point distances in 8 directions of a straight line and a diagonal line on the node, wherein the nearest jump point distances are calculated according to the judged jump point positions in the straight line direction; and judging whether the node is a jumping point according to the jumping point distances in the horizontal direction and the vertical direction of the node in the diagonal direction, and calculating the jumping point distance in the diagonal direction.
Furthermore, in the improved A path planning algorithm of the jumping point search, an exponentially weighted cost function is applied
And calculating the cost value, wherein f (n) represents the total cost of the current node, g (n) represents the real cost of the current node, h (n) represents the estimated cost of the current node, and h (n-1) represents the estimated cost of the father node of the current node.
The weighting idea is that as the way-finding proceeds, the real cost should occupy a larger proportion, and the estimated cost should occupy a smaller proportion.
Further, the method also comprises a step S4 of optimizing the planned path, deleting collinear intermediate nodes in the planned path, only keeping turning points, and optimizing the Bezier curve of the divided path.
The planned path is optimized to obtain a path with a smaller rotation angle and more suitable for the movement of the robot.
Further, in step S3, performing route finding based on the modified a × global path planning algorithm of the skip point search, specifically including adding a start point to an open _ set, and taking out a node with the minimum cost value from the open _ set; wherein, open _ set represents a node set needing to be explored, and closed _ set represents a node set of which the optimal shortest path from a starting point to the node is determined; if the obtained node is a starting point, respectively obtaining the nearest jumping points from 8 directions of the straight line and the diagonal line; if the current direction is not the starting point, determining the current direction according to the father node of the current direction, and acquiring the jumping points of the current direction, namely the natural neighbor direction and the forced neighbor direction; if the obtained jumping point is in the closed _ set, the jumping point is not processed, if the obtained jumping point is in the open _ set, the cost value of the jumping point is updated, otherwise, the jumping point is added into the open _ set; and repeating the steps until the target point is found.
The invention has the beneficial effects that:
1. performing grid division on the turning radius and the curvature of the grid map reference robot to enable the planned path to meet the turning requirement of the robot;
2. the jumping point distances in the directions of the straight line and the diagonal line are calculated, and the calculation redundancy and the memory load are reduced;
3. and obtaining a global track which is more consistent with actual movement based on the Bezier curve optimization path.
Drawings
Fig. 1 is a schematic flow chart of a path planning and path optimizing method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of grid map movement according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating a determination of key jumping points in a straight line direction of a grid map according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating a calculation result of jumping point distances in various directions according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a path planning according to an embodiment of the present invention;
FIG. 6 is a flow chart of path planning according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of a Bezier curve optimization according to an embodiment of the present invention;
fig. 8 is a comparison diagram of path planning and optimization effects according to an embodiment of the present invention.
Detailed Description
In order to facilitate a better understanding of the invention for those skilled in the art, the invention will be described in further detail with reference to the accompanying drawings and specific examples, which are given by way of illustration only and do not limit the scope of the invention.
As shown in fig. 1, a schematic flow diagram of a path planning and path optimization method for an indoor mobile robot with an improved a-x algorithm in this embodiment specifically includes, S1, acquiring a global static grid map of an indoor scene, where each node of the grid map represents that a current position is an obstacle or a passable area, and determining a starting point and a target point; s2, preprocessing the grid map, and respectively calculating the nearest jumping point distance of each passable node; and S3, carrying out route searching based on the improved A-global path planning algorithm of the jumping point search, and obtaining search nodes in the corresponding direction according to the current route searching direction and the obtained jumping point distance so as to obtain a planned path.
In an embodiment of the present invention, a schematic diagram of movement of a grid map is shown in fig. 2, where the grid map includes 8 neighbor nodes, and movement in the grid map can be divided into linear movement and diagonal movement according to a symmetry principle in the grid map.
And S1, acquiring a global static grid map of the indoor scene, wherein each node of the grid map represents that the current position is an obstacle or a passable area, and confirming a starting point and a target point.
In order to avoid repeated calculation of partial nodes, when a neighbor node n of a node x is selected, only a node with a path from x to n shorter than any path from x to n is selected, that is, the neighbor node n needs to satisfy the condition: l (< p (x), …, n | x >) > L (< p (x), x, n >), function L () represents the length of the path, < p (x), …, n | x > represents p (x) as the starting node, n is the target node and the path that does not pass x, < p (x), x, n > represents the path of p (x) → x → n, and p (x) represents the parent node of node x.
Such a node n that needs to be searched by x is made a neighbor of node x. The neighbor nodes are divided into natural neighbors and forced neighbors: the natural neighbor refers to an adjacent node which needs to be expanded through the node x when no obstacle exists around the node x, and the natural neighbor means an adjacent node which needs to be expanded and is forced to be excessive by the node x due to the surrounding obstacle. Fig. 2 is a diagram of linear and diagonal movement on a grid map, where a black grid represents an obstacle, a light gray grid represents a natural neighbor, and a dark gray grid represents a forced neighbor. For example, grid 4 in fig. 2(a) represents a natural neighbor, for example, grid 4 in fig. 2(b) represents a natural neighbor, and grid 3 represents a forced neighbor.
And S2, preprocessing the grid map, and respectively calculating the nearest jumping point distance of each passable node.
The preprocessing of the grid map is mainly to calculate the distance of the nearest next jumping point in each direction of each jumping point, and fig. 3 and 4 are schematic diagrams of preprocessing of the grid map, wherein a starting point and a target point are both jumping points. Fig. 3 shows the key jumping point judgment in the straight line direction in the grid map preprocessing, where the numbers at the upper, lower, left and right positions in the node respectively indicate whether the node is a jumping point in the corresponding straight line direction, where 0 indicates whether the node is a jumping point, and 1 indicates a jumping point; fig. 4 shows that the nearest skip point distance is calculated from the straight line and the diagonal direction respectively after the skip point is judged, and 0 indicates that no skip point exists in the direction.
And S3, carrying out route searching based on the improved A-global path planning algorithm of the jumping point search, and obtaining search nodes in the corresponding direction according to the current route searching direction and the obtained jumping point distance so as to obtain a planned path.
And planning a path on the preprocessed grid map, wherein the planning process is shown in fig. 5, and the planning process expands some nodes as shown in fig. 5. A route planning process based on jumping point search is shown in figure 6, firstly, a starting point is added into open _ set, a node cur with the minimum cost value is taken out from the open _ set every time, if the cur node is taken as the starting point, jumping points are respectively searched in 8 directions of the cur node in an expanding way, otherwise, the current direction is calculated according to the father node of the cur node, and if the cur node is in a straight line direction, the directions needing to be expanded are the current direction and the forced neighbor direction; if the direction is a diagonal direction, the directions to be expanded are horizontal and vertical directions in the same direction as the oblique direction and the current oblique direction. Wherein, open _ set represents the node set which needs to be explored, and closed _ set represents the node set which determines the optimal shortest path from the starting point to the node. The cost value refers to the result value calculated by the total cost function f (n), each node can calculate a specific cost value, and the cur node with the minimum total cost value in the open _ set is selected each time to perform path-finding expansion.
Respectively searching a first hop next from each expansion direction of the cur node, wherein the hop has the following three conditions: if the next is in the closed _ set, the skip point is not processed; if the next is in the open _ set, calculating a new cost from cur to the hop, and if the new cost is less than the original cost, updating the father node and the cost value of the hop; otherwise, the next is neither in open _ set nor closed _ set, at which point the hop is added to open _ set. If the end point is found before open _ set becomes empty, path planning succeeds, otherwise path planning fails.
In the embodiment of the application, the grids divide the grid granularity according to the turning radius and the curvature of the robot, wherein the length of each grid is equal to the turning radius of the robot, so that the global path planned under the granularity can meet the turning requirement of the robot, and the curvature refers to the inverse number of the curvature radius on each point on the actually generated path curve.
And S4, optimizing the planned path, deleting collinear intermediate nodes in the planned path, only keeping turning points, and optimizing the Bezier curve of the divided path.
In this embodiment, the path optimization is completed by a bezier curve, and the n-order bezier curve expression is:
the Bezier curve carries out interpolation through a control point between two points to obtain a curve which smoothly connects a starting point and an end point. There are two ways to optimize the planned path through the bezier curve, as shown in fig. 7, i.e., a way is as shown in fig. 7(a), all points on the path are used as anchor points, and the optimized curve path passes through all nodes on the original path; in the second mode, as shown in fig. 7(b), the upper part point of the path is used as an anchor point, the middle point of the anchor point is used as a control point, and the optimized curve path only passes through the upper part point of the original path. The optimization of the embodiment is combined with the two methods, two or three paths on the original path are selected each time to be optimized through the second method, and if the path optimized through the second method passes through the impassable area or the curvature of the path exceeds the curvature constraint, the first method is selectedAnd optimizing until the target point of the original path, and finishing the optimization process. The specific optimization steps are as follows:
step 1: dividing path points, traversing all nodes of a planned path, and completely deleting redundant nodes in the same direction between the two nodes;
step 2: b, carrying out Bezier curve optimization on the segmentation path points obtained in the step 1, selecting continuous 3 path points to carry out 2-order Bezier optimization, and if only the last 4 path points are left at present, completely selecting to carry out 3-order Bezier optimization;
and step 3: if the curve optimized in the step 2 meets the curvature requirement and the dynamic constraint and the optimized path does not pass through the infeasible area, jumping to a step 5, otherwise, jumping to a step 4;
and 4, step 4: when the current 2-order Bessel optimization fails, respectively calculating respective control points of the 2-segment paths to perform 3-order Bessel optimization;
and 5: and (4) selecting the next continuous 3 path points from the last optimized path point, continuously and circularly executing the steps 2-4 until the end point, finishing the circulation, and returning to all optimized path nodes.
As shown in fig. 8, for a comparison schematic diagram of the indoor mobile robot path planning and path optimization method using the improved a-algorithm of the present application and the conventional a-algorithm path planning, the planned path obtained by the present application can better satisfy the turning requirement of the robot, and the global trajectory better conforms to the actual movement.
The embodiments described above are intended to facilitate one of ordinary skill in the art in understanding and using the invention. It will be readily apparent to those skilled in the art that various modifications to the above-described embodiments may be made, and the generic principles defined herein may be applied to other embodiments without the use of inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications to the present invention based on the disclosure of the present invention within the protection scope of the present invention.
Claims (8)
1. The improved A-algorithm indoor mobile robot path planning and path optimization method is characterized by specifically comprising the following steps:
s1, acquiring a global static grid map of an indoor scene, wherein each node of the grid map represents that the current position is an obstacle or a passable area, and confirming a starting point and a target point;
s2, preprocessing the grid map, and respectively calculating the nearest jumping point distance of each passable node;
and S3, carrying out route searching based on the improved A-global path planning algorithm of the jumping point search, and obtaining search nodes in the corresponding direction according to the current route searching direction and the obtained jumping point distance so as to obtain a planned path.
2. The improved a-algorithm indoor mobile robot path planning and path optimization method according to claim 1, wherein step S1 specifically includes:
dividing the grid granularity based on the turning radius of the robot to form a R-C grid map, wherein R is the grid line number of the grid map, and C is the grid column number of the grid map;
determining that each node of the grid map represents that the current location is an obstacle or a passable area based on the probability that the grid is free;
the start point and target point coordinates are converted to coordinates on the grid map.
3. The method for path planning and path optimization of an indoor mobile robot by an improved a-algorithm according to claim 1, wherein the preprocessing of the grid map in step S2 at least includes a skip point judgment and a skip point distance backtracking, and the skip point judgment specifically includes: and judging whether the straight line of each passable point moves in 4 directions to be a jumping point.
4. The improved a-algorithm indoor mobile robot path planning and path optimization method according to claim 3, wherein the jumping point distance backtracking specifically comprises: based on the jump points obtained by judgment, calculating the nearest jump point distances in 8 directions of a straight line and a diagonal line on the node, wherein the nearest jump point distances are calculated according to the judged jump point positions in the straight line direction; and judging whether the node is a jumping point according to the jumping point distances in the horizontal direction and the vertical direction of the node in the diagonal direction, and calculating the jumping point distance in the diagonal direction.
5. The improved a algorithm indoor mobile robot path planning and path optimizing method according to claim 1, wherein in the step S3, in the improved a algorithm for the skip point search, an exponentially weighted cost function is applied
And calculating the cost value, wherein f (n) represents the total cost of the current node, g (n) represents the real cost of the current node, h (n) represents the estimated cost of the current node, and h (n-1) represents the estimated cost of the father node of the current node.
6. The improved a-algorithm indoor mobile robot path planning and path optimizing method according to claim 1, further comprising a step S4 of optimizing the planned path, deleting collinear intermediate nodes in the planned path, only preserving turning points, and performing bezier curve optimization on the segmented path.
7. The method for indoor mobile robot path planning and path optimization of an improved a-algorithm according to claim 6, wherein optimizing the segmented path specifically comprises: and selecting a 2-stage or 3-stage path based on the 2-stage or 3-stage Bezier curve, optimizing by adopting a partial path point mode, and optimizing by adopting a mode of passing all path points if the path passes through the impassable region.
8. The method for indoor mobile robot path planning and path optimization according to the improved a-algorithm of claim 6, wherein in step S3, the improved a-global path planning algorithm based on the skip point search performs the path search, specifically comprising,
adding a starting point into an open _ set, and taking a node with the minimum cost value from the open _ set, wherein the open _ set represents a node set which needs to be explored, and the closed _ set represents a set of nodes of which the optimal shortest path from the starting point to the node is determined;
if the obtained node is a starting point, respectively obtaining the nearest jumping points from 8 directions of the straight line and the diagonal line; if the current direction is not the starting point, determining the current direction according to the father node of the current direction, and acquiring the jumping points of the current direction, namely the natural neighbor direction and the forced neighbor direction;
if the obtained jumping point is in the closed _ set, the jumping point is not processed, if the obtained jumping point is in the open _ set, the cost value of the jumping point is updated, otherwise, the jumping point is added into the open _ set;
and repeating the steps until the target point is found.
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