Abstract
Path planning is a vital function of robotic systems. Different from existing roadmap algorithms which first determine the free space and then determine the collision-free path, researchers recently proposed several convex relaxation based smoothing algorithms which first select an initial path to link the starting configuration and the goal configuration and then reshape this path to meet other requirements (e.g., collision-free conditions) by using convex relaxation. However, convex relaxation based smoothing algorithms often fail to give a satisfactory path, since the initial paths are selected improperly. Moreover, the curvature constraints were not considered in many existing convex relaxation based smoothing algorithms. In this paper, we show that we can first grid the whole configuration space to pick a candidate path and reshape the shortest path to meet our goal. This new algorithm inherits the merit of roadmap algorithms and a convex feasible set algorithm. We further discuss how to meet the curvature constraints by using both the Beamlet algorithm to select a better initial path and an iterative optimization algorithm to adjust the curvature of a path. Theoretical analysis and numerical testing results show that our algorithm can almost surely find a feasible path and require a short computation time.
Highlights
Path planning refers to finding a collision-free and dynamically-feasible path from the given initial configuration to the final configuration and optimizing some criteria [1]–[3]
EVALUATING THE ALGORITHM2 In this subsection, the performance of Algorithm 2 (GPR-m algorithm) is compared with the original Convex Feasible Set (CFS) algorithm, the GPR(A*)-m algorithm, SQP_A* algorithm and ITP_A* algorithm in two criteria: 1) the success rate to find feasible paths; 2) the speed to find feasible paths
The main differences between our code and Liu’s code are that we add additional constraints to strict paths in the configuration space and the relative optimization problems are solved by CVX [44]
Summary
Path planning refers to finding a collision-free and dynamically-feasible path from the given initial configuration to the final configuration and optimizing some criteria (such as minimizing path length) [1]–[3]. Instead of a deterministic representation of the free space, sampling-based algorithms [15] explore the free space by randomly sampling, e.g., probabilistic roadmap [16], rapidly exploring random tree (RRT) [17], and its variants [18]–[20]. Since both graph search algorithms and sampling-based algorithms describe the free space by a graph or tree, we would like to uniformly call them as roadmap algorithms [3]. It is easy for roadmap algorithms to find collision-free paths, but their returned paths tend to be unsmooth and may have sharp turns
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