Closer to Optimal Angle-Constrained Path Planning

Abstract

Planning on grids and planning via sampling are the two classical mainstreams of path planning for intelligent agents, whose respective representatives are A* and RRT, including their variants, Theta* and RRT*. However, in the nonholonomic path planning, such us being under angle constraints, Theta* and Lazy Theta* may fail to generate a feasible path because the line-of-sight check (LoS-Check) will modify the original orientation of a state, which makes the planning process incomplete (cannot visit all possible states). Then, we propose a more delayed evaluation algorithm called Late LoS-Check A* (LLA*) to relax the angle constraints. Due to the nature of random sampling, RRT* is asymptotically optimal but still not optimal, then we propose LoS-Check RRT* (LoS-RRT*). In order to solve the problems caused by improper settings of the planning resolution, we propose the LoS-Slider (LoSS) smoothing method. Through experimental comparison, it can be found that angle-constrained versions of LLA* and LoS-RRT* can both generate the near-optimal paths. Meanwhile, the experiment result shows that LLA* performs better than Theta* and Lazy Theta* under angle constraints. The planned path will be even closer to the optimal (shortest) solution after the smoothing of LoSS algorithm.