An Online Motion Planning Approach of Mobile Robots in Distinctive Homotopic Classes by a Sparse Roadmap

Abstract

This paper presents a novel approach for online motion planning of mobile robots in distinctive homotopic classes. The approach contains two parts. Firstly, a local planner called TC-SQP (timed control and sequential quadratic programming) is proposed. An optimal trajectory is deformed from an initial path from a global planner, considering collision avoidance, time optimality and kino-dynamic constraints. Our approach takes the control variables rather than position variables as optimization variables in a time horizon. Hence, TC-SQP requires fewer optimization variables (3/4 comparing to the state-of-art method) and parameters. And the transition time is reduced by 14% from the global path. Then, to overcome the issue that there exist several trajectories of local minimum cost, a candidate of global paths of different homotopic classes is maintained by using a sparse graph spanner. These global paths are optimized in parallel, and the lowest cost trajectory is selected as the final trajectory. Our method can generate enough homotopic candidates, and it needs much fewer queries comparing with a Probability Road Map. Besides the simulations, some results are also proved theoretically.