Towards Optimizing a Convex Cover of Collision-Free Space for Trajectory Generation

TL;DR

This paper introduces an online iterative algorithm to optimize convex polytopes that approximate obstacle-free space, enabling efficient trajectory planning for autonomous robots in complex environments.

Contribution

The paper presents a novel heuristic-based iterative method for optimizing convex covers of free space, improving trajectory generation in dynamic, obstacle-rich environments.

Findings

Effective in various parameterized environments

Facilitates two-stage motion planning

Outperforms baseline methods in trajectory optimization

Abstract

We propose an online iterative algorithm to optimize a convex cover to under-approximate the free space for autonomous navigation to delineate Safe Flight Corridors (SFC). The convex cover consists of a set of polytopes such that the union of the polytopes represents obstacle-free space, allowing us to find trajectories for robots that lie within the convex cover. In order to find the SFC that facilitates trajectory optimization, we iteratively find overlapping polytopes of maximum volumes that include specified waypoints initialized by a geometric or kinematic planner. Constraints at waypoints appear in two alternating stages of a joint optimization problem, which is solved by a novel heuristic-based iterative algorithm with partially distributed variables. We validate the effectiveness of our proposed algorithm using a range of parameterized environments and show its applications for two-stage motion planning.