A Generalized Continuous Collision Detection Framework of Polynomial Trajectory for Mobile Robots in Cluttered Environments

TL;DR

This paper presents a generalized continuous collision detection framework for mobile robots following polynomial trajectories, enabling provable collision checking and exact impact timing in cluttered environments.

Contribution

It introduces a polynomial inequality-based collision detection method that is efficient, generalizable to various robot types, and integrates with navigation systems for safe operation.

Findings

Efficient polynomial inequality solver for collision detection

Proves collision checking and impact timing accuracy

Enables safe navigation in complex environments

Abstract

In this paper, we introduce a generalized continuous collision detection (CCD) framework for the mobile robot along the polynomial trajectory in cluttered environments including various static obstacle models. Specifically, we find that the collision conditions between robots and obstacles could be transformed into a set of polynomial inequalities, whose roots can be efficiently solved by the proposed solver. In addition, we test different types of mobile robots with various kinematic and dynamic constraints in our generalized CCD framework and validate that it allows the provable collision checking and can compute the exact time of impact. Furthermore, we combine our architecture with the path planner in the navigation system. Benefiting from our CCD method, the mobile robot is able to work safely in some challenging scenarios.