A Differentiable Signed Distance Representation for Continuous Collision Avoidance in Optimization-Based Motion Planning

TL;DR

This paper introduces a differentiable, support function-based collision avoidance method for optimization-based motion planning, enabling continuous, reliable collision avoidance with fewer variables and constraints.

Contribution

It presents a novel, continuously differentiable collision avoidance condition compatible with nonlinear optimization, improving efficiency and robustness in motion planning.

Findings

Reduces variables and constraints compared to existing methods.

Ensures continuous collision avoidance during vehicle transitions.

Prevents corner cutting and obstacle passing in motion planning.

Abstract

This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with standard nonlinear optimization solvers. The method represents convex shapes using a support function representation and is therefore quite general. For collision avoidance involving polyhedral or ellipsoidal shapes, the proposed method introduces fewer variables and constraints than existing approaches. Additionally the proposed method can be used to rigorously ensure continuous collision avoidance as the vehicle transitions between the discrete poses determined by the motion planning algorithm. Numerical examples demonstrate how this can be used to prevent problems of corner cutting and passing through obstacles which can occur when collision avoidance is only enforced at discrete time steps.