Decoupling Collision Avoidance in and for Optimal Control using Least-Squares Support Vector Machines

TL;DR

This paper introduces a novel method that linearizes collision avoidance constraints in optimal control problems for convex shapes by using support vector machines, significantly improving computational efficiency.

Contribution

It presents a bi-level algorithm that transforms non-convex collision constraints into linear ones by framing the separating hyperplane as a classification problem, reducing computation time.

Findings

Reduces trajectory computation times by 50-90%.

Demonstrates scalability in cluttered environments.

Applicable to various motion planning approaches.

Abstract

This paper details an approach to linearise differentiable but non-convex collision avoidance constraints tailored to convex shapes. It revisits introducing differential collision avoidance constraints for convex objects into an optimal control problem (OCP) using the separating hyperplane theorem. By framing this theorem as a classification problem, the hyperplanes are eliminated as optimisation variables from the OCP. This effectively transforms non-convex constraints into linear constraints. A bi-level algorithm computes the hyperplanes between the iterations of an optimisation solver and subsequently embeds them as parameters into the OCP. Experiments demonstrate the approach's favourable scalability towards cluttered environments and its applicability to various motion planning approaches. It decreases trajectory computation times between 50\% and 90\% compared to a state-of-the-art approach that directly includes the hyperplanes as variables in the optimal control problem.