A Linear and Exact Algorithm for Whole-Body Collision Evaluation via Scale Optimization

TL;DR

This paper introduces a fast, exact, and linear algorithm for whole-body collision evaluation that can be efficiently integrated into optimization processes, significantly improving accuracy and computational speed.

Contribution

The paper presents a novel zero-gap collision evaluation method formulated as a low-dimensional linear program, solvable analytically in linear time.

Findings

Analytical solution in O(m) time for collision evaluation

Efficient gradient computation for optimization

Zero-gap, accurate collision assessment

Abstract

Collision evaluation is of vital importance in various applications. However, existing methods are either cumbersome to calculate or have a gap with the actual value. In this paper, we propose a zero-gap whole-body collision evaluation which can be formulated as a low dimensional linear program. This evaluation can be solved analytically in O(m) computational time, where m is the total number of the linear inequalities in this linear program. Moreover, the proposed method is efficient in obtaining its gradient, making it easy to apply to optimization-based applications.