Locally Optimal Solutions to Constraint Displacement Problems via Path-Obstacle Overlaps

TL;DR

This paper introduces a unified two-stage method for solving constraint displacement problems in robotics, optimizing obstacle displacements to enable feasible, collision-free paths for robots.

Contribution

It proposes a novel two-stage process that computes obstacle displacements to facilitate feasible robot trajectories, unifying approaches for different constraint displacement problems.

Findings

Successfully demonstrated on multiple problem classes

Achieves locally optimal obstacle displacements

Enables feasible robot paths in complex environments

Abstract

We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle displacements to enable a feasible path for the robot. The first stage proceeds by computing a trajectory through the obstacles while minimizing an appropriate objective function. In the second stage, these obstacles are displaced to make the computed robot trajectory feasible, that is, collision-free. Several examples are provided that successfully demonstrate our approach on two distinct classes of constraint displacement problems.