CMC-Opt: Constraint Manifold with Corners for Inequality-Constrained Optimization

TL;DR

This paper presents CMC-Opt, a manifold-based framework that transforms constrained optimization problems in robotics into unconstrained problems on a specialized manifold with corners, enabling more robust solutions.

Contribution

The paper introduces constraint manifolds with corners and extends manifold optimization algorithms to handle inequality constraints directly on this new topological structure.

Findings

Successfully generated dynamically feasible trajectories in kinodynamic planning

Demonstrated robustness over standard methods in large-scale problems

Extended manifold optimization algorithms to new topological structures

Abstract

We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the constrained state space. To achieve this, we introduce ``constraint manifolds with corners" to represent the state space satisfying mixed nonlinear equality and inequality constraints. We further extend manifold optimization algorithms to operate on this new topological structure. We demonstrate the power and robustness of our framework in the context of a large-scale kinodynamic planning problem, successfully generating dynamically feasible trajectories where standard methods fail.