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

2026-05-20

AI Summary

This work addresses the challenge of nonlinear optimization with mixed equality and inequality constraints in robotic dynamics planning by introducing a novel approach based on “constraint manifolds with corners.” The method reformulates the original problem as an unconstrained optimization over a constrained state space, seamlessly embedding inequality constraints into the manifold structure through differential geometry and manifold optimization techniques. This formulation overcomes the conventional limitation of manifold optimization, which typically applies only to smooth equality constraints. Evaluated on large-scale dynamic planning tasks, the proposed approach successfully generates dynamically feasible trajectories and demonstrates superior robustness and solvability in scenarios where standard algorithms fail.

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.

Problem

• inequality-constrained optimization
• constraint manifold
• kinodynamic planning
• dynamically feasible trajectories
• nonlinear constraints

Innovation

• constraint manifolds with corners
• inequality-constrained optimization
• manifold optimization
• kinodynamic planning
• nonlinear constraints