CMC-Opt: Constraint Manifold with Corners for Inequality-Constrained Optimization
For robotics optimization problems with mixed constraints, this framework offers a novel geometric approach that outperforms standard methods in challenging scenarios.
The paper introduces a manifold-based framework for optimization with equality and inequality constraints, transforming them into an unconstrained problem on a 'constraint manifold with corners'. It demonstrates robustness in large-scale kinodynamic planning, generating feasible trajectories where standard methods fail.
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.