On the Surprising Robustness of Sequential Convex Optimization for Contact-Implicit Motion Planning

TL;DR

This paper introduces CRISP, a robust sequential convex programming method for contact-implicit motion planning that reliably finds solutions even from naive initializations, addressing challenges in mathematical programming with complementarity constraints.

Contribution

The paper presents CRISP, a novel convex optimization solver for contact-implicit motion planning that demonstrates robustness and convergence without relying on classical constraint qualifications.

Findings

CRISP reliably solves contact-implicit planning problems from naive initializations.

CRISP converges to first-order stationary points under certain conditions.

The implementation is high-performance and publicly available.

Abstract

Contact-implicit motion planning-embedding contact sequencing as implicit complementarity constraints-holds the promise of leveraging continuous optimization to discover new contact patterns online. Nevertheless, the resulting optimization, being an instance of Mathematical Programming with Complementary Constraints, fails the classical constraint qualifications that are crucial for the convergence of popular numerical solvers. We present robust contact-implicit motion planning with sequential convex programming (CRISP), a solver that departs from the usual primal-dual algorithmic framework but instead only focuses on the primal problem. CRISP solves a convex quadratic program with an adaptive trust region radius at each iteration, and its convergence is evaluated by a merit function using weighted penalty. We (i) provide sufficient conditions on CRISP's convergence to first-order stationary points of the merit function; (ii) release a high-performance C++ implementation of CRISP with a generic nonlinear programming interface; and (iii) demonstrate CRISP's surprising robustness in solving contact-implicit planning with naive initialization. In fact, CRISP solves several contact-implicit problems with all-zero initialization.