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Contact-implicit motion planning-embedding contact sequencing as implicitcomplementarity constraints-holds the promise of leveraging continuousoptimization to discover new contact patterns online. Nevertheless, theresulting optimization, being an instance of Mathematical Programming withComplementary Constraints, fails the classical constraint qualifications thatare crucial for the convergence of popular numerical solvers. We present robustcontact-implicit motion planning with sequential convex programming (CRISP), asolver that departs from the usual primal-dual algorithmic framework butinstead only focuses on the primal problem. CRISP solves a convex quadraticprogram with an adaptive trust region radius at each iteration, and itsconvergence is evaluated by a merit function using weighted penalty. We (i)provide sufficient conditions on CRISP's convergence to first-order stationarypoints 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-implicitplanning with naive initialization. In fact, CRISP solves severalcontact-implicit problems with all-zero initialization.

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