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We present a semi-infinite program (SIP) solver for trajectory optimizationsof general articulated robots. These problems are more challenging thanstandard Nonlinear Program (NLP) by involving an infinite number of non-convex,collision constraints. Prior SIP solvers based on constraint sampling cannotguarantee the satisfaction of all constraints. Instead, our method uses aconservative bound on articulated body motions to ensure the solutionfeasibility throughout the optimization procedure. We further use subdivisionto adaptively reduce the error in conservative motion estimation. Combined, weprove that our SIP solver guarantees feasibility while approaches the criticalpoint of SIP problems up to arbitrary user-provided precision. We have verifiedour method on a row of trajectory optimization problems involving industrialrobot arms and UAVs, where our method can generate collision-free, locallyoptimal trajectories within a couple minutes.

Provably Robust Semi-Infinite Program Under Collision Constraints via Subdivision