ContactIPM: A Structure-Exploiting Interior-Point Solver for Contact-Implicit Trajectory Optimization

2026-08-12

AI Summary

This work addresses the computational challenges posed by the degeneracy of Mathematical Programs with Complementarity Constraints (MPCCs) derived from contact-implicit trajectory optimization, which hinders efficient solution by conventional solvers. The authors propose a novel approach that integrates a phase-decomposition structure with complementarity constraint relaxation, embedding complementary inequality pairs via a barrier-coupled elastic interior-point method. The method performs stage-wise elimination and leverages Riccati recursion to efficiently solve the reduced Newton system. It pioneers the integration of structure-aware optimal control solvers with MPCC handling, introducing a multi-stage warm-start strategy and a physics-informed complementarity residual-based termination criterion. Experiments demonstrate that the proposed method achieves speedups of 2.17–8.87× over CRISP on multiple benchmarks and outperforms IMPACT by factors of 2.96× and 4.91× on Push T and Cart Transport tasks, respectively, while exhibiting superior robustness.

Abstract

Contact-implicit trajectory optimization avoids prescribing contact sequences, but yields mathematical programs with complementarity constraints (MPCCs) whose degeneracy challenges conventional primal--dual solvers. Existing contact-specific methods improve robustness to this degeneracy but do not leverage a stagewise optimal-control factorization and primal--dual consistency, while structure-exploiting optimal-control solvers are not designed for complementarity constraints. We show that these capabilities can be combined in a single primal--dual method. ContactIPM identifies complementary inequality pairs, embeds them through a barrier-coupled elastic interior relaxation, eliminates slack and dual variables stagewise, and solves the reduced Newton system using a Riccati recursion. A fixed multi-phase MPCC recovery schedule provides four continuation and restart attempts from naive initializations, while termination is gated by the unrelaxed physical complementarity residual. We compare ContactIPM with two contact-specific MPCC solvers, CRISP and IMPACT, using matched benchmark conditions and common post-solve acceptance criteria. On four fixed CRISP benchmark cases, ContactIPM is $2.17$--$8.87\times$ faster over 20 paired timing repetitions per case and achieves higher success on the Push Box and Push-T robustness suites. Against IMPACT, ContactIPM is \(2.96\times\) faster on Push T and \(4.91\times\) faster on Cart Transport, but \(4.46\times\) slower on Push Box. In 50 closed-loop Push Box rollouts spanning model mismatch, measurement noise, initial-pose errors, and state resets,

Problem

• contact-implicit trajectory optimization
• complementarity constraints
• MPCC
• degeneracy
• primal-dual solvers

Innovation

• contact-implicit trajectory optimization
• complementarity constraints
• structure-exploiting solver
• interior-point method
• Riccati recursion