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This paper introduces ContactIPM, a novel primal-dual method for solving contact-implicit trajectory optimization problems characterized by mathematical programs with complementarity constraints (MPCCs). By integrating a stagewise optimal-control factorization with primal-dual consistency, ContactIPM effectively addresses the degeneracy issues that challenge conventional solvers. The method demonstrates significant performance improvements, achieving up to 8.87 times faster solutions compared to existing contact-specific solvers in benchmark tests while maintaining higher success rates in robustness evaluations.
ContactIPM outperforms traditional solvers by up to 8.87 times in speed while tackling complex contact-implicit trajectory optimization problems.
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,
