Global Convergence of an SQP Method for Contact-Implicit Trajectory Optimization

arXiv:2406.01763v5 Announce Type: replace-cross Abstract: Contact-Implicit Trajectory Optimization (CITO) is a powerful framework for planning motions of robots that interact with complex environments, but its convergence behavior remains difficult to characterize. Existing formulations either rely on off-the-shelf nonlinear programming solvers whose guarantees require constraint qualifications that are hard to verify for contact-rich systems, or require differentiable explicit dynamics maps that are difficult to formulate in the presence of impacts, changing contact modes, and geometric non-smoothness. This paper studies CITO for a broader class of constraint-rich dynamic systems formulated through implicit physics constraints. By exploiting maximal-coordinate structure, penalty relaxations of equality and inequality constraints, and finite-horizon Hamiltonian bounds, we prove global convergence in the numerical-optimization sense for a specific line-search Sequential Quadratic Programming (SQP) method with adaptive timestep refinement. Under the stated constraint-rich dynamic-system assumptions and fixed pre-horizon data satisfying the strict-interior predecessor condition, the method terminates finitely from any finite discretized optimized trajectory guess at an epsilon-feasible, force-parameterized stationary point---a unit-objective, penalty-induced force-parameterized Fritz--John certificate for smooth damping, weakening to a homogeneous force-parameterized Clarke--Fritz--John certificate whose objective multiplier may vanish under nonsmooth frictional contact.

Source: arXiv cs.RO | 2026-08-14