Oct 14, 2026J/K move · Enter open · S save
César E. Ramos Chuquiure, Ryan Tsai, Yutong Zhou, Zihang Huang+7
Department of Robotics, University of Michigan, Ann Arbor, MI, USA. · Computer Science and Engineering, University of Michigan, Ann Arbor, MI, USA. · Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA.
Generating dynamically feasible motions for legged and manipulating robots requires solving a large, nonlinear, non-convex optimal control problem (OCP) in which contact wrenches must satisfy friction-cone constraints throughout the motion, not only at isolated instants. Existing solvers are sensitive to the initial guess and scale poorly with the number of joints. This paper introduces LEAP, which transcribes the OCP with pseudospectral collocation and, instead of a Newton or SQP solve, integrates a primal--dual gradient flow of a Powell--Hestenes--Rockafellar augmented Lagrangian to compute a solution. Because the flow is stiff, this paper designs a linearly implicit integrator with a Gauss--Newton metric, momentum, and a merit-based step controller that keeps the augmented Lagrangian monotone. Across locomotion benchmarks on five robot platforms, from planar hoppers to 32-joint humanoids, LEAP is the only method to solve every tested problem, achieves substantial speedups over Crocoddyl and Aligator on several benchmarks, and reaches trackable references at smaller compute budgets. The resulting trajectories are validated by tracking them in a high-fidelity simulator and on hardware. We will make the code public upon final acceptance of this paper.