GPU-Accelerated Continuous-Time Successive Convexification for Contact-Implicit Legged Locomotion
Samuel Buckner, Purnanand Elango
AI summary
Problem
Existing contact-implicit trajectory optimization methods rely on fine time discretization to capture contact events, which inflates problem size, increases runtime, and ties solution quality to grid resolution.
Approach
The authors extend continuous-time successive convexification to contact-implicit optimization by introducing integral cross-complementarity constraints that prevent missed contact events, solved via a GPU-accelerated sequential convex programming framework.
Key results
- Integral cross-complementarity constraints guarantee contact switches at discretization nodes
- GPU-accelerated Python implementation achieves over 10x speedup over existing SCP solvers
- Validated on HalfCheetah with physically consistent trajectories and lower energy consumption than MPC baselines
- Maximal-coordinate dynamics with time-dilation enable scalable real-time planning
Why it matters
Eliminates the accuracy-runtime tradeoff in contact-implicit planning, providing a scalable, real-time optimization tool for legged robotics researchers and autonomous system developers.
Abstract
Contact-implicit trajectory optimization (CITO) enables the automatic discovery of contact sequences, but most methods rely on fine time discretization to capture all contact events accurately, which increases problem size and runtime while tying solution quality to grid resolution. We extend the recently proposed sequential convex programming (SCP) approach for trajectory optimization, continuous-time successive convexification (CT-SCVX), to CITO by introducing integral cross-complementarity constraints, which eliminate the risk of missing contact events between discretization nodes while preserving the flexibility of contact mode changes. The result- ing framework, contact-implicit successive convexification (CI- SCVX), models full multibody dynamics in maximal coordinates, including stick-slip friction and partially elastic impacts. To handle complementarity constraints, we embed a backtracking homotopy scheme within SCP for reliable convergence. We implement this framework in a stand-alone Python software, leveraging JAX for GPU acceleration and a custom canonical- form parser for the convex subproblems of SCP to avoid the overhead of general-purpose modeling tools such as CVXPY. We demonstrate CI-SCVX on diverse legged-locomotion tasks. In particular, we validate the approach in MuJoCo with the Gymnasium HalfCheetah model against the MuJoCo MPC baseline, showing that a tracking simulation with the optimized torque profiles from CI-SCVX produces physically consistent trajectories with lesser energy consumption. We also show that the resulting software achieves faster solve times than existing state-of-the-art SCP implementations by over an order of magnitude, thereby demonstrating a practically important contribution to scalable real-time trajectory optimization.