GPU-Accelerated Continuous-Time Successive Convexification for Contact-Implicit Legged Locomotion

Researchers Samuel C. Buckner and Purnanand Elango have introduced ci-SCvx (contact-implicit successive convexification), a breakthrough framework for optimizing how legged robots move. The system tackles a fundamental challenge in robotics: planning motions where limbs make and break contact with surfaces. Traditional methods require finely discretized time steps to capture every potential contact event, which dramatically increases computation time and ties solution quality to grid resolution. ci-SCvx solves this by using integral cross-complementarity constraints within a sequential convex programming (SCP) approach, allowing it to model complex dynamics—including stick-slip friction and partially elastic impacts—while automatically discovering optimal contact sequences without missing events between time nodes.

The team implemented the framework as standalone Python software leveraging JAX for GPU acceleration, bypassing slower general-purpose modeling tools like CVXPY. This architectural choice is key to its performance. In validation tests using the Gymnasium HalfCheetah model in MuJoCo, trajectories optimized by ci-SCvx consumed less energy than those from the standard MuJoCo MPC baseline. Most impressively, the software achieves solve times that are over an order of magnitude (more than 10x) faster than existing state-of-the-art SCP implementations. This performance leap, presented in a paper accepted to IEEE ICRA 2026, moves complex trajectory optimization from an offline planning task toward a scalable tool for real-time robot control.