CacheMPC: Certified Cached Model Predictive Control for Quadruped Locomotion

2026-06-26

AI Summary

This work addresses the high computational cost of solving quadratic programs (QPs) in model predictive control (MPC) for quadrupedal robots on embedded platforms. The authors propose a certified caching MPC framework that exploits gait periodicity by constructing locality-sensitive hash caches based on contact modes to reuse contact force trajectories. Safety is ensured through primal feasibility verification and an upper bound on suboptimality derived from the duality gap. Coupled with a bounded-budget scheduling strategy, the method enables efficient deployment on an NVIDIA Orin NX platform. Experiments demonstrate a 25× speedup in MuJoCo simulation (18.7× on hardware) while maintaining closed-loop stability comparable to the baseline across 2,038 simulation trials and 50 edge-case tests.

Abstract

Model Predictive Control (MPC) is the standard predictive layer in hierarchical quadruped controllers, but the per-cycle QP solve limits the update rate achievable on embedded processors. Because legged gaits revisit a bounded region of state space, MPC solutions admit caching and reuse. This paper proposes \emph{Certified CacheMPC}: a Locality-Sensitive-Hashed cache of horizon contact-force trajectories, partitioned by contact mode, retrieved at query time and accepted only when an a-posteriori per-query certificate confirms primal feasibility and a Lagrangian dual-gap upper bound on cost suboptimality. A bounded-budget controller schedule combines top-$K$ certified retrieval, a deadline-bounded QP solve, and a shifted last-certified fallback. The framework is evaluated on a Unitree Go2 across $2{,}038$ usable cold-controller MuJoCo trials, including a $600$-trial $n\!=\!50$ campaign at three failure-boundary cells, and a first-deploy session on the on-robot NVIDIA Orin NX. The un-gated cache delivers a $25\times$ median solve-time speedup in simulation and an $18.7\times$ median speedup on hardware. At $n\!=\!50$ no statistically significant difference in closed-loop stable rate is detected between the cache variants and the no-cache baseline at any tested cell. The certificate's contribution to closed-loop safety is not resolvable at the present sample size.

Problem

• Model Predictive Control
• Quadruped Locomotion
• Real-time Optimization
• Embedded Control
• QP Solve

Innovation

• Certified CacheMPC
• Locality-Sensitive Hashing
• Model Predictive Control
• Dual-gap Certificate
• Quadruped Locomotion