CacheMPC: Certified Cached Model Predictive Control for Quadruped Locomotion

Nimesh Khandelwal, Mehul Anand, Shakti S. Gupta, Mangal Kothari

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.