RC-MPPI: New adaptive control algorithm boosts robot safety when models are wrong

Hyung-Jin Yoon and Hunmin Kim have introduced Residual-Conservative Model Predictive Path Integral Control (RC-MPPI), a sampling-based MPC framework that dynamically adjusts safety conservatism based on the prediction-execution residual—the difference between what a model predicts and what actually happens. Traditional MPPI methods use fixed constraint penalties that don't adapt to model-plant mismatch, leading to either overly aggressive or overly conservative behavior. RC-MPPI tackles this with three coupled mechanisms: residual-dependent constraint tightening (making constraints stricter when the model is unreliable), adaptive safety-cost shaping, and residual-adaptive sampling modulation (contracting exploration and relaxing temperature). The temperature relaxation is a key insight—when the model is inaccurate, rollout cost evaluations become unreliable, so increasing temperature reduces overcommitment to apparent cost rankings.

Under Lipschitz dynamics and sub-Gaussian disturbances, the authors derive probabilistic bounds on constraint violation, showing that the joint adaptive mechanisms reduce violation probability as the residual grows. A rollout-cost uncertainty analysis reveals that model-plant mismatch perturbs MPPI importance weights proportionally to residual magnitude and inversely with temperature, providing theoretical justification for the adaptive approach. Simulations on both an LTI point-mass system and a planar 2R manipulator demonstrate that RC-MPPI achieves better safety margins, higher success rates, and improved control efficiency compared to vanilla MPPI under significant model-plant mismatch. The paper is part of a companion series on MPPI closed-loop reliability and robustness.