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This paper introduces Residual-Conservative Model Predictive Path Integral Control (RC-MPPI), a novel sampling-based MPC framework that dynamically adjusts safety constraints based on prediction-execution residuals to address model-plant mismatches. By integrating mechanisms such as residual-dependent constraint tightening and adaptive safety-cost shaping, RC-MPPI effectively enhances control performance in the presence of nonlinear dynamics and complex cost landscapes. The results demonstrate that RC-MPPI significantly improves safety margins and success rates in simulations compared to traditional MPPI methods, particularly under conditions of substantial model inaccuracies.
Adaptive safety mechanisms in RC-MPPI reduce constraint violations by leveraging prediction-execution residuals, outperforming traditional methods in uncertain environments.
Sampling-based model predictive control methods handle nonlinear dynamics and complex cost landscapes through Monte Carlo rollouts, yet typically employ fixed constraint penalties that do not adapt to model-plant mismatch. This paper proposes Residual-Conservative Model Predictive Path Integral Control (RC-MPPI), a sampling-based MPC framework that modulates safety conservatism online using the prediction-execution residual. RC-MPPI combines three coupled mechanisms: residual-dependent constraint tightening, adaptive safety-cost shaping, and residual-adaptive sampling modulation through exploration contraction and temperature relaxation. The temperature adaptation reflects a key insight: when the model is inaccurate, rollout cost evaluations become unreliable, and increasing temperature reduces overcommitment to apparent cost rankings. Under Lipschitz dynamics and sub-Gaussian disturbances, we derive probabilistic bounds on constraint violation and show that the joint effect of the adaptive mechanisms reduces violation probability as the residual grows. A rollout-cost uncertainty analysis further shows that model-plant mismatch perturbs MPPI importance weights in proportion to residual magnitude and inversely with temperature, providing theoretical justification for residual-adaptive temperature relaxation. Simulations on an LTI point-mass system and a planar 2R manipulator show improved safety margin, success rate, and control efficiency compared with vanilla MPPI under significant model-plant mismatch.
