Residual-Conservative Model Predictive Path Integral Control

2026-07-07

AI Summary

This work addresses the safety limitations of Model Predictive Path Integral (MPPI) control under model-plant mismatch, where fixed constraint penalties can lead to inadequate safety guarantees. To overcome this, the paper proposes a Residual-aware Constrained MPPI framework (RC-MPPI) that dynamically adjusts constraint boundaries, safety cost weights, and sampling temperature online using prediction-execution residuals. This enables adaptive conservatism by tightening constraints, relaxing sampling temperature, and perturbing importance weights based on residual feedback. The authors derive probabilistic bounds on constraint violation through rigorous analysis of these residual-driven adjustments, thereby reducing reliance on potentially unreliable cost evaluations. Simulations on both a linear time-invariant point-mass system and a 2R planar manipulator demonstrate that RC-MPPI significantly outperforms standard MPPI, achieving notable improvements in safety, task success rate, and control efficiency.

Abstract

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.

Problem

• model-plant mismatch
• constraint violation
• sampling-based MPC
• safety conservatism
• nonlinear dynamics

Innovation

• Residual-Conservative MPC
• Adaptive Temperature Relaxation
• Model-Plant Mismatch
• Constraint Tightening
• Path Integral Control