Residual-Conservative Model Predictive Path Integral Control is proposed, a sampling-based MPC framework that modulates safety conservatism online using the prediction-execution residual and shows improved safety margin, success rate, and control efficiency compared with vanilla MPPI under significant model-plant mismatch.
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.
Model Predictive Path Integral (MPPI) control is directly implementable on nonlinear systems because its online update requires only forward rollouts of the dynamics, not gradients, linearizations, or convex optimization. However, this algorithmic flexibility does not by itself provide a closed-loop stability certificate. This paper establishes such a certificate through a stability-inheritance argument. We assume that there exists a deterministic nonlinear MPC policy whose disturbance-free closed loop is certified by a Control Lyapunov Function terminal cost and a contraction metric, and we show that finite-sample MPPI inherits the nominal contraction when its sampling-based update approximates this reference policy with sufficient accuracy. The approximation error decomposes into a finite-temperature bias floor and a Monte Carlo term that vanishes at the inverse square-root rate in the sample count. Under an explicit small-gain condition, the resulting MPPI closed loop satisfies a finite-horizon, high-probability localized mean practical stability bound with residual floors due to MPPI approximation error, Gaussian process noise, and bad sampling events. The paper also gives an ISS-type restatement and a finite-horizon design procedure for choosing the localization set, temperature, and sample count.
Multi-step rollouts are essential for model-based reinforcement learning (RL) and predictive control, yet learned dynamics models often become unstable when recursively applied, leading to divergence and unreliable policy updates. This paper proposes a model-agnostic hybrid dynamics framework that blends a provably contracting nominal model with a flexible excursion model through an uncertainty-guided switching law. The switching signal is derived from calibrated epistemic uncertainty and activates only when the system leaves the nominal region, ensuring that each model operates within its reliability regime. Under clearly stated smoothness and boundedness assumptions, we show that the resulting hybrid predictor yields globally bounded recursive multi-step rollouts: trajectories remain Lyapunov-stable in the nominal region and exhibit at most affine growth during excursions. To illustrate the theory in practice, we instantiate the hybrid dynamics framework within a model-based RL scheme that uses real one-step transitions for value learning and hybrid rollouts for policy improvement. Experiments on a nonlinear Duffing oscillator demonstrate stable long-horizon prediction and improved cost-effort trade-offs relative to a stabilizing baseline.
This study presents and validates a minimum-lap-time planning (MLTP) framework for motorsport applications that embeds robustness against both state disturbances and parameter uncertainty. The methodology builds upon a prior disturbance-aware framework that, at each track point, propagates stochastic vehicle dynamics over a short horizon and tightens tyre-friction constraints based on the worst-case scenario at horizon end. We extend the formulation to account for uncertainty in key vehicle parameters: moment of inertia, centre-of-mass position, and aerodynamic drag coefficient. To keep the extended formulation computationally tractable, a spatially selective, parsimonious activation strategy confines the robust constraints to the circuit segments where they are most critical. We demonstrate the improved driveability of the robust references by employing a model predictive controller (MPC) as a virtual test driver. For each reference, the same MPC drives a simulated FSAE (Formula SAE) car over 1000 runs on a representative Barcelona-Catalunya sector, with randomly realised impulsive disturbances and parameter scatter. We compare a nominal reference, planned without robustness, against its robust counterparts. The latter yield consistently fewer failed runs and, at a moderate sector-time cost, show tighter dispersion of key signals (vehicle inputs, axle saturations) around the reference values, evidence of better trackability.
Martino Gulisano, Matteo Masoni, M. Gabiccini· 0 citations