Full-Order Safety for Nonlinear Reduced-Order MPC

Safe robot control often requires combining long-horizon performance optimization with hard state and input constraints, but existing approaches tend to address this tradeoff partially. Sampling-based model predictive control (MPC) methods such as model predictive path integral (MPPI) are effective in handling nonlinear and nonconvex environments, yet their finite-sample rollouts and unconstrained weighted-average update can return an unsafe control. Deterministic nonlinear MPC can explicitly incorporate constraints, but its real-time safety and performance depends strongly on warm starts and local convergence. Hamilton--Jacobi reachability (HJR) provides rigorous safety certificates, but offline value-function computation remains practical only for reduced-order models. We propose ReSQ-MPPI, a reachability-informed generation--refinement architecture that combines these complementary strengths. An HJR value function computed offline for a reduced-order model guides online MPPI sampling toward safe, promising trajectory candidates. The MPPI solution is then refined by a small number of sequential quadratic programming (SQP) iterations in a full-order MPC problem. A key observation is that the standard MPPI inference step is an unconstrained weighted least-squares problem; ReSQ-MPPI replaces it with a constrained MPC refinement that recovers the MPPI update when it is feasible and minimally modifies it otherwise. Simulations in cluttered navigation and autonomous racing environments demonstrate that ReSQ-MPPI improves safety and performance over standalone MPPI, MPC, and reachability-filtered sampling-based control baselines.

The practical deployment of nonlinear model predictive control (NMPC) is often limited by online computation: solving a nonlinear program at high control rates can be expensive on embedded hardware, especially when models are complex or horizons are long. Learning-based NMPC approximations shift this computation offline but typically demand large expert datasets and costly training. We propose Sequential-AMPC, a sequential neural policy that generates MPC candidate control sequences by sharing parameters across the prediction horizon. For deployment, we wrap the policy in a safety-augmented online evaluation and fallback mechanism, yielding Safe Sequential-AMPC. Compared to a naive feedforward policy baseline across several benchmarks, Sequential-AMPC requires substantially fewer expert MPC rollouts and yields candidate sequences with higher feasibility rates and improved closed-loop safety. On high-dimensional systems, it also exhibits better learning dynamics and performance in fewer epochs while maintaining stable validation improvement where the feedforward baseline can stagnate.

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.