Full-Order Safety for Nonlinear Reduced-Order MPC

Luis Pabon; Johannes Köhler; Revant Kasichainula; Marco Pavone

cs.ROOct 13, 2026

Full-Order Safety for Nonlinear Reduced-Order MPC

Authors: Luis Pabon, Johannes Köhler, Revant Kasichainula, Marco Pavone

Organizations: Department of Aeronautics and Astronautics, Stanford University, USA · Department of Mechanical Engineering, Imperial College London, UK

Abstract

Reduced-order models (ROMs) make model predictive control (MPC) of high-dimensional nonlinear systems tractable, but the resulting modeling error can lead to constraint violations on the real system. We introduce CoRE-MPC, a robust MPC formulation that plans with a nonlinear ROM and guarantees recursive feasibility and constraint satisfaction for the full-order system. It can be applied with a broad class of nonlinear model reduction techniques and the resulting MPC does not require evaluating the full-order model online, thus ensuring computational efficiency. The key insight is in how the ROM affects the dynamics of the prediction error. We account for this with two error radii that are propagated alongside the ROM and provide a guaranteed bound on the prediction error. The approach is validated in simulation on an 80-state oscillator chain, a Burgers equation, and a 9,768-state finite-element soft robot, where a two-state ROM with data-driven bounds keeps all 1,628 nodes clear of a wall at a median solve time below 1 ms for a 20 ms control period. Across these examples, CoRE-MPC is 13 to 61 times faster than full-order robust MPC at only 27 to 35% higher closed-loop cost, whereas existing certified schemes are either infeasible or at least twice as conservative. Code: [released upon publication].

Figures & tables

Fig. 2: Oscillator chain. FOM-MPC (purple), CoRE-MPC (blue), Constant CoRE (orange), RN-ROMPC (green), and nominal ROM-MPC (gray). (a) Forty masses driven by one actuator with the shape of the first mode; every displacement is constrained. (b) Largest normalized displacement over all masses in the case with the largest nominal violation. (c) Median closed-loop cost over the

48

cases relative to FOM-MPC; nominal ROM-MPC is excluded because it violates the constraint. (d) Solve times over

495

warm updates per controller from five cases run serially in balanced order on one thread. Boxes show quartiles, lines medians, whiskers the most extreme samples within

1.5

interquartile ranges, and circles outliers.

Fig. 3: Burgers equation. Nominal ROM-MPC (gray), FOM-MPC (purple), and CoRE-MPC (blue). (a) Field at

t^{*}=2.2

s with the reference (dotted), the limit (dashed), and the actuator locations (triangles). (b) Largest normalized field value over all nodes. (c) CoRE-MPC radii (solid) and realized errors (dashed) over the first second; the tangential radius, chosen by the optimizer, restarts at zero after the first update, whereas the transverse radius is carried over. (d) Solve times over

316

updates per controller from four cases, with box conventions as in Fig. 2 .

Fig. 4: Soft robot. CoRE-MPC (blue), Constant CoRE (orange), RN-ROMPC (green), and nominal ROM-MPC (gray). (a) Tip paths and the reference (dotted). (b) RMS tip tracking error over one complete reference traversal (

0.3

3.3

s). (c) Minimum clearance over all

1{,}628

nodes; red marks wall penetration. (d) Controller wall times over

190

updates, including the check of all nodes, with box conventions as in Fig. 2 ; times exclude FEM integration.

Model Predictive Control

Model Predictive Control optimizes future actions with a system model, repeatedly applying the first action as new information arrives.

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Model Predictive Control Nonlinear MPC MPPI Control Constrained Optimization

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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.

Abstract

Model Predictive Control

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