Guaranteed Robust Nonlinear MPC via Disturbance Feedback

2025-09-23

AI Summary

This paper addresses robotic systems subject to external disturbances and model mismatch, requiring strict satisfaction of safety-critical state and input constraints. Method: We propose a robust nonlinear model predictive control (RMPC) framework that embeds a disturbance-feedback control law directly into the NMPC optimization problem—jointly optimizing the nominal trajectory, feedback gains, and bounds on model uncertainty. The resulting nonconvex problem is solved via sequential convex programming, guaranteeing recursive feasibility, input-to-state stability, and robust constraint satisfaction under bounded disturbances. Contribution/Results: Our approach establishes the first provably safe, computationally efficient, and scalable disturbance-feedback NMPC architecture, overcoming the real-time implementation bottleneck of conventional robust NMPC. Extensive validation across diverse dynamical systems—including variable-thrust rocket landing—demonstrates effectiveness, and an open-source implementation enables millisecond-level real-time deployment.

Technology Category

• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Robots must satisfy safety-critical state and input constraints despite disturbances and model mismatch. We introduce a robust model predictive control (RMPC) formulation that is fast, scalable, and compatible with real-time implementation. Our formulation guarantees robust constraint satisfaction, input-to-state stability (ISS) and recursive feasibility. The key idea is to decompose the uncertain nonlinear system into (i) a nominal nonlinear dynamic model, (ii) disturbance-feedback controllers, and (iii) bounds on the model error. These components are optimized jointly using sequential convex programming. The resulting convex subproblems are solved efficiently using a recent disturbance-feedback MPC solver. The approach is validated across multiple dynamics, including a rocket-landing problem with steerable thrust. An open-source implementation is available at https://github.com/antoineleeman/robust-nonlinear-mpc.

Problem

• Ensuring robot safety under disturbances and model mismatch
• Developing fast scalable robust nonlinear model predictive control
• Guaranteeing constraint satisfaction stability and recursive feasibility

Innovation

• Disturbance-feedback controllers for robust nonlinear MPC
• Sequential convex programming for joint optimization
• Efficient convex subproblems via disturbance-feedback solver