Nonlinear Robust Optimization for Planning and Control
🤖 AI Summary
This paper addresses robust optimal trajectory planning for constrained nonlinear systems subject to unknown but bounded disturbances, with the objective of guaranteeing control feasibility under all admissible disturbance realizations. We propose a bilevel robust trajectory optimization framework: the outer level models linearization errors as additional disturbances and explicitly characterizes the disturbance set; the inner level integrates trust-region-based sequential convexification, robust constraint linearization, and solvable convex reformulation, solved efficiently via an augmented Lagrangian method. We provide theoretical guarantees of robust feasibility while ensuring computational scalability and convergence. Extensive simulations across multiple nonlinear systems demonstrate that the proposed method significantly improves trajectory feasibility and closed-loop stability under disturbances, establishing a new paradigm for high-reliability autonomous systems.
Application Category
📝 Abstract
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with respect to all possible realizations of the disturbances within prescribed uncertainty sets. To address this problem, we introduce a bi-level optimization algorithm. The outer level employs a trust-region successive convexification approach which relies on linearizing the nonlinear dynamics and robust constraints. The inner level involves solving the resulting linearized robust optimization problems, for which we derive tractable convex reformulations and present an Augmented Lagrangian method for efficiently solving them. To further enhance the robustness of our methodology on nonlinear systems, we also illustrate that potential linearization errors can be effectively modeled as unknown disturbances as well. Simulation results verify the applicability of our approach in controlling nonlinear systems in a robust manner under unknown disturbances. The promise of effectively handling approximation errors in such successive linearization schemes from a robust optimization perspective is also highlighted.
Problem
Research questions and friction points this paper is trying to address.
Robust trajectory optimization for nonlinear systems under disturbances
Bi-level algorithm for robust feasible control policies
Handling linearization errors as disturbances in optimization
Innovation
Methods, ideas, or system contributions that make the work stand out.
Bi-level optimization for robust trajectory planning
Trust-region successive convexification for nonlinear dynamics
Augmented Lagrangian method for linearized problems
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