Robust Control

Reach-Avoid-Stay (RAS) tasks are essential in applications where systems must safely reach a target set and remain within it under all bounded disturbances. Existing approaches either struggle to compute the maximal robust RAS set, the set of all states from which the RAS task is achievable, or are limited in handling general dynamic systems. To address these challenges, this paper proposes a two-step deep reinforcement learning framework that jointly learns the maximal robust RAS set and the corresponding control policy. The first step identifies the maximal robust control-invariant set within the target set and derives a policy that ensures the system remains within it. The second step computes the maximal robust reach-avoid (RA) set using this invariant set as the target, and it is proven that this RA set is equivalent to the maximal robust RAS set. Leveraging this result, a switching policy is constructed from the two step-wise policies, which constitutes a valid policy guaranteeing completion of the RAS task. Simulation results demonstrate that the proposed framework (1) computes the exact maximal robust RAS set in the absence of training errors, yielding the least restrictive RAS policy, and (2) identifies the RAS set with high accuracy while outperforming baseline methods on RAS tasks.

We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over $50$ states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.

Robotic cutting is a challenging, contact-rich manipulation task where the robot must simultaneously negotiate unknown object mechanics, large contact forces, and precise motion requirements. Our hypothesis is that this complexity can be alleviated through the design of a physically structured virtual-model controller that uses switched virtual mechanisms to generate a robust, rhythmic rock-chop motion for robotic cutting, without requiring pre-planned trajectories or precise environmental information. Motion is generated by the interaction between the environment, the robot's dynamics, and the virtual forces of the switching virtual mechanism, ultimately realized through the available actuation. Through theoretical and numerical analysis, together with experimental validation, we demonstrate that the controlled robot behavior settles into a stable periodic motion. Experiments with a Franka manipulator demonstrate robust cuts across five different vegetables, achieving sub-millimeter slice accuracy for thicknesses from 1 mm to 7 mm at a rate of nearly one cut per second. The controller maintains high performance despite changes in knife shape or cutting board height, and successfully adapts to a different humanoid manipulator, demonstrating robustness and platform independence.

This paper presents a systematic framework for computing formally guaranteed trajectory tracking error bounds for autonomous helicopters based on Robust Positive Invariant (RPI) sets. The approach establishes a closed-loop translational error dynamics which is cast into polytopic linear parameter-varying form with bounded additive and state-dependent disturbances. Ellipsoidal RPI sets are computed, yielding explicit position error bounds suitable as certified buffer zones in upper-level trajectory planning. Three controller architectures are compared with respect to the conservatism of their error bounds and tracking performance. Simulation results on a nonlinear helicopter model demonstrate that all architectures satisfy the derived bounds, while highlighting trade-offs between performance and the conservatism of the computed invariant set.