Set-based Optimal, Robust, and Resilient Control with Applications to Autonomous Precision Landing

TL;DR

This paper introduces a real-time set-based predictive control framework for autonomous systems that ensures optimality, robustness, and resilience, demonstrated through autonomous precision landing with guarantees against uncertainties and capabilities for large maneuvers.

Contribution

The authors develop a novel offline precomputation method for controllable sets using constrained zonotopes, enabling real-time optimal control with robustness and resilience features.

Findings

Achieved globally optimal free-final-time guidance.

Demonstrated robustness to stochastic uncertainties.

Enabled large divert maneuvers and maximal decision-deferral.

Abstract

We present a real-time-capable set-based framework for closed-loop predictive control of autonomous systems using tools from computational geometry, dynamic programming, and convex optimization. The control architecture relies on the offline precomputation of the controllable tube, i.e, a time-indexed sequence of controllable sets. Sets are represented using constrained zonotopes (CZs), which are efficient encodings of convex polytopes that support fast set operations and enable tractable dynamic programming in high dimensions. Online, we obtain a globally optimal control profile by solving a series of one-step optimal control problems. Our key contributions are: (1) free-final-time optimality: we devise an optimal horizon computation algorithm to achieve global optimality; (2) robustness: we handle stochastic uncertainty in both the state and control, with probabilistic guarantees, by constructing bounded disturbance sets; (3) resilience: we develop (i) an optimization-free approach to computing the instantaneous reachable set, i.e., the reachable set from the current state, to enable, for example, large/maximal divert maneuvers, and (ii) an approach to achieving maximal decision-deferral, i.e., maintaining reachability/divert-feasibility to multiple targets for as long as possible. By means of an autonomous precision landing case study, we demonstrate globally optimal free-final-time guidance, robustness to navigation and actuation uncertainties, instantaneous divert envelope computation, and maximal decision-deferral.