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, which are sets that contain all possible states that can reach a terminal set under state and control constraints. 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 via a forward rollout, i.e., by solving a series of one-step optimal control problems, each of which takes the current state to the next controllable set in the tube. Our key contributions are: (1) free-final-time optimality: we devise an optimal horizon computation algorithm to achieve global optimality, and (2) robustness: we handle stochastic uncertainty in both the state and control, with probabilistic guarantees, by constructing bounded disturbance sets. The optimal control approach we propose is exact (approximation-free) for optimal control problems with polytopic feasible sets, and conservative in the right direction for their robust variants. By means of an autonomous precision landing case study, we demonstrate globally optimal free-final-time guidance and robustness to navigation and actuation uncertainties.