Constrained Control and Online Safety Filtering for Autonomous Space Systems

Abstract

This dissertation presents advances in the design of constrained control laws, specifically control barrier function (CBF) quadratic program (QP) based control laws, herein called safety filters, with a focus on space systems applications. At present, most complex space systems tasks are solved by computing trajectories on the ground and then uplinking these trajectories to the spacecraft to follow. As humans venture further into the Solar System, and launch an ever increasing number of Earth-orbiting satellites each year, there is a need for control laws that can perform more complex tasks with less ground-based supervision. At the same time, on the ground, people are surrounded by more and more autonomous systems, and there is a need for controls tools for the safety supervision of such systems. CBF-QP safety-filters provide a computationally efficient framework for both constructing constrained control laws for these ground and space applications, including nonlinear systems, and for provably demonstrating that systems satisfy given safety constraints without requiring an engineer to review every trajectory. However, constructing a CBF and safety filter for given system dynamics is still a nontrivial problem.

In brief, this dissertation presents 1) tools to constructively design CBFs that are applicable to common spacecraft dynamics, and 2) extensions to safety filters that account for realistic control law implementation in space. Though motivated by spacecraft, both of these topics are equally relevant to other robotic systems.

Following an introductory chapter reviewing constrained control methodologies, the second chapter provides a thorough technical overview of CBFs and safety filters. The third chapter presents the "high relative-degree problem", and constructive methodologies for deriving CBFs that solve this problem while respecting input constraints. This chapter assumes a deterministic system, so the fourth chapter extends safety filters to provably guarantee safety for systems with bounded uncertainties, and then modifies these constructions accordingly. Notably, these constructions still provably satisfy input constraints, whereas prior work usually relaxes input constraints if the model is uncertain. This chapter also presents conditions on when so-called "tight-tolerance objectives" are feasible with an uncertain model, and constructive tools for achieving such objectives with safety filters.

The fifth chapter considers the effect of sampled measurements and both zero-order-hold and impulsive actuators. These phenomena more closely model how real spacecraft hardware operates. Emphasis is placed on quantifying and then minimizing conservatism. The sixth chapter presents results on how to modify the CBF construction when the safety filter is tasked with enforcing many constraints simultaneously.

The seventh chapter presents one more tool for constructing CBFs, specifically for systems with large time-scales and small actuators. This type of CBF relies on future predictions of the state trajectory, but is distinct from model predictive control (MPC) and incurs a fraction of the computational cost of MPC. The eighth chapter presents conclusions and application remarks. Rather than focusing on a single space system, case studies for various robotic and space systems are presented throughout. In summary, this dissertation presents an array of tools for designing CBFs for several space (weak gravity asteroid, high gravity asteroid, planetary orbits, attitude control, relative-motion/docking) and robotic (unicycle, double integrator, car intersection) domains and safety filters for several implementation scenarios (continuous, zero-order-hold, impulsive, perturbed), and thus enables space missions and other constrained control applications that would require higher degrees of autonomy than was previously achievable.