Fast and Resilient Optimization-based Control with Spacecraft Applications

Abstract

Trajectory optimization, which forms a key component of modern guidance, navigation, and control (GNC) systems, occupies the middle layer within a three-layer hierarchy, where the top layer is mission planning (or high-level decision making) and the bottom layer consists of low-level computation in the form of general-purpose solvers for optimization problems and feedback controllers. In this dissertation, we develop fast and resilient optimization-based solution methods that cover the full stack---spanning the three layers and tightly integrating them---while remaining anchored to the middle layer. First, we develop a convergence-guaranteed, real-time-capable solution method for nonconvex trajectory optimization, based on sequential convex programming (SCP) and isoperimetric constraint reformulation, that ensures continuous-time path constraint satisfaction. Next, we customize a first-order conic optimization algorithm, by exploiting the sparsity structure of trajectory optimization problems, to obtain a real-time-capable solver implementation that is suitable for embedded applications. Consequently, the overhead of a parser layer between the middle and bottom layers is eliminated. Finally, we embed a class of mission requirements (to ensure resilience to unmodeled uncertainties and contingencies) within a trajectory optimization problem, which can then be solved using the solution methods that we developed. We demonstrate the suite of solution methods via numerical examples based on real-world optimal control applications: precision six-degree-of-freedom (6-DoF) rocket landing, quadrotor motion planning, dynamic obstacle avoidance, and three-degree-of-freedom (3-DoF) rocket landing with lossless convexification. Furthermore, we develop optimization-based closed-loop control strategies specialized to spacecraft applications in the cislunar space, such as station keeping, autonomous optical navigation, and passively-safe rendezvous on the near rectilinear halo orbit (NRHO). Again, the motivation is to design solution methods that combine two layers of the hierarchy---(middle) feedforward trajectory optimization and (bottom) feedback control. We demonstrate that exploiting properties of the dynamic behavior of the system and its environment is useful for designing lightweight algorithms (suitable for onboard deployment) that can deliver the required performance.