Real-time Optimization in Aerospace Systems

Abstract

Algorithm design for autonomous vehicles has been attracting immense research interest, and with the proliferation of self-driving cars, autonomous drone delivery systems, and the increasing availability of commercial off--the--shelf UAVs, interest will only continue growing. The goal of this dissertation is to leverage recent advances in optimal control theory and optimization to provide methods that aid in the design and safe operation of autonomous vehicles (i.e., operating vehicles without violating mission constraints or hardware limits). To this end, we leverage convex optimization and a recent result from optimal control theory called lossless convexification, whereby problems with non-convex control constraints are cast into equivalent convex ones. Convex optimization is then applied to all stages of a mission: from top level vehicle design, to high-level autonomy onboard the vehicle, to trajectory planning, and finally down to allocating desired controls to individual actuators. This dissertation first presents an architecture for generating customized C solvers that were designed specifically for use onboard systems with limited computational resources. Solver customization exploits knowledge of the problem structure to generate solvers that are 2-3 orders of magnitude more efficient than generic solvers. One such customized solver was flight tested onboard Masten's Xombie rocket during the summers of 2012 and 2013. For mission planning and high-level autonomy, this document develops a convex optimization based method for approximating constrained, finite-time-horizon reachable and controllable sets with inner and outer bounding polytopes. These sets can be used to quickly understand the impact of different design parameters during the design process, or to determine the feasibility of goal states once in flight. Then, the document extends the theory of lossless convexification to cover maximal divert trajectories with simultaneously active thrust pointing and velocity constraints, and develops a method for computing locally optimal trajectories that avoid obstacles. Finally, for a momentum control system, this document presents a convex optimization based real-time control allocation algorithm to optimally utilize multiple actuators without violating their physical constraints.