A Tutorial on Real-time Convex Optimization Based Guidance and Control for Aerospace Applications

Abstract

Challenging control problems are ubiquitous in aerospace engineering applications. Such applications include reusable rockets, spacecraft rendezvous and docking, satellite constellation management for terrestrial imaging, and many other ones where vehicles are required to perform reliably while adhering to physical and mission constraints. Physical constraints are due to limitations like finite fuel, whereas mission constraints can arise from sensor pointing requirements or safety keep-out zones. Often, mission success necessitates that these constraints be satisfied in real-time, using limited on-board computational resources. In this paper, we present a tutorial on how to formulate some aerospace control problem examples in an optimization based control framework. Specifically, we decompose the control problem into two levels: guidance (trajectory optimization), and feedback control. In guidance, we use recent convexification results to formulate non-convex trajectory optimization problems as finite-dimensional convex optimization problems, which we solve using fast and reliable Interior Point Method (IPM) algorithms. We discuss the current state of the art of convexification techniques, and outline the context in which these techniques should be used. Lastly, we present an overview of synthesis methods for feedback control laws. These control laws are used to track the guidance trajectories within specified error bounds, and in the presence of model uncertainties and environmental disturbances.