Data-driven approaches for mixed integer convex programming in robot control
Keywords: Aeronautics and Astronautics.

Advances in sensing and actuation capabilities have allowed for the proliferation of robots across many fields, including aerial, industrial, and automotive applications. A driving factor in being able to deploy such robots in everyday applications is algorithms that imbue real-time decision making capabilities. Such decision-making capabilities can be formulated using the modeling framework of optimization programs. However, such optimization-based approaches are still limited by computational resources available on robot platforms. For example, in many aerospace applications, spacecraft robotic systems are equipped with embedded computers much less capable than the hardware typically used to solve such optimization algorithms. Thus, there is a pressing need to be able to scale and extend optimization-based planning and control algorithms to robotics applications with severely constrained computational resources. In this work, we turn towards recent advances in nonlinear optimization, supervised learning, and control theory to accelerate solving optimization-based controllers for online deployment. We then show how data-driven approaches can exploit powerful computational resources offline to learn the underlying structure of optimization problems such that the online decision making problem can be reduced to an approximate problem that is much easier to solve on embedded computers. In the first part of this dissertation, we present a local trajectory optimization framework known as Guaranteed Sequential Trajectory Optimization (GuSTO) that provides a theoretically-motivated algorithm that iteratively solves a series of convex optimization problems until convergence. We demonstrate how this framework can accommodate a broad class of trajectory optimization problems, including free-final time, free final-state, and problems on a manifold. We further discuss how GuSTO enables new applications, specifically in the domain of spacecraft robotic manipulation, and discuss the development of a novel gecko-inspired adhesive robot gripper design for the Astrobee assistive free-flying robot. In the second part of this dissertation, we turn towards global trajectory optimization problems, specifically those that can be formulated as mixed-integer convex programs (MICPs). MICPs are a popular modeling framework that can be used to model planning and control problems that are inherently combinatorial or discrete. However, existing algorithms fall short in being able to provide reliable solution approaches that can be deployed for real-time applications (i.e., 10-100Hz computation rates) on embedded systems. In this work, we turn towards data-driven approaches that can be used to find high quality feasible solutions to such MICPs and present Combinatorial Offline, Convex Online (CoCo). We demonstrate how such approaches can leverage the underlying structure of optimal control problems and compare our proposed approach against state-of-the-art commercial solvers. Numerical simulations are provided through this work to demonstrate the efficacy of our proposed approach and present hardware results on a free-flying spacecraft robotic test bed