A Modular and Hierarchical Framework for Motion Planning with Feedback-based Motion Primitives

Abstract

As robots become more integrated into everyday society, an increasing emphasis is being placed on their ability to execute complex tasks while maintaining safety. One of the most fundamental tasks in motion planning and control is the coordination of multiple robots to safely and efficiently reach target destinations. In recent years, a hybrid systems approach, that which combines both continuous and discrete system descriptions, has proven to be an attractive methodology for control with complex specifications. Although there is extensive literature on both the design of continuous time feedback controllers and discrete motion planning algorithms, relatively few works address the rigorous integration of these two components, especially in the context of multi-vehicle coordination. In this dissertation, we leverage the hybrid systems paradigm to formulate a novel framework for motion planning and control of multi-vehicle systems that is modular, robust, and provably safe. This dissertation contains three distinct contributions. The first contribution considers the synthesis of low level continuous time feedback controllers for guiding system trajectories along a desired direction; to this end, an open problem in classical linear quadratic control was solved. The second contribution broadens the scope to develop a modular motion planning framework that combines low level feedback-based motion primitives with high level planning algorithms. Finally, the third contribution extends this modular framework towards a multi-hierarchy of motion primitives in order to improve scalability with respect to the number of vehicles. Both the second and third contributions include experimental validation on a collection of quadrocopters.