Specification composition and controller synthesis for robotic systems

Abstract

From precision agriculture to autonomous-transportation systems, robotic systems have been proposed to accomplish a number of tasks. However, these systems typically require satisfaction of multiple constraints, such as safety or connectivity maintenance, while completing their primary objectives. The objective of this thesis is to endow robotic systems with a Boolean-composition and controller-synthesis framework for specifications of objectives and constraints. Barrier functions represent one method to enforce such constraints via forward set invariance, and Lyapunov functions offer a similar guarantee for set stability. This thesis focuses on building a system of Boolean logic for barrier and Lyapunov functions by using min and max operators. As these objects inherently introduce nonsmoothness, this thesis extends the theory on barrier functions to nonsmooth barrier functions and, subsequently, to controlled systems via control nonsmooth barrier functions. However, synthesizing controllers with respect to a nonsmooth function may create discontinuities; as such, this thesis develops a controller-synthesis framework that, despite creating discontinuities, still produces valid controllers (i.e., ones that satisfy the objectives and constraints). These developments have been successfully applied to a variety of robotic systems, including remotely accessible testbeds, autonomous-transportation scenarios, and leader-follower systems.