A Nonsmooth Approach to Controller Synthesis for Boolean Specifications

Robotic systems have been proposed as a solution to a wide array of problems, from autonomous warehousing to precision agriculture. Yet these systems typically require satisfaction of multiple constraints, such as collision avoidance and connectivity maintenance, while completing their primary objectives. Many such problems may be decomposed into stability and invariance criteria (e.g., monitor crop patches while avoiding collisions), and this article utilizes Lyapunov and barrier functions to encode stability and invariance, respectively. Barrier functions provide constraint-satisfaction guarantees, and prior results have established a Boolean composition and controller-synthesis framework for these objects via nonsmooth analysis. However, this past work has yet to address Boolean composition of Lyapunov functions directly and does not apply to all Boolean expressions. This article resolves these issues by providing a general method to encode Boolean expressions of Lyapunov or barrier functions. Moreover, this article develops an associated controller-synthesis algorithm that yields discontinuous yet validating controllers with respect to these Boolean expressions. Experimental results show the efficacy of this article in a precision-agriculture scenario, where a robot swarm must visit crop patches while avoiding collisions.