Nonlinear Controller Synthesis and Automatic Workspace Partitioning for Reactive High-Level Behaviors

Motivated by the provably-correct execution of complex reactive tasks for robots with nonlinear, under-actuated dynamics, our focus is on the synthesis of a library of low-level controllers that implements the behaviors of a high-level controller. The synthesized controllers should allow the robot to react to its environment whenever dynamically feasible given the geometry of the workspace. For any behaviors that cannot guarantee the task given the dynamics, such behaviors should be transformed into dynamically-informative revisions to the high-level task. We therefore propose a framework for synthesizing such low-level controllers and, moreover, offer an approach for re-partitioning and abstracting the system based on the synthesized controller library. We accomplish these goals by introducing a synthesis approach that we call conforming funnels, in which controllers are synthesized with respect to the given high-level behaviors, the geometrical constraints of the workspace, and a robot dynamics model. Our approach computes controllers using a verification approach that optimizes over a wide range of possible controllers to guarantee the geometrical constraints are satisfied. We also devise an algorithm that uses the controllers to re-partition the workspace and automatically adapt the high-level specification with a new discrete abstraction generated on these new partitions. We demonstrate the controllers generated by our synthesis framework in an experimental setting with a KUKA youBot executing a box transportation task.