Sequential Composition of Robust Controller Specifications

Abstract — We present a general notion of robust motion specification and a mechanism for sequentially composing them. These motion specifications form tubular abstrac-tions of the trajectories of a robot in different control modes, and are inspired by the techniques available for the design and analysis of low-level controllers. In particular, characterizations of input to output stability with respect to the disturbance inputs and trajectory tracking error output provide a suitable parametrization of the tubes. We also describe a randomized planner that composes different motion specifications from a given database to guarantee that any corresponding sequence of control modes steers a robot to a given region while avoiding obstacles. The main features of this compositional framework are that: i) at the planning level, it does not require the integration of the robot dynamics and the knowledge of how the con-trollers operate, but only the specification of the tracking performance achieved by these controllers. This enables a rigorous separation of concerns between establishing the feasibility of the high-level planning task and refining the low-level controller designs; ii) it can account quantitatively for robustness to unmodeled dynamics and various sources of disturbance and sensor noise. In particular it can help evaluate the impact of the sensing and actuation quality on the overall feasibility of a task. I