Optimal, Efficient Sequential Control of a Soft-Bodied, Peristaltic Sorting Table

A peristaltic, soft-bodied xy-sorting table manipulates objects by producing moving wave shapes on its surface. The waves exert forces on the objects which can be used for transportation, reorientation, and local repositioning. The control of such peristaltic robots is mostly unsolved, because important properties of the kinematics, dynamics, and effect of actuation are unknown. Fundamental and practical limitations in measuring the system state lead to numerical difficulties in the form of discontinuous signals in non-Euclidean spaces. To solve these problems, we introduce a probabilistic automaton that models the static and dynamic effect of actuation based on a discretized representation of the objects to be manipulated. The automaton only considers the qualitative input-output behavior of the system. It is therefore mostly independent of a particular hardware setup and controls the behavior of objects on the table without explicitly predicting mechanical forces. Our theoretical findings advance the field significantly: We show that the proposed class of automata is suited to model both static and dynamic movements. We introduce a cost function that enables the search and identification of optimal sequences of control patterns to bring the system into a desired state. We prove that the optimal control sequence can be found efficiently and give the respective algorithm.