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Robots often interact with the world via attached parts such as wheels,joints, or appendages. In many systems, these interactions, and the manner inwhich they lead to locomotion, can be understood using the machinery ofgeometric mechanics, explaining how inputs in the shape space of a robot affectmotion in its configuration space and the configuration space of itsenvironment. In this paper we consider an opposite type of locomotion, whereinrobots are influenced actively by interactions with an externally forcedambient medium. We investigate two examples of externally actuated systems; onefor which locomotion is governed by a principal connection, and is usuallyconsidered to possess no drift dynamics, and another for which no suchconnection exists, with drift inherent in its locomotion. For the driftlesssystem, we develop geometric tools based on previously understood internallyactuated versions of the system and demonstrate their use for motion planningunder external actuation. For the system possessing drift, we employnonholonomic reduction to obtain a reduced representation of the systemdynamics, illustrate geometric features conducive to studying locomotion, andderive strategies for external actuation.

The Geometric Structure of Externally Actuated Planar Locomoting Systems in Ambient Media