Scott David Kelly

Hamidreza Moradi, Scott David Kelly

An asymmetric two-link robot supported atop a flat platform by wheels that roll and pivot freely, but do not slip laterally, will develop forward momentum if the joint between the links is actuated internally. In particular, oscillations in the joint angle will generate undulatory locomotion suggesting fishlike swimming. If two such robots surmount a common platform that's free to translate with its own inertial dynamics, then the individual robots' dynamics will be coupled so that the locomotion of either robot is affected by that of the other. We develop a mathematical model for this system and present simulations demonstrating its behavior. We then consider a single robot with an unactuated joint rolling atop a platform that moves under control, and show that actuation of the platform is sufficient to dictate the robot's behavior. In particular, with the acceleration of the platform as an input, the robot's heading can be made to track a chosen function of time. This is sufficient to guarantee that the robot can be induced to orbit a fixed point on the platform or to locomote persistently in a desired direction.

Blake Buchanan, Tony Dear, Scott Kelly et al.

Robots often interact with the world via attached parts such as wheels, joints, or appendages. In many systems, these interactions, and the manner in which they lead to locomotion, can be understood using the machinery of geometric mechanics, explaining how inputs in the shape space of a robot affect motion in its configuration space and the configuration space of its environment. In this paper we consider an opposite type of locomotion, wherein robots are influenced actively by interactions with an externally forced ambient medium. We investigate two examples of externally actuated systems; one for which locomotion is governed by a principal connection, and is usually considered to possess no drift dynamics, and another for which no such connection exists, with drift inherent in its locomotion. For the driftless system, we develop geometric tools based on previously understood internally actuated versions of the system and demonstrate their use for motion planning under external actuation. For the system possessing drift, we employ nonholonomic reduction to obtain a reduced representation of the system dynamics, illustrate geometric features conducive to studying locomotion, and derive strategies for external actuation.