Conventional approaches in prescribing controls for locomoting robots assume control over all input degrees of freedom (DOFs). Many robots, such as those with non-holonomic constraints, may not require or even allow for direct command over all DOFs. In particular, a snake robot with more than three links with non-holonomic constraints cannot achieve arbitrary configurations in all of its joints while simultaneously locomoting. For such a system, we assume partial command over a subset of the joints, and allow the rest to evolve according to kinematic chained and dynamic models. Different combinations of actuated and passive joints, as well as joints with dynamic elements such as torsional springs, can drastically change the coupling interactions and stable oscillations of joints. We use tools from nonlinear analysis to understand emergent oscillation modes of various robot configurations and connect them to overall locomotion using geometric mechanics and feedback control for robots that may not fully utilize all available inputs. We also experimentally verify observations and motion planning results on a physical non-holonomic snake robot.

Many multi-agent systems in nature are comprised of agents that interact with, and respond to, the dynamics of their environment. In this paper, we approach the study of such agent environment interactions through the study of passively compliant vehicles coupled to their environment via simple nonholonomic constraints. We first consider a single passively compliant Chaplygin beanie atop a platform having translational compliance, introduce the reduced equations for the system using the notion of nonholonomic momentum, and provide proof for its stability under arbitrary deformations of the elastic element modeling its compliance. We then direct our focus to results concerning the frequency response and control of passive Chaplygin beanies under actuation of the platform, discuss rich dynamical features arising from periodic actuation, and develop rules by which control can be exerted to collect and disperse multiple passive vehicles. We then discuss how the latter of these results clarifies the extent to which stable behavior can be excited in the system through exogenous control.

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.