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Abstract 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 

The coupling interactions between two spherical swimmers in an ideal fluid have known analytic approximations for certain types of motion. We apply these results to produce locomotion and coordination through the actuation of internal masses inside each swimmer. Through control of either both swimmers or one of them, the latter case taking advantage of compliance in the passive swimmer, desired motion along the spheres' line of centers can be achieved. We subsequently treat general 2D motion as a superposition of motion components along and perpendicular to the spheres' line of centers, leading to a derivation of a full model of controlled locomotion and coordination of two spheres in a planar fluid. 

Robot system models often have difficulty allowing for direct command over all input degrees of freedom if the system has a large number of imposed constraints. A snake robot with more than three links and a nonholonomic wheel on each link cannot achieve arbitrary configurations in all of its joints simultaneously. 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 commanded and passive joints, as well as the presence of dynamic elements such as torsional springs, can drastically change the coupling interactions and stable oscillations of the joints. We use the oscillation modes that emerge to inform feedback controllers that achieve desired overall locomotion of the robot.