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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 

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.