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Kinematic reduction and planning using symmetry for a variable inertia mechanical system

Motivated by finding locomotion primitives for a legged robot, we present controllability results and a technique for kinematic reduction for a variable inertia mechanical system. We demonstrate configuration controllability for the system under consideration and use the symmetry resulting from angular momentum conservation to develop a kinematic representation of the mechanical system. We also show through simulation how plans for the kinematic representation can be implemented on the full dynamical mechanical system. It is hoped that this technique leads us to a general procedure for solving the gait synthesis problem.