Abstract — We show through experiment and simulation that a high-centered round-bodied legged robot can locomote by generating out-of-phase motions of reaction masses attached to its legs. These leg motions create body attitude oscillations which, when coupled with the slipfree contact constraints, locomote the robot. By varying the mean position of the leg oscillations, the robot can move in different directions in the plane. We also present some simplified models, where body attitude dynamics and contact kinematics are decoupled, to explain this form of legless locomotion.

Abstract — Motivated by finding locomotion primitives for a legged robot, we present controllability results and kinematic reduction for a variable inertia mechanical system. We show that the mechanical system is configuration controllable 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. Our hope is that this technique will lead us to a general procedure for solving the gait synthesis problem. I.

Abstract — Motivated by an error-recovery locomotion problem, we propose a control technique for a complex mechanical system by decomposing the system dynamics into a collection of simplified models. The robot considered, The Rocking and Rolling Robot (RRRobot), is a highcentered round-bodied robot that locomotes on a plane by swinging its legs and rocking on its shell. We identify the elements contributing to locomotion through two steps: 1) decoupling the leg-body rotation dynamics from the body-plane contact kinematics, and 2) decoupling the body rotational dynamics into dynamics along each rotational axis. We show, using simulation, that such decoupling provides a good approximation to RRRobot’s locomotion and use these models to find an approximate control solution for RRRobot: a mapping between planar translation and leg motions. I.

We present a novel locomotion strategy called legless locomotion that allows a round-bodied legged robot to locomote approximately when it is high-centered. Typically, a high-centered robot is stuck since the robot’s legs do not touch the ground. Legless locomotion uses the legs as a reaction mass to set up oscillatory body rotations which when coupled with ground contact gradually translate the robot. Legless locomotion’s continuous dynamics differs from previously studied locomotion methods because of the simultaneous interaction of gravityinduced oscillations, a configuration-dependent system inertia, and non-holonomic contact constraints. This paper employs simple models to capture the complex dynamics and uses the intuition developed from the models to develop gaits that provide planar accessibility. We also present a quantification of legless locomotion’s properties using simulations and motion-capture experiments. KEY WORDS—legged robots, mobility, dynamics and kinematics. 1.