Frictional Locomotion of a Radially Symmetric Tripedal Robot

This study seeks to provide physical insight into the friction-driven crawling locomotion of systems with radially symmetric bodies. Laboratory experiments with a tripedal robot show that both translation and rotation can be achieved with just three independently actuated rigid limbs, i.e., with 3 degrees-of-freedom. These observations are rationalized using a simple mathematical model, which assumes that the friction at each limb is linearly proportional to the normal force at the contact point, and opposes the direction of motion. This dynamic model reproduces experimental observations across an extensive parametric sweep involving sinusoidal rotation of the limbs with varying amplitudes and phase shifts. Model predictions highlight the role played by time-varying normal forces at the contact points. These predictions are confirmed using embedded force transducers in the limbs. We present a further simplified analysis explaining that a geometric nonlinearity is induced in the dynamics from the radial symmetry and that this nonlinearity is essential to the generation of pure translation. We also show that this nonlinearity can be amplified by a cyclic time-varying limb length variation. These results provide a framework for further study of radially symmetric movers.