The three-link nonholonomic snake as a hybrid kinodynamic system

Abstract

Motion planners often avoid the so-called singular configurations of a locomoting system because they can change a system's dynamics and cause it to incur unbounded input controller costs. However, such configurations can also allow a system to exhibit new modes of locomotion, which can be incorporated into previously established planning techniques. Here we take a nonholonomic kinematic system and present the formalism for representing it as a hybrid system taking advantage of the singular configuration and the associated dynamics. We show how to achieve the transition maps between the modes of operation by allowing actuated joints to become passive or locked, circumventing problems with unbounded constraint forces. This new model offers a new capability to take advantage of drift dynamics and rolling motions, which we demonstrate using a switching controller involving established kinematic techniques and preliminary dynamic maneuvers.