Dynamic Ambiguities in Frictional Rigid-body Systems with Application to Climbing via Bracing

Constructing climbing behaviors for hyper-redundant robots that account for the system dynamics requires a model of robot dynamics under contact and friction. One common model, rigid-body dynamics with coulomb friction, unfortunately is both an ambiguous and inconsistent set of dynamic axioms. This paper addresses the ambiguity problem by developing an algorithm which computes the set of joint torques such that all solutions are guaranteed to produce the desired system behavior. This algorithm is applied to a type of robot climbing which we denote climbing via bracing where a hyper-redundant robot stabilizes itself against gravity by pressing outward to induce friction. By bracing with a fraction of the robot, which we term a brace the remainder of the robot remains free to move upward and brace at a higher location. A sequence of braces thus moves the robot upward.