Robot motion planning with nonholonomic constraints

A study is made of a fundamental problem in dextrous manipulation by a robot hand: the motion of two rigid bodies rolling relative to one another. A systematic procedure for deriving the configuration space of contact and the differential equation for rolling is presented. This approach is applicable to objects of arbitrary shapes and contact constraints. An algorithm that determines the existence of an admissible path between two contact configurations is given. First, the distribution generated by the two constrained vector fields is computed. One then checks to see if the distribution is nonsingular. If so, an admissible path exists between any two contact configurations. It is also shown that the path-finding problem is equivalent to a nonlinear control problem. Thus, existing work in nonlinear control theory can be used. A geometric algorithm that finds a path when one object is flat is given