Optimal Nonholonomic Motion Planning for a Falling Cat

Abstract

How does a falling cat change her orientation in midair without violating the angular momentum constraint? This has become an interesting question to both control engineers and robotists. In this paper, we address this problem together with a constructive solution. First, we show that a falling cat problem is equivalent to the constructive nonlinear controllability problem. Thus, the same principle and algorithm used by a falling cat can be used for space robotic applications such as reorientation of a satellite using rotors, attitude control of a space structure using internal motion and for other robotic tasks such as dextrous manipulation with multifingered robotic hands and nonholonomic motion planning for mobile robots. Then, using ideas from Ritz Approximation Theory we develop a simple algorithm for motion planning by a falling cat. Finally, we test the algorithm through simulation on two widely accepted models of a falling cat. It is interesting to note that one set of simulated trajectories is close to trajectories used by a real cat.