NEAR-OPTIMAL NONHOLONOMIC MOTION PLANNING FOR A SYSTEM OF COUPLED RIGID BODIES

How does a falling cat change her orientation in midair without violat ing angular momentum constraint? This has become an interesting proble m to both control engineers and roboticists. In this paper, we address this problem together with a constructive solution. First, we show th at a falling cat problem is equivalent to the constructive nonlinear c ontrollability problem. Thus, the same principle and algorithm used by a falling cat can be used for space robotic applications, such as reo rientation of a satellite using rotors and attitude control of a space structure using internal motion, and other robotic tasks, such as dex trous manipulation with multifingered robotic hands and nonholonomic m otion planning for mobile robots. Then, using ideas from Ritz Approxim ation Theory, we develop a simple algorithm for motion planning of a f alling cat. Finally, we test the algorithm through simulation on two w idely accepted models of a falling cat. It is interesting to note that one set of simulation results closely resembles the real trajectories employed by a falling cat.