Finite-time control of cross-chained nonholomic systems by switched state feedback

This paper is concerned with the control problem of a class of nonholonomic systems having cross-chained structure. Such systems are structurally incompatible with the chained systems, so the conventional methods proposed for chained systems are not valid any more and an entirely new control approach is required. In this paper, we propose a switched state feedback law which delivers the initial state to the origin in finite time using bounded control inputs, without infinitely high gain and frequent switchings in spite of its discontinuity. The effectiveness of the proposed method is shown by numerical simulations. Possible mechanical applications of this study include snake robots, rolling sphere problem and attitude control of free-flying robots.