Polynomial motion of non-holonomic mechanical systems of chained form

In this study a simple general motion planning approach for non-holonomic mechanical systems of chained form is proposed, in which the intricate motion planning problem (steering the system from an initial state to a final state) is converted to a simple curve-fitting problem (satisfying a set of end-point conditions). By means of this approach, other geometric constraints, such as passing a channel and avoiding collision with obstacles, and minimizing some cost functions, such as the minimum path length, can be easily handled, while the control inputs can be derived directly from the smooth path planned. For verifying the effectiveness of the proposed approach, a number of simulations are conducted for various task requirements and environments, with respect to a four-wheel mobile chart (one-chain system) and a three-input firetruck (two-chain system).