## Motion Planning of Discrete-time Nonholonomic Systems

### H. Arai

#### Proc. of 9th International Conference on Advanced Robotics ('99 ICAR), pp. 577-583, Tokyo, Japan, 1999.

#### [Abstract]

The concept of discrete-time nonholonomic systems, in which the constraints are represented as difference equations of generalized coordinates, is introduced. Such systems can be seen in the digital control of continuous-time nonholonomic systems, and in mechanical systems with repetitive and discontinuous constraints. A two-wheeled mobile robot and pivoting manipulation of a polyhedral object are described as simple examples. The k-step reachable region is defined as the set of the k-th state which the system can reach from the initial state, and the reachability of such systems is discussed. A motion planning method using the Jacobian matrix of the state with regard to the input series is proposed.

#### [keywords]

Nonholonomic system, Discrete-time system, Difference equation, Motion planning