Abstract. This paper addresses the motion planning problem in non-holonomic robotic systems. The system's kinematics and dynamics are represented as a control affine system with outputs. The problem is defined in terms of the end-point map of this system, using the endogenous configuration space approach. Special attention is paid to the multiple-task motion planning problem, i.e. a problem that beyond the proper motion planning task includes a number of additional tasks. For multiple-task motion planning two strategies have been proposed, called the egalitarian approach and the prioritarian approach. Also, two computational strategies have been launched of solving the motion planning problem: the parametric and the non-parametric. The motion planning and computational strategies have been applied to a motion planning problem of the trident snake robot. Performance of the motion planning algorithms is illustrated with computer simulations.