We deal with motion planning problems for nonholonomic systems. Our approach is based on optimal control algorithms. First, we formulate motion planning problems for nonholonomic systems as trajectory optimization problems, which are (singular) optimal control problems. Next, we develop a new algorithm for (singular) optimal control problems, and prove its convergence property. Finally, applying the algorithm, we solve the motion planning problems for nonholonomic space robot systems, and show the efficiency of the proposed algorithm.