Discusses the optimal trajectory planning problem of classical nonholonomic systems. Most conventional studies have discussed the nonholonomic motion planning problem considering only kinematics. However, when a trajectory is required to minimize the traveling time or the energy used in performing tasks, the dynamics must be taken into consideration. In this paper, a trajectory planning method that considers the full nonlinear dynamics of the system is proposed. This method is based on the concept of geometric phase and the minimum cost trajectory planning algorithm which were previously developed for motion planning of robotic manipulators. Simulation results show the effectiveness of the proposed method.
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