This paper designs a desired trajectory on the state space of a system without considering the real time explicitly. The proposed method focuses on one of the state variables which strictly increases or decreases on the trajectory plan, and designs a virtual time scale as a function of the state variable in order to blind the real time. By transforming the system written in the real time scale into the one written in the virtual time scale, the proposed method generates the optimal trajectory as a path in the state space that does not include information of the real time.
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