A telepresence system enables a user in a local environment to maneuver in a remote or virtual space through a robotic operator (agent). In order to ensure a high degree of telepresence realism, it is critical that the local user has the ability to control the remote agent's movement through the user's own locomotion. The required motion of the remote agent is determined according to its environment and the specific task it is to perform. The local user's environment is usually different from that of the remote agent in terms of the shapes and dimensions. A motion mapping is needed from the remote agent to the local user to ensure the similarity of the paths in the two environments. In particular, the terminal position of the local user after a segment of movement is also an important portion in such a motion mapping. This paper progressively addresses these issues from the optimization point of view. Two strategies are suggested for solving the motion mapping problem for the single user case. The resulting solutions are then extended to the multiuser case where several local users share a local environment to control different remote agents. Extensive simulations and comparisons show the feasibility and effectiveness of the proposed approaches.