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This paper studies an approach of minimizing the energy consumption of a mobile robot by controlling its traveling speed and its on-board processor's frequency simultaneously. The problem is formulated as a discrete-time optimal control problem with a random terminal time and probabilistic state constraints. A general solution procedure suitable for arbitrary power functions of the motor and the processor is proposed. Furthermore, for a class of practically important power functions, the optimal solution is derived analytically. Simulation result shows that the proposed method can save up to 30% energy compared with some heuristic schemes.