This paper addresses a new type of optimal control problem for obstacle avoidance, where the observation of the allowable state region, the selection of the state waypoints of the controlled plant, and its motion between the waypoints are simultaneously optimized. In particular, the problem on the observation, that is, the problem of optimizing the available information on the allowable state region subject to information amount constraints, is formulated, and then an approximate solution method of the whole problem is presented. It is shown by simple simulations that the proposed method is useful.
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