A hopping rover is a robot that can move in low gravityplanets by the characteristic motion called the hopping motion. For itsautonomous explorations, the so-called SLAM (Simultaneous Localizationand Mapping) is a basic function. SLAM is the combination of estimatingthe position of a robot and creating a map of an unknown environment.Most conventional methods of SLAM are based on odometry to estimatethe position of the robot. However, in the case of the hopping rover, theerror of odometry becomes considerably large because its hopping motioninvolves unpredictable bounce on the rough ground on an unexplored planet.Motivated by the above discussion, this paper addresses a problem of findingan optimal movement of the hopping rover for the estimation performance ofthe SLAM. For the problem, we first set the model of the SLAM system forthe hopping rover. The problem is formulated as minimizing the expectationof the estimation error at a pre-specified time with respect to the sequenceof control inputs. We show that the optimal input sequence tends to forcethe final position to be not at the landmark but in front of the landmark, andfurthermore, the optimal input sequence is constant on the time interval foroptimization.
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