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We study a trajectory tracking problem for a mobile robot moving in the plane using combinatorial observations from the state. These combinatorial observations come from crossing binary detection beams. A binary detection beam is a sensing abstraction arising from physical sensor beams or virtual beams that are derived from several sensing modalities, such as actual detection beams in the environment, changes in the angular order of landmarks around the robot, or recognizable markings in the plane. We solve the filtering problem from a geometric perspective and present its relation to linear recursive filters in control theory. Subsequently, we develop the acceleration control of the robot to track a given input trajectory, with a finite control set consisting on moving toward landmarks naturally modeling the robot as a switched dynamical system. We present experiments using an e-puck differential-drive robot, in which a useful estimate of the state for tracking is produced regardless of nontrivial uncertainty.
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