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This paper proposes a coordinate-free controller to drive a mobile robot toencircle a target at unknown position by only using range measurements.Different from the existing works, a backstepping based controller is proposedto encircle the target with zero steady-state error for any desired smoothpattern. Moreover, we show its asymptotic exponential convergence under a fixedset of control parameters, which are independent of the initial distance to thetarget. The effectiveness and advantages of the proposed controller arevalidated via simulations.

Target Encirclement with any Smooth Pattern Using Range-only Measurements