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This paper introduces a sliding mode control strategy for tracking the gradient of an artificial potential field. The control methodology is applicable to fully actuated holonomic robotic systems with n-degrees of freedom. The controller yields exact tracking of the gradient lines and is invariant with respect to parametric uncertainty and disturbances in system dynamics. A detailed case study for mobile robots introduces the equilibrium point placement method for designing harmonic planar potential fields for circular obstacle security zones. Diffeomorph mappings can be utilized for more complex obstacle security zones. The gradient of the harmonic potential field is shown to always lead away from the obstacle security zone and to continuously approach the goal point.>
Guldner et al. (Sat,) studied this question.