Autonomous operation of robots requires on-line obstacle avoidance. A wide-spread tool for obstacle avoidance, employed both for mobile robots and for manipulator arms, is the artificial potential field method. This paper extends previous results for planar problems to the general n-dimensional case. A significant decrease in computational complexity is achieved by projecting the n-dimensional workspace into a two-dimensional subspace called the operation plane. Furthermore, only the closest obstacle is taken into account when designing the artificial potential field. The effects of the required switching between potential fields of different obstacles are examined using sliding mode theory. A tracking controller is presented which allows exact following of the gradient of the artificial potential field. The methodology is illustrated with several numerical examples.

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