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This paper describes the algorithm used to point the high gain antennae on NASA/JPL's Mars exploration rovers. Each rover's gimballed antenna must track the Earth as it moves across the Martian sky during communication sessions. The pointing algorithm accounts for obstacles to the line-of-sight posed by (1) features on the rover and in the surrounding environment (2) gimbal range limitations, and (3) kinematic singularities in the gimbal mechanism. The algorithm treats all obstacles with a generalized approach that computes the intercept-times to each obstacle. Where possible, the algorithm takes advantage of pairs of joint-space solutions arising from the mechanism design. The algorithm chooses the solution that provides the longest obstruction-free tracking time. Upon encountering an obstacle, the algorithm automatically switches to the other solution if it is not also obstructed. This algorithm has successfully provided obstruction-free pointing for both rovers throughout the mission.