A medical system includes a manipulator arm including a movable distal portion, a proximal portion coupled to a base, and joints between the distal portion and the base. A processor coupled to the manipulator arm performs operations including calculating a first movement of the joints in a null-space of a Jacobian of the manipulator arm, the first movement being calculated in accordance with a first objective for arm-to-patient collision avoidance. The operations further include calculating a second movement of the joints in the null-space, the second movement being calculated in accordance with a second objective for arm-to-arm collision avoidance, and combining at least the first and second movements into a combined movement in a manner allowing the first objective to overpower the second objective, and driving the joints to effect the combined movement.