Manipulator safeguarding is a critical need for operations on planetary rovers. The computing environment on a Mars rover is extremely limited, which necessitates a highly efficient collision checking algorithm. We present such an algorithm that uses the oriented bounding box (OBB) and a primitive called the oriented bounding prism (OBP) to detect potential self-collisions and collisions with terrain objects sensed with the rover's onboard stereo cameras; the algorithm thus has both model-based and sensor-based components. We have implemented the algorithm on JPL's FIDO rover and have tested it under realistic field conditions. Performance analysis indicates this method is significantly faster than previously reported results in the literature, in addition to incorporating sensed geometry. The method is also being used on board NASA's twin Mars Exploration Rovers, which are scheduled to launch in 2003.