The main goal of this paper is to report recent progress on two example projects supported within the Ground Robotics Reliability Center (GRRC), a TARDEC supported research center headquartered at the University of Michigan. In the first project, the concept of Velocity Occupancy Space (VOS), a new navigation algorithm that allows a robot to operate using only a range finding sensor in an unknown environment was developed. This method helps a mobile robot to avoid stationary and moving obstacles while navigating towards a target. The second project highlighted is related to energy and power requirement of mobile robots. Hazardous terrains pose challenges to the operation of mobile robots. To enable their safe and efficient operations, it is necessary to detect the terrain type and to modify operation and control strategies in real-time. A research project supported by GRRC has developed a closed-form wheel-soil model. Computational efficiency of this model is improved by avoiding traditional recursive solution of the model under binary search. Results from these two projects are expected to improve the safety and mobility of mobile robots.