Optimal navigation of wheeled or tracked vehicles through a particular off-road terrain is primarily governed by terrain properties, and the capabilities of the vehicle itself. Reconciling vehicle operation with a terrain’s trafficability, termed mobility mapping, is a complex and multi-faceted problem that involves geophysics, vehicle dynamics, optimization, meta-modeling, and statistical modeling. A mobility map in turn informs path planning, which is the process of creating optimal routes through the trafficable areas to successfully arrive at a destination. This optimality can be in the sense of the length of the path taken, energy consumption, or any other metric that the operator considers important. This paper presents a procedure that first models the terrain by including factors affecting trafficability, uses a kriging interpolator for terrain modeling, then utilizes an existing path planning algorithm to create a rough path between start and goal points. Subsequently, a differential geometry based algorithm is presented to optimize the path. In the proposed method, the height of the terrain is augmented with multiple factors beneficial or detrimental to mobility to define a composite surface, thereby simultaneously considering them in path planning. A geodesic connecting the start and goal points is then found on this composite surface. We present examples on terrains acquired from geospatial data gateway of the United States Geological Survey, showing the efficacy of the method. Comparisons with an existing approach are made and avenues for future work are also identified.