Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

Figure 6

The symmetric case in the plane. The initial geodesic is simply the straight line from the initial position to the terminal position . The circle designates a hazardous region with a user-defined hazard grade . As the initial geodesic cuts the circle in half (i.e., passes through the center of the circle), the two symmetric routes (purple) and (green) are piecewise linear line segments connected via critical points.