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Assuming the obstacles are polygons, the will always be a line of shortest distance between the robot and the obstacle that contains a vertex of at least one of them. So, to get an exact answer, you can search among minimal lines connecting vertices to edges between the robot and the obstacle. In practice that will not scale well, so you may want to look at something involving bounding volumes to get fast approximations.
| | 2 | No.2 Revision |
Assuming the obstacles are polygons, polygons (or polylines), the will always be a line of shortest distance between the robot and the obstacle that contains a vertex of at least one of them. So, to get an exact answer, you can search among minimal lines connecting vertices to edges between the robot and the obstacle. In practice that will not scale well, so you may want to look at something involving bounding volumes to get fast approximations.
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