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Collision detection using point clouds

Hi all,

I'm presently using dynamic edt3d library to compute the closest obstacle to a point. If this distance is greater than a certain clearance, I say that the point is collision free for the robot. However, let's say I'm planning to use a robot of dimensions 4 * 2 * 0.5, then my clearance will have to be 4m which is too much. How can I effectively collision check keeping robot dimensions in mind? Finding the intersection of point cloud with robot shape point cloud might not be the most effective way I'm guessing.

Any and all suggestions are welcome. Thank you for your time!