collision checking
Collision checking is the act of asking a sharp yes-or-no question about a single robot pose: in this exact pose, does any part of the robot overlap an obstacle — or overlap itself? It is the tool that tells a planner which side of the line a pose falls on, free or forbidden. Under the hood it is geometry: the software holds simple stand-in shapes for the robot's links (boxes, cylinders, spheres) and for the obstacles, and it tests whether any of those shapes intersect. If nothing overlaps, the pose is safe; if anything does, the pose is in collision.
This humble test is the workhorse of motion planning, because planners call it thousands or even millions of times while searching for a route, so it has to be fast above all else. There is also a subtler trap: checking single poses is not enough. A robot could be safe at the start of a small move and safe at the end, yet sweep straight through a wall in between. So planners must also do continuous or swept checking along each candidate step — verifying the whole sliver of motion, not just its two endpoints. The constant tension in collision checking is speed against caution: check too coarsely and you miss a collision; check too finely and planning crawls.
To speed things up, a robot arm is first wrapped in coarse spheres. If those big spheres do not even come close to an obstacle, the pose is instantly declared safe; only when they do overlap does the checker zoom in on the exact link shapes to decide for sure.
A cheap coarse test first, an exact test only when needed — the standard way to keep collision checking fast.
Checking the two endpoints of a move is not enough; the swept path between them must be checked too, or the robot can tunnel through a thin obstacle.