Collision detection algorithms for motion planning

Collision detection is a basic tool whose performance is of capital importancein order to achieve eciency in many robotics and computer graphics applica-tions, such as motion planning, obstacle avoidance, virtual prototyping, com-puter animation, physical-based modeling, dynamic simulation, and, in general,all those tasks involving the simulated motion of solids which cannot penetrateone another. In these applications, collision detection appears as a module orprocedure which exchanges information with other parts of the system concern-ing motion, kinematic and dynamic behaviour, etc. It is a widespread opinionto consider collision detection as the main bottleneck in these kinds of appli-cations.In fact, static interference detection, collision detection and the generationof con guration-space obstacles can be viewed as instances of the same prob-lem, where objects are tested for interference at a particular position, along atrajectory and throughout the whole workspace, respectively. The structure ofthis chapter reects this fact.Thus, the main guidelines in static interference detection are presented inSection 2. It is shown how hierarchical representations allow to focus on relevantregions where interference is most likely to occur, speeding up the whole inter-ference test procedure. Some interference tests reduce to detecting intersectionsbetween simple enclosing shapes, such as spheres or boxes aligned with the co-ordinate axes. However, in some situations, this approximate approach does notsuce, and exact basic interference tests (for polyhedral environments) are re-quired. The most widely used such test is that involving a segment (standing foran edge) and a polygon in 3D space (standing for a face of a polyhedron). In thiscontext, it has recently been proved that interference detection between non-convex polyhedra can be reduced, like many other problems in ComputationalGeometry, to checking some signs of vertex determinants, without computingnew geometric entities.Interference tests lie at the base of most collision detection algorithms,which are the subject of Section 3. These algorithms can be grouped into fourapproaches: multiple interference detection, swept volume interference, space-