Harry H. Cheng
A real-time collision detection technique for four-dimensional (three spatial dimensions and time) objects is presented in this paper. The developed collision detection method separates the geometrical information from time and complicated motion characteristics through s-formulations. The collision detection of moving objects then becomes a geometrical problem so that it can be solved in real time by using a modified bisection method. The algorithm can predict the exact time and location of the collision of moving objects even for cases when dimensions of moving objects change during the motion. Our collision detection algorithm has been integrated into the real-time control system of the UPSarm which is a ten degree-of-freedom hybrid serial-and-parallel-driven redundant robot manipulator. The capabilities and features of this collision detection technique are demonstrated by manipulating the UPSarm in an environment where an object presents. For our practical application, formulations of intersection for two rectangular solids and polyhedra based upon the s-formulation are also derived in detail in this paper.