Iterative algorithms for detecting the collision of convex objects whose motion is characterized by a path in configuration space are described. They use as an essential substep the computation of the distance between the two objects. When the objects are polytopes in either two-dimensional or three-dimensional space, an algorithm is given which terminates in a finite number of iterations. It either determines that no collision occurs or locates the first collision point on the path. For practical problems it appears that the computational time is short and grows only linearly in the total number of vertices of the two polytopes. Numerical examples are presented.>