The paper explores the collision recognition of two objects in both crisscross and revolution motions A mathematical model has been established based on the continuation theory. The objects of any shape may be regarded as being built of many 3siniplexes or their convex hulls. Therefore the collision problem of two object in motion can be reduced to the collision of two corresponding 3siinplexes on two respective objects accordingly. Thus an optimized algorithm is developed for collision avoidance which is suitable for computer control and eliminating the need for vision aid. With this algorithm computation time has been reduced significantly. This algorithm is applicable to the path planning of mobile robots And also is applicable to collision avoidance of the anthropomorphic arms grasping two complicated shaped objects. The algorithm is realized using LISP language on a VAX8350 minicomputer.