Abstract: This paper discusses the problem of interference checking among robots and environment.Three cate-gories of discriminants are derived to determine collisions of geometric entities including non-completed,non-convex objects.The relation discriminants are used in boundary control problem,the general discriminants in intersection determination of completed entities and the particular discriminants in collision checking of non-completed entities.Method of identification is analyzed for cases of one object beingcntirely within another.An example is given to illustrate the applicaion of the discriminants.