Abstract: This paper deals with the collision detection problem by investigating the distance function between 3-D convex polyhedra in the sense of L₁ metric and L_∞ metric. The characteristics of both the L₁ distance and L_∞ distance, such as their topological property, Lipschitz continuity, equivalence to the Euclidean distance, etc, are investigated. The linear programming based approaches for the evaluating of L₁ distance and L_∞ distance are also proposed. The results of this paper form a basis of collision free path planning for robot manipulators.

Key words: collision-free path planning, convex polyhedra, L₁(L_∞) distance, robot