定义了凸多面体之间的伪最小平移距离 ,分析了它与Euclid度量意义下最小平移距离的上、下界关系及其关于多面体刚体运动的Lipschitz连续性、可微性等性质 .给出了伪最小平移距离及其导数的计算方法 .研究结果可应用于机器人无碰撞运动规划等领域 . The pseudo minimum translation distance between convex polyhedrons is defined, the relationship between the upper and lower bounds of the convex polyhedron and the minimum translation distance in the Euclid metric, and the Lipschitz continuity and the differentiability of the polyhedron rigid body motion are analyzed. The translational distance and the derivative calculation method.The research results can be applied to the robot collision-free motion planning and other fields.