This paper presents an algorithm for planning collision-free paths for a polyhedral object moving among known polyhedral obstacles. The algorithm transforms the obstacles to represent the forbidden positions of a reference point on the moving object, reducing the problem to finding a safe path for this reference point. Trajectories are found by searching a network that indicates which vertices in the transformed obstacles can be reached safely. The key steps involve growing the obstacles to account for the moving object's dimensions and searching a visibility graph to find the shortest path. The algorithm is applicable to objects with various degrees of freedom and can be generalized to three dimensions. The method has been successfully implemented and used to plan trajectories for a seven-degree-of-freedom manipulator.This paper presents an algorithm for planning collision-free paths for a polyhedral object moving among known polyhedral obstacles. The algorithm transforms the obstacles to represent the forbidden positions of a reference point on the moving object, reducing the problem to finding a safe path for this reference point. Trajectories are found by searching a network that indicates which vertices in the transformed obstacles can be reached safely. The key steps involve growing the obstacles to account for the moving object's dimensions and searching a visibility graph to find the shortest path. The algorithm is applicable to objects with various degrees of freedom and can be generalized to three dimensions. The method has been successfully implemented and used to plan trajectories for a seven-degree-of-freedom manipulator.