This paper presents an algorithm for planning collision-free paths for a polyhedral object moving among polyhedral obstacles. The algorithm transforms obstacles into forbidden regions for a reference point on the moving object. A trajectory avoiding these regions is collision-free. The algorithm searches a network of vertices to find safe paths. The key idea is to reduce the problem of finding a safe path for a polyhedron to finding a safe path for a point by transforming obstacles into forbidden regions. This transformation allows the use of graph searching techniques to find safe paths. The algorithm is extended to handle rotation and more degrees of freedom. It uses a growing operation to compute forbidden regions and a visibility graph to find paths. The algorithm is tested on a seven-degree-of-freedom manipulator and has been successfully executed. The paper also discusses the use of approximations to reduce computational complexity, particularly in three-dimensional space. The algorithm is based on the visibility graph approach, which is extended to handle more complex moving objects and obstacles. The paper also addresses the challenges of quantizing configuration parameters and the need for efficient heuristic search methods to find optimal paths. The algorithm is implemented in PL/1 on an IBM 370/168 and has been used to plan collision-free trajectories for a computer-controlled manipulator. The paper concludes with a discussion of the algorithm's limitations and potential improvements.This paper presents an algorithm for planning collision-free paths for a polyhedral object moving among polyhedral obstacles. The algorithm transforms obstacles into forbidden regions for a reference point on the moving object. A trajectory avoiding these regions is collision-free. The algorithm searches a network of vertices to find safe paths. The key idea is to reduce the problem of finding a safe path for a polyhedron to finding a safe path for a point by transforming obstacles into forbidden regions. This transformation allows the use of graph searching techniques to find safe paths. The algorithm is extended to handle rotation and more degrees of freedom. It uses a growing operation to compute forbidden regions and a visibility graph to find paths. The algorithm is tested on a seven-degree-of-freedom manipulator and has been successfully executed. The paper also discusses the use of approximations to reduce computational complexity, particularly in three-dimensional space. The algorithm is based on the visibility graph approach, which is extended to handle more complex moving objects and obstacles. The paper also addresses the challenges of quantizing configuration parameters and the need for efficient heuristic search methods to find optimal paths. The algorithm is implemented in PL/1 on an IBM 370/168 and has been used to plan collision-free trajectories for a computer-controlled manipulator. The paper concludes with a discussion of the algorithm's limitations and potential improvements.