Collision-free path planning for a manipulator using free form surface

This paper provides a new method for obtaining a collision free path for a manipulator. The proposal in this paper consists of two steps. First, a free form surface is defined that covers collision regions and includes start and goal points in the configuration space, called the path restricted curved surface (PRCS). The PRCS is described by Bezier's surface and it is a collision-free area. The second step is to generate the optimized path on the PRCS. The path on the PRCS is selected to connect the geodesic from start to goal points. The geodesic in the configuration space is the most suitable path in the point to minimize the total value of manipulator's joint angle changes. The effectiveness of this method is clarified by computer simulation with 30 graphics. This method can be said to apply differential geometry to the configuration space method.