Singularity-free path planning of parallel manipulators using clustering algorithm and line geometry

This paper presents a numerical technique for path planning inside the workspace of parallel manipulators avoiding singularity. A generic numerical algorithm for generating the reachable workspace of parallel manipulators is described. The singularity points are determined inside the workspace. These points are grouped into several clusters and modeled as obstacles. Subsequently, a path planning algorithm is used to find an optimal path avoiding these obstacle. If any singularity point lies on or very close to the path, the path is restructured to avoid the singularity point by a local routing method based on Grassmann's line geometry. The path planning algorithm is uniformly applicable to parallel manipulators with any combinations of revolute and prismatic joints. An example is demonstrated for the effectiveness of the algorithm.