A method based on the vanishing of self-motion manifolds to determine the collision-free workspace of redundant robots
It is well known that there exist interior barriers within the boundaries of the workspace of redundant robots. These interior barriers, which are drastically affected by kinematic constraints, are very important for trajectory planning since they imply motion impediments for the robot. Existing geometrical and singularity-based methods that obtain such interior barriers cannot accommodate complex (yet common) kinematic constraints, such as the condition that collisions between different links should be forbidden. This paper presents a new sampling method to obtain the boundaries and interior barriers of the workspace of redundant robots considering collision constraints. The proposed method identifies the occurrence of barriers with the vanishing of connected components of self-motion manifolds. Our method consists of three phases: (1) densely sampling self-motion manifolds by solving the inverse kinematics, (2) clustering phase to identify disjoint self-motion manifolds, and (3) matching phase to detect the vanishing of self-motion manifolds. The presented method is illustrated with several examples involving redundant parallel robots, considering joint limits and collisions. These examples demonstrate the feasibility and usefulness of the proposed method, and illustrate the drastic changes suffered by workspace barriers due to collision constraints.