Multiple Center of Mass Space Images of Single Objects and Their Impact on Path Planning

The center of mass space is a convenient space for planning motions that minimize reaction forces at the manipulator’s base or optimize the stability of a mechanism. A unique problem associated with path planning in the center of mass space is the potential existence of multiple center of mass images for a single Cartesian obstacle, since a single center of mass location can correspond to multiple manipulator joint configurations. The existence of multiple images results in a need to either maintain multiple center of mass obstacle maps or to update obstacle locations when the manipulator passes through a singularity, such as when it moves from an elbow-up to an elbow-down configuration. To illustrate the concepts presented in this paper, a path is planned for an example task requiring motion through multiple center of mass space maps. The object of the path-planning algorithm is to locate the path with a bang-bang acceleration profile that minimizes the manipulator’s base reactions in the presence of a single Cartesian obstacle. To simplify the presentation, only nonredundant manipulators are considered and joint nonlinearities are neglected.