Constrained Manipulability for Humanoid Robots Using Velocity Polytopes

Robot performance measures are important tools for quantifying the ability to carry out manipulation tasks. Generally, these measures examine the system’s kinematic transformations from configuration to task space. This means that environmental constraints are neglected in spite of the significant effects they may have on the robot’s admissible motions. In this paper, we propose a new measure called the constrained manipulability polytope (CMP) that considers the system’s kinematic structure, including closed chains or composite sub-mechanisms, joint limits and the presence of obstacles. For an illustrative planar case, we demonstrate how the CMP can evaluate a robot’s performance in a cluttered scene and how this evaluation can be extrapolated to obtain a workspace visualization. Additionally, we show the advantages and limitations of the CMP compared to the state of the art. Furthermore, the method is demonstrated both in simulation and experimentally for NASA’s Valkyrie robot. We show how the CMP provides a measure for single-arm and dual-arm manipulation tasks, analyze the workspace and be used to optimize the robot’s posture.