Polytope-Based Continuous Scalar Performance Measure with Analytical Gradient for Effective Robot Manipulation

Performance measures are essential to characterize a robot’s ability to carry out manipulation tasks. Generally, these measures examine the system’s kinematic transformations from configuration to task space, but the Capacity margin, a polytope based kinetostatic index, provides additionally, both an accurate evaluation of the twist and wrench capacities of a robotic manipu- lator. However, this index is the minimum of a discontinuous scalar function leading to difficulties when computing gradients thereby rendering it unsuitable for online numerical optimization. In this letter, we propose a novel performance index using an approxi- mation of the capacity margin. The proposed index is continuous and differentiable, characteristics that are essential for modelling smooth and predictable system behavior. We demonstrate its ef- fectiveness in inverse kinematics and trajectory optimization ap- plication. Moreover, to show its practical use, two opposing robot architectures are chosen: (i) Serial robot - Universal Robot- UR5 (6-dof); Rethink Robotics- Sawyer Robot (7-dof) and (ii) Parallel manipulator - Cable Driven Parallel Robot to validate the results through both simulation and experiments. A visual representation of the performance index is also presented.