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

Abstract

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Capacity margin</i> , a polytope based kinetostatic index, provides additionally, both an accurate evaluation of the twist and wrench capacities of a robotic manipulator. 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 approximation 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 effectiveness in inverse kinematics and trajectory optimization application. Moreover, to show its practical use, two opposing robot architectures are chosen: (i) Serial robot - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Universal Robot- UR5</i> (6-dof); <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rethink Robotics- Sawyer Robot</i> (7-dof) and (ii) Parallel manipulator - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cable Driven Parallel Robot</i> to validate the results through both simulation and experiments. A visual representation of the performance index is also presented.