Certified kinematic tools for the design and control of parallel robots

Abstract

This paper presents a methodology for the design and control of Parallel Kinematic Robots (PKRs). First, one focuses on the problematics of design. In particular, given a parallel mechanism defined by its design parameters and its kinematic modeling as well as its prescribed workspace, the idea is to certify the absence of any numerical instabilities (computational and physical singularities) that may jeopardize the integrity of the robot. This is achieved through two complementary approaches: a global method using symbolic computation and a local one based on continuation techniques and interval calculus, accounting for uncertainties in the design. The methodology is then applied to real PKR examples. Secondly, the paper proposes a control strategy that limits the active joint velocities to ensure the robot remains within its certified workspace. It will be applied to a special class of parallel robots: Spherical Parallel Manipulators (SPM) with coaxial input shafts (CoSPM).