Workspace Computation of Planar Continuum Parallel Robots

Abstract

Continuum parallel robots ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CPRs</i> ) comprise several flexible beams connected in parallel to an end-effector. They combine the inherent compliance of continuum robots with the high payload capacity of parallel robots. Workspace characterization is a crucial point in the performance evaluation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CPRs</i> . In this paper, we propose a methodology for the workspace evaluation of planar continuum parallel robots ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PCPRs</i> ), with focus on the constant-orientation workspace. An explorative algorithm, based on the iterative solution of the inverse geometrico-static problem is proposed for the workspace computation of a generic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PCPR</i> . Thanks to an energy-based modelling strategy, and derivative approximation by finite differences, we are able to apply the Kantorovich theorem to certify the existence, uniqueness, and convergence of the solution of the inverse geometrico-static problem at each step of the procedure. Three case studies are shown to demonstrate the effectiveness of the proposed approach.