Modeling parallel continuum robots with general intermediate constraints

Abstract

Parallel continuum robots consist of a parallel arrangement of flexible legs and are dexterous, compliant, and easily miniaturized for minimally invasive surgery. By design, parallel continuum robots exhibit large, nonlinear deformations in their legs to achieve multi-DOF end effector articulation, but excess leg bowing can limit their reachable workspace, especially for long slender designs. In this paper, we investigate a parallel continuum robot design with a passive spring backbone carrying disks that constrain the legs at intermediate points. The constraints route the legs in helical paths around the backbone and prevent large divergence of the legs, expanding the reachable workspace for slender form factors while preserving the manipulator's six degrees of freedom. We present a novel forward and inverse kinematics model, based on Cosserat rod theory, that accommodates general leg routing paths and any number of intermediate constraint disks. We also explore manipulator workspace with experiments and simulations, demonstrating that intermediate constraints expand the reachable workspace of slender parallel continuum robots.