CDPR Forward Kinematics with Error Covariance Bounds for Unconstrained End-Effector Attitude Parameterizations

This paper presents two methods to solve the forward kinematics of an overconstrained six degree-of-freedom cable-driven parallel robot (CDPR) that explicitly account for cable length measurement noise and are applicable to any unconstrained attitude parameterization of the CDPR’s end-effector. Nonlinear weighted least-squares optimization is used to solve the CDPR’s forward kinematics and determine covariance bounds on the pose estimation error using loop-closure equations based on either the magnitude of the CDPR’s cable lengths or the square of the CDPR’s cable lengths. It is shown through numerical simulations that the error covariance bounds obtained when using the cable length loop-closure equations are significantly more accurate than those found when using the cable length squared loop-closure equations.