Uncertainty Analysis and Experimental Study of a Cable-Driven Parallel Lumbar Rehabilitation Robot Based on Evidence Theory

Abstract The cable-driven parallel robot combines the high rigidity of parallel mechanisms with the lightweight characteristics of cable-driven systems. However, due to the existence of various sources of error, it is unavoidable to bring uncertainty of cable lengths and lead to pose errors of the end effector. In this article, the inverse kinematic model of a cable-driven parallel lumbar rehabilitation robot (CDPLRR) is established by considering the geometric structure of fixed pulleys. The influence of fixed pulley radius on errors of cable lengths is explored. The error transfer model of the CDPLRR is constructed to analyze the effects of cable length errors, pulley installation errors, and the sagging effect of cables on the robotic system. In addition, an evidence theory and reliability analysis-based uncertainty method (ETRAM) is presented. Based on the error transfer model, the performance function for structural kinematic response is derived, and the belief and plausibility measures of the joint focal elements are calculated at the given threshold. Compared with the vertex method and the Monte Carlo method (MCM), it is verified that the ETRAM exhibits higher precision and computational efficiency in the kinematic uncertainty analysis of the CDPLRR. Additionally, by comparing the experimental results with numerical examples, the effectiveness and accuracy of the ETRAM in kinematic uncertainty analysis are further demonstrated.