This paper discusses the positioning control of an elastic tendon-driven robot arm under gravity. The robot is driven by rubber string tendons and winding drums attached on the outside frames. Low-cost rubber strings that are available commercially are used as tendons. The goal is to utilize the nonlinear nature of the rubber materials to control a low-cost and soft robot arm. Theoretically, a mathematical model with accurate parameters and accurate measurement of the payload weight is necessary for rigorous gravity compensation. However, the necessity for the information of the robot parameters is hindering easy adaptability, versatility, and cost-efficiency. This paper presents an iterative estimation and compensation method for unknown payloads based on the steady-state position error and the nominal stiffness coefficient. Owing to the nonlinearity of the actual rubber strings, the position error remains after a single operation of the gravity compensation. However, experiments indicate that the error reduces by a simple iteration of the same compensation operation. Considering the nonlinearity in rubber strings, the mechanism of the error reduction is analyzed theoretically. Although the iterative process is time consuming, the method requires less prior information. In addition, it is cost effective because a sophisticated force sensor is not required. As the mechanism of error reduction applies to typical rubber string materials, it is useful for significant cost-reduction and reconfigurable robotics.

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