AMC2014-Yokohama March 14-16,2014, Yokohama, Japan Consideration of Tension Limits in Joint Space for 3 Pairs of 6 Tendon Arms with Nonlinear Springs Masashi Oishi Graduate School of Engineering Faculty of Engineering, Mie University, Mie, Japan Email: oishi@ems.elec.mie-u.ac.jp Abstrct-Safety and versatility are necessary for robots to perform various tasks in human living area. There are tendon manipulators with nonlinear springs as a manipulator for the requirement. The manipulator can control joint torque and joint mechanical stiffness simultaneously. This paper proposes a generation method of commands in joint space considering tension limit. The method generates commands so that command error as small as possible. Because it is controlled in tendon space, the tendon mechanisms has a tension limiter. The proposed method takes account not only of weaknesses of torque limit, but also of tension limit. Effectiveness of the proposed method is confrmed by a simulation. I. INTRODUCTION In recent years, robot working areas are expanding fom restricted areas such as factories to human living areas such as hospitals. Accordingly, robot tasks are expanding from simple tasks such as assembly task to various tasks such as assistant. Thus, there are two requirements for robots. First one is safety for contact with environment. Second one is versatility for various tasks. Since conventional robots have high gear ratio and rigid joint in order to output high torque, safety for human is not acquired by them[1]. Tendon based manipulators with nonlinear springs have been studied to resolve the problem. N S T (Nonlinear Spring Tensioner)[2], NLEM (Nonlinear Elastic Module)[3], and SAT (Stifness Adjustable Tendon)[4][5] are developed as a kind of nonlinear spring. The manipulators with these nonlinear springs are light-weight arms and stiffness adjustable joints. The light-weight arms contribute to safety. The adjustable joint stiffness contributes to versatility. Generally, we convert joint torque and stiffness into tension to control the tendon manipulators. However, the joint com mand is not always realized because of tension limits which are caused by motor maximum torque and tendon slack avoidance. The tension limit is included in not only limit of spring but also torque limit. As a result, There are the joint command that cannot achieve the requirement. To solve the problem, it is necessary to generate a Jomt command considering tension limits. One method is utilization of feasible area of joint torque and joint stiffness drawn fom tension limit and equation related to joint space and tendon space. The other method is solution of an optimization problem in joint space to adjust commands inside the feasible area so 978-l-4799-2323-6114/$3l.00 ©20l4 IEEE 645 Satoshi Komada, Daisuke Yashiro and, Junji Hirai Graduate School of Engineering Faculty of Engineering, Mie University, Mie, Japan Email: {komada, yashiro, hirai} @elec.mie-u.ac.jp Motor f �E em ': �-- :: <=>-" Fig. 1. One-link tendon mechanism Arm that the close response to the command is obtained as much as possible. II. TENDON MANIPULATORS WITH NONLINEAR SPRINGS A. Tendon Mechanisms In order to explain tendon mechanisms, a mechanism of single joint with two tendons is depicted in Fig. 1. Two actuators and an arm are connected with a wire through two nonlinear springs. The tendon structure is able to construct lightweight and soft manipulators because of no actuators in joints. The main feature is that the joint stifness and joint torque are controlled by tension. In Fig. 1, 8 m , T m ' and r m are rotation angle, torque, and radius of the motors, respectively. qj and T j are rotation angle and torque of the joint, respectively. f is tension of nonlinear springs. B. Nonlinear Springs Fig. 2 shows characteristics of nonlinear springs, whose gradient shows stifness. Although stifness of linear springs is constant, stiffness of nonlinear springs is varied by the dis placement of nonlinear springs. Tendon mechanisms can adjust joint stifness according to the variable stiffness characteristics of nonlinear springs. The equation fom displacement l to tension f of i-th nonlinear spring among l nonlinear springs is represented by the following formula with constant a 1 ,a 2 , and a : . (1)