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)