full Paper - Nguyen Dang Binh

G. Cini, A. Frisoli, S. Marcheschi, F. Salsedo, M. BergamascoPERCRO Scuola Superiore S. Anna, Italy / Future directions
Figure 8: The device is driven by a set of a sheathed tendons
connected to the motorization group
Figure 9: The CAD model of the final design
6. Control of the device
The scheme in Figure 11 represents the actuation system of
one leg, composed of of one motor, the sheathed tendon, the
actuation cable and the return spring for each leg.
The dynamic equations of the motor for each leg were
assumed as follows:
τm − Tinr = Jm ¨θ + bm ˙θ
(1)
Tout = Kmx + m ¨x = r(Kmθ + m¨θ)
where Jm and bm are respectively the motor inertia and
damping constant, τm is the motor torque, Tin and Tout represent
the cable tension, τm the motor torque, Km the spring
axial stiffness, while x0 is the length at rest of the spring Km.
The friction of the sheath has been modeled according
to the theory of belt (β and f representing respectively the
winding angle of the tendon on the pulley and the friction
coefficient between the groove and the cable) plus a viscous
coefficient b. The relation between Tin and Tout was determined
by the direction of motion, according to the drive ei-
c○ The Eurographics Association 2005.
49
Figure 10: The final implementation of the first prototype
ther by the motor or by the spring.
Tin = Toute f β + b˙θ = Tout(1 + µ) + b˙θ
Tin =
if ˙θ > 0
Tout
e f β + b˙θ = Tout
(1+µ) + b˙θ if ˙θ < 0
Motor Jm bm
r
Tin
θ
sheath
Tout
Km
Figure 11: Scheme of the actuation system of one leg
The control was implemented with local position controllers
at the joint level. An inverse kinematic module was
used to convert the desired position expressed in cartesian
coordinates to the corresponding joint coordinates. The
non-linear term due to the spring pre-load Kmx0 was precompensated,
by adding it in feedforward to the motor
torque τm in the control loop.
In order to compensate the friction generated by the
sheath, a simple experimental apparatus was set-up to measure
the values of the friction coefficients between the steel
cable and the sheath in different geometric configurations
(for different curvature radii). The cable was fixed on one
side to a position-controlled DC motor and on the other one
to a weight of known mass. The motor was then moved on a
trajectory with constant speed, in order to lift the weight at
constant velocity.
6.1. Experimental results from control
Figure 12 reports the step response of the translational stage
of the system in two opposite directions. The observed dif-
lo
m
X
(2)