A novel fingertip haptic device
6. Control of the device
The scheme in Figure11represents 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=Jmθ¨+bmθ˙
Tout=Kmx+m ¨x=r(Kmθ+m ¨θ) (1) where Jm and bmare respectively the motor inertia and damping constant,τmis the motor torque, Tinand Tout rep-resent the cable tension,τmthe motor torque, Kmthe spring axial stiffness, while x0is the length at rest of the spring Km. The friction of the sheath has been modeled according to the theory of belt (βand 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 deter-mined by the direction of motion, according to the drive
ei-Figure 10: The final implementation of the first prototype
ther by the motor or by the spring.
( Tin=Toutefβ+b ˙θ=Tout(1+µ) +b ˙θ if ˙θ>0 Tin=Teoutfβ +b ˙θ=(1+µ)Tout +b ˙θ if ˙θ<0 (2)
Tin
sheath r θ
Motor Jm bm
X Tout
lo Km
m
Figure 11: Scheme of the actuation system of one leg
The control was implemented with local position con-trollers at the joint level. An inverse kinematic module was used to convert the desired position expressed in carte-sian coordinates to the corresponding joint coordinates. The non-linear term due to the spring pre-load Kmx0 was pre-compensated, by adding it in feedforward to the motor torqueτmin the control loop.
In order to compensate the friction generated by the sheath, a simple experimental apparatus was set-up to mea-sure 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
Figure12reports the step response of the translational stage of the system in two opposite directions. The observed
dif-c
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G. Cini, A. Frisoli, S. Marcheschi, F. Salsedo, M. BergamascoPERCROScuola Superiore S. Anna, Italy / Future directions ference in the response of the system is due to the fact that
either the spring or the motor is active according to the se-lected motion direction.
Figure 12: The difference of the time response in the two directions is due to the different response of the motor and of the antagonist spring
Figure13reports the tracking of a circular trajectory of the central point of the translating stage.
Figure 13: Tracking of a circular trajectory
6.2. Preliminary evaluation
In this first phase, only a preliminary evaluation of the de-vice is being conducted. The trajectories to be followed by the device have been defined off-line. Two tests have been carried out to evaluate the ability of the user to perceive the influence of direction and orientation of approaching of the plate The two schemes that have been adopted are reported in table1:
Direction Orientation Condition 1 Variable Fixed Condition 2 Fixed Variable
Table 1: Representation of the preliminary tests currently on-going
• The plate is brought in contact with the fingerpad with the same orientation but along different directions.
• The plate is put in different orientations and brought to contact with the fingerpad with the same direction.
The two tests have still not completed, but preliminary re-sults show the efficacy of the device for the haptic display of virtual surfaces with different orientation.
Figure 14: The approach of the plate to the fingerpad with different orientations.
7. Conclusion
A new concept of fingertip haptic display has been proposed in the paper. A prototype of the device has been constructed and tests are currently on going for the assessment of the capability of the device and further more will be required for the assessing the validity of this new concept of haptic display.
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