Page 79 - Human Inspired Dexterity in Robotic Manipulation

Modeling and Human Performance in Manipulating Parallel Flexible Objects 75

Note that the haptic device has its own inertia and its mass, reduced to
the task space (the end-point of the haptic device), is denoted as m stylus .To
estimate the mass of the stylus, a reference payload of mass m load ¼ 0.47 kg
was rigidly attached to the stylus. The object dynamics (5.42) with no
human involvement were simulated (the fourth-order Runge-Kutta
method with constant step 0.001 s), and the average of the differences of
the peak amplitudes of the object dynamics,

2F
Δx o ¼ , (5.55)
ðm stylus + m load + m o ÞΩ 2

was recorded. The average (over 50 samples) amplitude was registered as Δx o
206.61 mm, and the mass of the stylus was estimated as m stylus ¼ 0.295 kg.
The subjects were requested to hold the PHANToM stylus at the con-
figuration similar to the one they had used in the production of reaching
movements in the previously completed experiments. The subjects were
instructed not to resist the motion of the virtual object and follow it in
the most comfortable mode, without exerting their own driving force, or
minimizing it as much as possible.
The object dynamics (5.42) were simulated (the fourth-order Runge-
Kutta method with constant step 0.001 s). The positions of the hand (proxy
point) and the object were displayed on the computer monitor. In addition
to this standard visual feedback, a digital oscillograph was implemented in a
pop-up window. Two signals were displayed on the digital oscillograph, the
simulated object position and the reference signal (Eq. 5.48), computed ini-
tially with m h ¼ 1 kg. The subjects were instructed to synchronize frequen-
cies of these two signals. They could also adjust the amplitude of the
reference signal (the reference value of m h ) by pressing a button on the com-
puter keyboard.
Each subject underwent 20 trials, and each trial lasted, on average, 3 min.
The samples of the differences of the peak amplitudes Δx o at the synchro-
nized fragments of the reference and simulated signals were collected for
analysis. The number of samples in each trial exceeded 50. The measured
data of the object amplitudes are presented in Table 5.1. The mass of the
hand, m h , was estimated from
2F
Δx o ¼ , (5.56)
ðm stylus + m o + m h ÞΩ 2
and the results are presented in Table 5.1.