full Paper - Nguyen Dang Binh

Figure 4: Grab system
The £rst one is been implemented to identify the correct
joint positions. In fact, once the system has been turned
on, encoder signals indicate a value which do not match
the absolute con£guration of the mechanical arm. In order
to achieve the best force/torque design the position sensors
(differential encoders) have been placed on motors’ axes and
they can only measure the relative motion between a reset
angle (at power on) and current position. Such a solution offer
the best design solution between position accuracy measurement
and low cost sensor choice. In order to £nd the
absolute position of the arms, in this phase, the calibration
should £nd drive the arms in a safe (for the user) and accurate
manner. The procedure consists of following steps:
HI controller provides to control the arm in a speed/torque
controlled and saturated operation. Such a control will
move each arm towards some mechanical stopper placed
in a well known con£guration;
once this position has been reached, the control will provide
to register the offsets between actual (real) joint positions
and measured read at differential encoders.
This type of calibration allows to minimize £nger position
errors for each arm separately.
The objective of the second calibration phase if to £nd the
relative posture among the mechanical arms. Even having
identical kinematics and being placed symmetrically on the
user desktop, the £ne placement of the two HIs is left to the
user which is free of adapt the device collocation in order to
match the constraints of his desktop. In this case, the controller
can not anymore assume that the relative position of
left and right arms is a £xed pre-computed transformation
matrix.
The goal of second calibration procedure is to £nd the exact
content of this transformation matrix in terms of arms’
relative position and orientation. This feature will allow to
control the two different arms (placed in any relative con-
£guration) as they would share the same coherent system
Massimo Bergamasco / Haptic Rendering: Control Strategy
62
Table 2: Finger position vectors
Symbol Meaning
Σ0 Σ1
O 0 O 1 O W
P 0 P 1
P 0 1
Respectively, local frames of
right and left arm
Respectively, origin positions
of Σ0, Σ1 and ΣW
Respectively, thimble positions
of right and left arm
position of left arm thimble expressed
respect to Σ0
P 0 1 = R 0 1 P 1 1 + O 0 1
where R 0 1 is the matrix rotation
between Σ0 and Σ1,
calculated by RPY
0
1 angles
P W 0 P W 1 position of right and left arm
thimbles expressed respect to
ΣW
P W 0 =(R 0 W )T (P 0 0 − O 0 W )
P W 1 =(R 0 W )T (P 0 1 − O 0 W )
where R 0 W is the matrix rotation
between Σ0 and ΣW ,
calculated by RPY
0
W angles
of forces and position. In order to introduce the calibration
steps, some information about kinematic model are preliminarily
given.
Thimbles coordinates and forces are expressed in control
software respect to three different reference systems: two local
frames, associated to right (Σ0) and left (Σ1) arm (frame
shown in Fig. 3) and an independent frame (ΣW ). In order to
de£ne the relative position and orientation between two local
frames, depending on current arm con£guration on the desktop,
and the position and orientation of independent frame
respect to local ones, Σ0 is the chosen as the absolute one
and ΣW and Σ1 are de£ned respect to Σ0 by the vector which
indicates the origin coordinates (respectively O 0 W and O 0 1 )
and the three angular rotations of axis respect to absolute
one (respectively RPY
0
W and RPY
0
1) according to Roll-Pitch-
Yaw angles conventions.
Different type of thimble position and force vectors are
used in control software, as shown in Table 2 and 3.
The relative positions vectors are calculate for each arm
by applying the direct kinematic equations for the mechanical
device (3 DOF shoulder) and are rarely used in control
scheme. Most important are the positions vectors expressed
respect to absolute frame (independent position vectors), be-
c○ The Eurographics Association 2005.