Sensorimotor Coordination in a Humanoid Robot: Building Intelligence on the iCub - Bioinspired Approaches for Human-Centric Technologies - page 186

j 8 corner points of the minimum enclosing bounding box, the

preference for points on the top part of the object can be formulated as follows:

ﾼ 1, ... , nc ﾼ

q

X

nc

p z

c z =

p ˀ j

tp ðÞﾼ dim z þ ð 6 : 33 Þ

nc

jﾼ 1

where p z is the z component of the point p, c z is the z component of the center of the
object, and dim z is the dimension of the object along the z -axis with respect to the
robot's root frame.

6.6.3 Grasp Parameters Estimation

Once a number of suitable candidate points has been computed as illustrated above,
we have to determine the best grasping point and the corresponding pose of the
robots end-effector. This last step has to take into account the robot kinematics in
order to ensure a feasible grasp. For each candidate point, we evaluate a set of
possible orientations in terms of their manipulability index; given this measure, the
most suitable point and orientation of the end-effector is selected.
We would like the hand to be parallel to the surface at the contact point, and thus
we ask that the z -axis of the end-effector be parallel and opposite to the surface
normal computed at the point under evaluation. We then sample the plane deter-
mined by the z -axis and passing through the point p by identifying n possible
orientations for the x - and y -axes. We make use of Ipopt (W¨tcher and Biegler
2006 ) as before to solve the inverse kinematics resulting in the joint configuration
that satisfies the desired position and orientation of the hand using 10 degrees of
freedom of the robot (7 for the arm and 3 for the torso). Notably, we find a reliable
solution in only about 0.04[ s ], and we can consequently explore hundreds of
possible robot configurations in a handful of seconds. Each resulting joint config-
uration is evaluated using the standard manipulability measure (Yoshikawa 1985 ):

r

det J

T

w ðÞﾼ ðÞ J ðÞ ð 6 : 34 Þ

where is the current joint configuration and J is the Jacobian matrix of the robot.

Manipulability is further augmented with a penalty term that considers the distance
from the joint limits:

ʸ