Sensorimotor Coordination in a Humanoid Robot: Building Intelligence on the iCub - Bioinspired Approaches for Human-Centric Technologies - page 159

results both through FEM analysis and later experimentally on the robot. The
experimental results yielded about 30 % lower stiffness than expected, a fact to
be corrected in the future, although it was not critical for the current release of the
iCub (i.e., our design safety margins were large enough to accommodate this
variation). For a complete description and evaluation of the SEAs, the reader is
referred to the Parmiggiani et al. ( 2012a ) paper and a more recent comparison of
SEA vs. stiff actuation in Eljaik et al. ( 2013 ).

6.3 Torque Control

Torque control lays at the lowest level in the hierarchy of sensorimotor problems
since it results in the calculation of the joint reference torques that drive the motors.
Torque control requires the computation of the body dynamics to separate internal
from external wrenches. In its simplest possible version, the microcontroller cards
implement a 1 ms feedback loop relying on the error e defined as

e ﾼ τ τ d , ð 6 : 1 Þ

where τ

directly on the iCub but we have access to estimates through the force/torque
sensors (FTSs). They are mounted as indicated in Fig. 6.3 in the upper part of the
limbs and can therefore be used to detect wrenches at any location in the iCub limbs
and not only at the end-effector as it is more typical for industrial manipulators.
We show that τ can be estimated from the FTS measurements of each limb
(equations repeat identical for each limb). Let's indicate with w s the wrench
measured by the FTS and assume that it is due to an actual external wrench at a
known location (e.g., at the end-effector) which we call w e . We can estimate w e by
propagating the measurement on the kinematic chain of the limb (changing
coordinates):

τ is the vector of joint torques and τ d its desired value. We do not know

I 0

w e ﾼ ^ ð w s w i Þ , ð 6 : 2 Þ

r s ﾽ I

with r s ﾽ the skew-symmetric matrix representing the cross product with the

vector r se , w e the estimat e of w e , and w i the internal wrench (due to internal forces

and moments). Note that r s ﾽ

^

is a function of q , the vector of joint angles. w i can be
estimated from the dynamics of the limb (either with the Lagrange or Newton-
Euler formulation). To estimate τ e we only need to project w e to the joint torques

using the transposed Jacobian, i.e.:

J T q τ e ﾼ ðÞ^ w e : ð 6 : 3 Þ

We can then use this estimate in a control loop by defining the torque error e as