Biomedical Engineering Reference
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Fig. 6.5 Representation of iCub's kinematic and dynamic graph. In (a): iCub's kinematics. The
inertial sensor measure ( black traingle ) is the unique source of kinematic information for the
whole branched system. (b): iCub's dynamics when the robot is standing on the mainstay and
moving freely in space. Given the four FTSs, the main graph is cut by the four links hosting the
sensors, and a total of five subgraphs are finally generated. The unknowns are the external
wrenches at the end-effectors: if the robot does not collide with the environment, they are zero,
whereas if a collision happens, then an external wrench arises. The displacement between the
expected and the estimated wrenches allows detecting contacts with the environment under the
hypothesis that interactions can only occur at the end-effectors. The external wrench on top of the
head is assumed to be null. Notice that the mainstay is represented by an unknown wrench white
rhombus .(c): iCub's dynamics when the robot is crawling (four points of contact with the ground).
As in the previous case, five subgraphs are generated after the insertion of the four FTSs
measurements, but unlike the free-standing case, here the mainstay wrench is removed, being
the iCub on the floor. Specific locations for the contacts with the environment are given as part of
the task: the unknown external wrenches ( white rhombus ) are placed at wrists and knees, while
wrenches at the feet and palms are assumed known and null ( black triangle ). Interestingly, while
moving on the floor, the contact with the upper part could be varying (e.g., wrists, palms, elbows),
so the unknown wrenches could be placed in different locations than the ones shown in the graph
6.3.2 Validation and Further Improvements
In order to validate computation of the dynamics, we compared measurements from
the FTSs with their model-based prediction. The wrenches w s from the four
six-axes FTSs embedded in the limbs are compared with the analogous quantities
^
w s predicted by the dynamical model during unconstrained movements (i.e., null
external wrenches). Kinematic and dynamic parameters are retrieved from the CAD
model of the robot. Sensor measurements w s can be predicted assuming known
wrenches at the limb extremities (hands or feet) and then propagating forces up to
the sensors. In this case, null wrenches are assumed because of the absence of
contact with the environment. Table 6.1 summarizes the statistics of the errors
w s ^
ð
for each limb during a given, periodic sequence of movements, with the
robot supported by a rigid metallic mainstay and with the limbs moving freely
w s
Þ
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