A class of three-legged modular reconfigurable parallel robots is
designed and constructed for precision assembly and light machining tasks
by using standard active and passive joint modules in conjunction
with custom designed links and mobile platforms. Since kinematic errors,
especially the assembly errors, are likely to be introduced, kinematic
calibration becomes particularly important to enhance the positioning accuracy of
a modular reconfigurable robot. Based on the local frame representation
of the Product-Of-Exponentials (Local POE) formula, a self-calibration method is
proposed for these three-legged modular reconfigurable parallel robots. In this
method, both revolute and prismatic joint axes can be uniformly
expressed in twist coordinates by their respective local (body) frames.
Since these local frames can be arbitrarily defined on their
corresponding links, we are able to calibrate them, and yet
retain the nominal local description of their respective joints, i.e.,
the nominal twist coordinates and nominal joint displacements, to reflect
the actual kinematics of the robot. The kinematic calibration thus
becomes a procedure of fine-tuning the locations and orientations of
the local frames. Using mathematical tools from differential geometry and
group theory, an explicit linear calibration model is formulated based
on the leg-end distance errors. An iterative least-square algorithm is
employed to identify the error parameters. A simulation example of
calibrating a three-legged (RRRS) modular parallel robot shows that the
robot kinematics can be fully calibrated within two to three
iterations.
Self-Calibration of an Industrial Robot Using a Novel Affordable 3D Measuring Device