Nonholonomic mechanical systems pose a challenge to roboticists. Indeed,
different from holonomic systems, a paradigm of which is the standard industrial
manipulator, their nonholonomic counterparts require, for the description
of their configurations, a number of variables greater than their degree
of freedom. As a consequence, some of the state variables of these systems
are neither controllable nor observable. This kind of systems is studied
here with the purpose of devising novel mechanical designs and control
strategies that will make the operation of rolling robots more reliable
and efficient. In the process of this study, we came across a new class
of nonholonomic mechanical systems that lead to mathematical models resembling
holonomic systems because of their simplicity. We term these systems quasiholonomic.
In order to fully characterize quasiholonomic systems, we undertook an
intense review of the Frobenius Theorem, that led to the concept of holonomy
matrix. Currently we are investigating mechanical design criteria under
which a given robotic topology can lead to a quasiholonomic system. Our
aim in this project is to design rolling robots with omnidirectional wheels
that will be capable of either quasiholonomic or fully holonomic motions
with suitable control schemes. A major issue in this investigation is the
loss of holonomy, or quasiholonomy, due to disturbances from the environment.
We will thus have a plant to control that is capable to undergo topological
changes, when switching from holonomic (or quasiholonomic) mode to nonholonomic
mode, and vice versa.
Rolling robot with three ball-wheels: (a) top view; (b) cross section