  In this work, we consider a group of robots working together to manipulate a
rigid object to track a desired trajectory in $SE(3)$. The robots do not know
the mass or friction properties of the object, or where they are attached to
the object. They can, however, access a common state measurement, either from
one robot broadcasting its measurements to the team, or by all robots
communicating and averaging their state measurements to estimate the state of
their centroid. To solve this problem, we propose a decentralized adaptive
control scheme wherein each agent maintains and adapts its own estimate of the
object parameters in order to track a reference trajectory. We present an
analysis of the controller's behavior, and show that all closed-loop signals
remain bounded, and that the system trajectory will almost always (except for
initial conditions on a set of measure zero) converge to the desired
trajectory. We study the proposed controller's performance using numerical
simulations of a manipulation task in 3D, as well as hardware experiments which
demonstrate our algorithm on a planar manipulation task. These studies, taken
together, demonstrate the effectiveness of the proposed controller even in the
presence of numerous unmodeled effects, such as discretization errors and
complex frictional interactions.
