  We present three classes of distributed formation controllers for achieving
and maintaining the 2D/3D formation shape of manipulator end-effectors to cope
with different scenarios due to availability of modeling parameters. We firstly
present a distributed formation controller for manipulators whose system
parameters are perfectly known. The formation control objective is achieved by
assigning virtual springs between end-effectors and by adding damping terms at
joints, which provides a clear physical interpretation of the proposed
solution. Subsequently, we extend it to the case where manipulator kinematic
and system parameters are not exactly known. An extra integrator and an
adaptive estimator are introduced for gravitational compensation and
stabilization, respectively. Simulation results with planar manipulators and
with seven degree-of-freedom humanoid manipulator arms are presented to
illustrate the effectiveness of the proposed approach.
