  Cranes come in various sizes and designs to perform different tasks.
Depending on their dynamic properties, they can be classified as gantry cranes
and rotary cranes. In this paper we will focus on the so called 'knuckle boom'
cranes which are among the most common types of rotary cranes. Compared with
the other kinds of cranes (e.g. boom cranes, tower cranes, overhead cranes,
etc), the study of knuckle cranes is still at an early stage and very few
control strategies for this kind of crane have been proposed in the literature.
Although fairly simple mechanically, from the control viewpoint the knuckle
cranes present several challenges. A first result of this paper is to present
for the first time a complete mathematical model for this kind of crane where
it is possible to control the three rotations of the crane (known as luff,
slew, and jib movement), and the cable length. The only simplifying assumption
of the model is that the cable is considered rigid. On the basis of this model,
we propose a nonlinear control law based on energy considerations which is able
to perform position control of the crane while actively damping the
oscillations of the load. The corresponding stability and convergence analysis
is carefully proved using the LaSalle's invariance principle. The effectiveness
of the proposed control approach has been tested in simulation with realistic
physical parameters and in the presence of model mismatch.
