  Robotic cloth manipulation is a relevant challenging problem for autonomous
robotic systems. Highly deformable objects as textile items can adopt multiple
configurations and shapes during their manipulation. Hence, robots should not
only understand the current cloth configuration but also be able to predict the
future possible behaviors of the cloth. This paper addresses the problem of
indirectly controlling the configuration of certain points of a textile object,
by applying actions on other parts of the object through the use of a Model
Predictive Control (MPC) strategy, which also allows to foresee the behavior of
indirectly controlled points. The designed controller finds the optimal control
signals to attain the desired future target configuration. The explored
scenario in this paper considers tracking a reference trajectory with the lower
corners of a square piece of cloth by grasping its upper corners. To do so, we
propose and validate a linear cloth model that allows solving the MPC-related
optimization problem in real time. Reinforcement Learning (RL) techniques are
used to learn the optimal parameters of the proposed cloth model and also to
tune the resulting MPC. After obtaining accurate tracking results in
simulation, the full control scheme was implemented and executed in a real
robot, obtaining accurate tracking even in adverse conditions. While total
observed errors reach the 5 cm mark, for a 30x30 cm cloth, an analysis shows
the MPC contributes less than 30% to that value.
