  Move blocking (MB) is a widely used strategy to reduce the degrees of freedom
of the Optimal Control Problem (OCP) arising in receding horizon control. The
size of the OCP is reduced by forcing the input variables to be constant over
multiple discretization steps. In this paper, we focus on developing
computationally efficient MB schemes for multiple shooting based nonlinear
model predictive control (NMPC). The degrees of freedom of the OCP is reduced
by introducing MB in the shooting step, resulting in a smaller but sparse OCP.
Therefore, the discretization accuracy and level of sparsity is maintained. A
condensing algorithm that exploits the sparsity structure of the OCP is
proposed, that allows to reduce the computation complexity of condensing from
quadratic to linear in the number of discretization nodes. As a result,
active-set methods with warm-start strategy can be efficiently employed, thus
allowing the use of a longer prediction horizon. A detailed comparison between
the proposed scheme and the nonuniform grid NMPC is given. Effectiveness of the
algorithm in reducing computational burden while maintaining optimization
accuracy and constraints fulfillment is shown by means of simulations with two
different problems.
