  Robotic tasks can be accomplished by exploiting different forms of
redundancies. This work focuses on planning redundancy within Model Predictive
Control (MPC) in which several paths can be considered within the MPC time
horizon. We present the nullspace structure in MPC with a quadratic
approximation of the cost and a linearization of the dynamics. We exploit the
low rank structure of the precision matrices used in MPC (encapsulating
spatiotemporal information) to perform hierarchical task planning, and show how
nullspace computation can be treated as a fusion problem (computed with a
product of Gaussian experts). We illustrate the approach using proof-of-concept
examples with point mass objects and simulated robotics applications.
