  This paper proposes an MPC-based controller to efficiently execute multiple
hierarchical tasks for underactuated and constrained robotic systems. Existing
task-space controllers or whole-body controllers solve instantaneous
optimization problems given task trajectories and the robot plant dynamics.
However, the task-space control method we propose here relies on the prediction
of future state trajectories and the corresponding costs-to-go terms over a
finite time-horizon for computing control commands. We employ acceleration
energy error as the performance index for the optimization problem and extend
it over the finite-time horizon of our MPC. Our approach employs quadratically
constrained quadratic programming, which includes quadratic constraints to
handle multiple hierarchical tasks, and is computationally more efficient than
nonlinear MPC-based approaches that rely on nonlinear programming. We validate
our approach using numerical simulations of a new type of robot manipulator
system, which contains underactuated and constrained mechanical structures.
