  This paper proposes a real-time model predictive control (MPC) scheme to
execute multiple tasks using robots over a finite-time horizon. In industrial
robotic applications, we must carefully consider multiple constraints for
avoiding joint position, velocity, and torque limits. In addition,
singularity-free and smooth motions require executing tasks continuously and
safely. Instead of formulating nonlinear MPC problems, we devise linear MPC
problems using kinematic and dynamic models linearized along nominal
trajectories produced by hierarchical controllers. These linear MPC problems
are solvable via the use of Quadratic Programming; therefore, we significantly
reduce the computation time of the proposed MPC framework so the resulting
update frequency is higher than 1 kHz. Our proposed MPC framework is more
efficient in reducing task tracking errors than a baseline based on operational
space control (OSC). We validate our approach in numerical simulations and in
real experiments using an industrial manipulator. More specifically, we deploy
our method in two practical scenarios for robotic logistics: 1) controlling a
robot carrying heavy payloads while accounting for torque limits, and 2)
controlling the end-effector while avoiding singularities.
