  Optimal control is often used in robotics for planning a trajectory to
achieve some desired behavior, as expressed by the cost function. Most works in
optimal control focus on finding a single optimal trajectory, which is then
typically tracked by another controller. In this work, we instead consider
trajectory distribution as the solution of an optimal control problem,
resulting in better tracking performance and a more stable controller. A
Gaussian distribution is first obtained from an iterative Linear Quadratic
Regulator (iLQR) solver. A short horizon Model Predictive Control (MPC) is then
used to track this distribution. We show that tracking the distribution is more
cost-efficient and robust as compared to tracking the mean or using iLQR
feedback control. The proposed method is validated with kinematic control of
7-DoF Panda manipulator and dynamic control of 6-DoF quadcopter in simulation.
