Controlling the quantum state of isolated or interacting correlated atoms has emerged as a promising research field in modern quantum information science. In particular, engineering methods for the high-fidelity preparation of quantum states play a central role in the development of quantum technologies, including quantum computers and communication devices. The Wigner function formalism provides an ideal tool for describing the quantum evolution of systems with continuous degrees of freedom and has been widely used to represent entangled states in quantum optics. Furthermore, the Wigner formalism has proven to be an excellent tool for rigorously investigating the classical limit of the quantum dynamics of interacting systems. In this contribution, we discuss recent results concerning the application of the Wigner formalism to the optimal control of atoms moving in the presence of external fields. We present recent results in the control of the quantum dynamics of single neutral atoms and interacting pairs. We describe an optimal control problem aimed at steering atoms along prescribed trajectories and modulating the Aharonov-Anandan geometric phase in interacting systems. Our approach is based on a quantum phase-space framework and relies on mobile optical trap technology. Furthermore, our mathematical study focuses on the well-posedness of the optimal control problem within the Wigner phase-space. Finally, the implementation of numerical algorithms and simulations of the controlled dynamics in realistic scenarios are also presented.