  This paper considers the joint optimization of trajectory and beamforming of
a wirelessly connected robot using intelligent reflective surface
(IRS)-assisted millimeter-wave (mm-wave) communications. The goal is to
minimize the motion energy consumption subject to time and communication
quality of service (QoS) constraints. This is a fundamental problem for
industry 4.0, where robots may have to maximize their battery autonomy and
communication efficiency. In such scenarios, IRSs and mm-waves can dramatically
increase the spectrum efficiency of wireless communications providing high data
rates and reliability for new industrial applications. We present a solution to
the optimization problem that exploits mm-wave channel characteristics to
decouple beamforming and trajectory optimizations. Then, the latter is solved
by a successive-convex optimization (SCO) algorithm. The algorithm takes into
account the obstacles' positions and a radio map and provides solutions that
avoid collisions and satisfy the QoS constraint. Moreover, we prove that the
algorithm converges to a solution satisfying the Karush-Kuhn-Tucker (KKT)
conditions.
