Energy-efficient communication in wireless networks of mobile autonomous agents mandates joint optimization of both transmission and propulsion energy. In Faqir et al. (2017) we developed communication-theoretic data transmission and Newtonian flight mechanics models to formulate a nonlinear optimal control problem. Here we extend the previous work by generalizing the communication model to include UAV-appropriate slow fading channels and specifically investigate the potential from joint optimization of mobility and communication over a multiple access channel. Numerical results exemplify the potential energy savings available to all nodes through this joint optimization. Finally, using the slow fading channel problem formulation, we generate a chance-constrained nonlinear model predictive control scheme for control of a terrestrial network served by a single UAV relay. Closed-loop simulations are performed subject to uncertainties in both transmission and mobility models.