  In this paper we present a model predictive control (MPC) approach to
optimize vehicle scheduling and routing in an autonomous mobility-on-demand
(AMoD) system. In AMoD systems, robotic, self-driving vehicles transport
customers within an urban environment and are coordinated to optimize service
throughout the entire network. Specifically, we first propose a novel
discrete-time model of an AMoD system and we show that this formulation allows
the easy integration of a number of real-world constraints, e.g., electric
vehicle charging constraints. Second, leveraging our model, we design a model
predictive control algorithm for the optimal coordination of an AMoD system and
prove its stability in the sense of Lyapunov. At each optimization step, the
vehicle scheduling and routing problem is solved as a mixed integer linear
program (MILP) where the decision variables are binary variables representing
whether a vehicle will 1) wait at a station, 2) service a customer, or 3)
rebalance to another station. Finally, by using real-world data, we show that
the MPC algorithm can be run in real-time for moderately-sized systems and
outperforms previous control strategies for AMoD systems.
