  The development of connected and automated vehicles is the key to improving
urban mobility safety and efficiency. This paper focuses on cooperative vehicle
management at a signal-free intersection with consideration of vehicle modeling
uncertainties and sensor measurement disturbances. The problem is approached by
a hierarchical robust control strategy in a decentralized traffic coordination
framework where optimal control and tube-based robust model predictive control
methods are designed to hierarchically solve the optimal crossing order and the
velocity trajectories of a group of CAVs in terms of energy consumption and
throughput. To capture the energy consumption of each vehicle, their powertrain
system is modeled in line with an electric drive system. With a suitable
relaxation and spatial modeling approach, the optimization problems in the
proposed strategy can be formulated as convex second-order cone programs, which
provide a unique and computationally efficient solution. A rigorous proof of
the equivalence between the convexified and the original problems is also
provided. Simulation results illustrate the effectiveness and robustness of the
proposed strategy and reveal the impact of traffic density on the control
solution. The study of the Pareto optimal solutions for the energy-time
objective shows that a minor reduction in journey time can considerably reduce
energy consumption, which emphasizes the necessity of optimizing their
trade-off. Finally, the numerical comparisons carried out for different
prediction horizons and sampling intervals provide insight into the control
design.
