  The paper considers the problem of controlling Connected and Automated
Vehicles (CAVs) traveling through a three-entry roundabout so as to jointly
minimize both the travel time and the energy consumption while providing
speed-dependent safety guarantees, as well as satisfying velocity and
acceleration constraints. We first design a systematic approach to dynamically
determine the safety constraints and derive the unconstrained optimal control
solution. A joint optimal control and barrier function (OCBF) method is then
applied to efficiently obtain a controller that optimally track the
unconstrained optimal solution while guaranteeing all the constraints.
Simulation experiments are performed to compare the optimal controller to a
baseline of human-driven vehicles showing effectiveness under symmetric and
asymmetric roundabout configurations, balanced and imbalanced traffic rates and
different sequencing rules for CAVs.
