  We derive time and energy-optimal policies for a Connected Autonomous Vehicle
(CAV) to execute lane change maneuvers in mixed traffic, i.e., in the presence
of both CAVs and Human Driven Vehicles (HDVs). These policies are also shown to
be robust with respect to the unpredictable behavior of HDVs by exploiting CAV
cooperation which can eliminate or greatly reduce the interaction between CAVs
and HDVs. We derive a simple threshold-based criterion on the initial relative
distance between two cooperating CAVs based on which an optimal policy is
selected such that the lane-changing CAV merges ahead of a cooperating CAV in
the target lane; in this case, the lane-changing CAV's trajectory becomes
independent of HDV behavior. Otherwise, the interaction between CAVs and
neighboring HDVs is formulated as a bilevel optimization problem with an
appropriate behavioral model for an HDV, and an iterated best response (IBR)
method is used to determine an equilibrium. We demonstrate the convergence of
the IBR process under certain conditions. Furthermore, Control Barrier
Functions (CBFs) are implemented to ensure the robustness of lane-changing
behaviors by guaranteeing safety in both longitudinal and lateral directions
despite HDV disturbances. Simulation results validate the effectiveness of our
CAV controllers in terms of cost, safety guarantees, and limited disruption to
traffic flow. Additionally, we demonstrate the robustness of the lane-changing
behaviors in the presence of uncontrollable HDVs.
