  Control design of autonomous vehicles (AVs) has mostly focused on achieving a
prespecified goal for an individually controlled AV or for a swarm of
cooperatively controlled AVs. However, the impact of autonomous driving on
human-driven vehicles (HVs) has been largely ignored in AV controller
synthesis, which could result in egoistic AV behavior detrimental to the safety
of passengers and surrounding traffic. In this study we develop a general
framework for socially compliant control design of AVs with a useful metric of
social psychology, called social value orientation (SVO), allowing AVs to
leverage their impact on the behavior of the following HVs. This is critical
since AVs that behave in a socially compliant manner enable human drivers to
comprehend their actions and respond appropriately. Within the proposed
framework, we define the utilities of the controlled AV and its following
vehicle, to be maximized in a weighted fashion determined by the AV's SVO. The
utility maximization covers an array of design objectives given the goal of the
AV and the benefits for the following HV stemming from the courtesy of socially
compliant AV controls. An optimal control problem is then formulated to
maximize the utility function defined, which is numerically solved using
Pontryagin's minimum principle with optimality guarantees. The methodology
developed is applied to synthesize socially compliant control for eco-driving
of AVs. A set of numerical results are presented to show the mechanism and
effectiveness of the proposed approach using real-world experimental data
collected on Highway 55 in Minnesota.
