A Convex Optimal Control Framework for Autonomous Vehicle Intersection Crossing

TL;DR

The underlying optimization problem subject to safety constraints for powertrain operation, cornering and collision avoidance, after convexification and relaxation in some aspects can be formulated as two second-order cone programs, which ensures a rapid solution search and a unique global optimum.

Abstract

Cooperative vehicle management emerges as a promising solution to improve road traffic safety and efficiency. This paper addresses the speed planning problem for connected and autonomous vehicles (CAVs) at an unsignalized intersection with consideration of turning maneuvers. The problem is approached by a hierarchical centralized coordination scheme that successively optimizes the crossing order and velocity trajectories of a group of vehicles so as to minimize their total energy consumption and travel time required to pass the intersection. For an accurate estimate of the energy consumption of each CAV, the vehicle modeling framework in this paper captures 1) friction losses that affect longitudinal vehicle dynamics, and 2) the powertrain of each CAV in line with a battery-electric architecture. It is shown that the underlying optimization problem subject to safety constraints for powertrain operation, cornering and collision avoidance, after convexification and relaxation in some aspects can be formulated as two second-order cone programs, which ensures a rapid solution search and a unique global optimum. Simulation case studies are provided showing the tightness of the convex relaxation bounds, the overall effectiveness of the proposed approach, and its advantages over a benchmark solution invoking the widely used first-in-first-out policy. The investigation of Pareto optimal solutions for the two objectives (travel time and energy consumption) highlights the importance of optimizing their trade-off, as small compromises in travel time could produce significant energy savings.

Figures (12)

• Figure 1: Autonomous intersection with connected and autonomous vehicles.
• Figure 2: Theoretical driving comfort limits represented by an acceleration diamond chen:2019 (thick solid lines) and the theoretical performance envelope of the BEV (light gray area). For simplicity of implementation, a practical performance region of the BEV (dark gray area) under cornering conditions is assumed to be enveloped by longitudinal acceleration saturated at $\pm F_{w,\max}/m$ (horizontal dashed lines) and conservative lateral acceleration limits (vertical dotted lines). $F_{w,\max}$ is calculated based on the BEV motor torque limits shown in Fig \ref{['fig:motormap']} and $a_{\min}$ is given in Table \ref{['tab:vehicledata']}.
• Figure 3: Illustration of potential collisions \ref{['eq:sideconstraint1']} between CAVs $i$ (white vehicle) and $j$ (yellow vehicles) at the MZ with $j>i$.
• Figure 4: Efficiency map of the electric motor (positive torque indicates battery discharging and negative torque represents battery charging) and operational bounds (dotted lines) for the reversible motor. The area surrounded by red dashed lines denotes the operational region for the feasible vehicle speed specified by \ref{['eq:vbound']}.
• Figure 5: The hierarchical centralized coordination scheme. $\mathcal{N}_i$ and $\mathcal{N}_o$ represent the resulting CAV orders solved by \ref{['prob:ocp1']} based on the entry and exit times at MZ, respectively, defined in \ref{['subsec:Scheduler']}.

Theorems & Definitions (1)

• Remark 1