A Convex Optimal Control Framework for Autonomous Vehicle Intersection Crossing (2203.16870v3)

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.

• The paper presents a novel hierarchical convex optimal control framework that determines optimal vehicle crossing order and trajectories to minimize energy consumption and travel time.
• It transforms nonconvex optimal control problems into convex second-order cone programs using linearized vehicle dynamics and battery energy estimation.
• Simulations demonstrate energy savings of up to 21.8% and improved traffic flow compared to traditional FIFO policies, ensuring efficient intersection management.

A Convex Optimal Control Framework for Autonomous Vehicle Intersection Crossing

Introduction

This paper introduces a novel optimization framework aimed at enhancing the coordination of connected and autonomous vehicles (CAVs) at unsignalized intersections. It presents a hierarchical control strategy that optimizes both the trajectory paths and crossing sequence of CAVs to minimize energy consumption and travel time. By embedding detailed vehicle dynamics and powertrain models within an optimal control problem, the research addresses comprehensive vehicular characteristics, offering a practical approach for energy-efficient traffic management.

Optimization Problem and Methodology

The paper formulates the problem as a two-level hierarchical optimization task. At the upper level, a centralized controller determines the optimal crossing order using a formulated optimal control problem (OCP) without safety constraints on crossing order. At the lower level, the velocity trajectories of CAVs are optimized under safety constraints to prevent collisions and ensure adherence to the specified sequence. The central innovation lies in transforming these nonconvex OCPs into convex second-order cone programs (SOCPs), achieved through vehicle dynamics captured in a space-domain setting, enabling rapid solution search and guaranteeing global optima.

Key transformations include:

• Vehicle Dynamics Transformation: Reformulated vehicle longitudinal dynamics in the space domain into a linear form, overcoming nonconvexities.
• Battery Energy Estimation: Introduced a convex representation of battery energy consumption considering CAV powertrain efficiency.
• Safety Constraints: Devised relaxed linearized constraints for collision avoidance, preserving the convexity and feasibility of the optimization problem.

Simulation Results

Simulation studies affirm the effectiveness of the proposed framework. The results demonstrate substantial energy savings and travel time efficiency in comparisons with a FIFO policy, with energy consumption reduced by up to 21.8% while achieving similar travel times. The hierarchical coordination effectively manages vehicle interactions at intersections, showing improved system throughput and energy efficiency, particularly under variable traffic conditions.

Comparison to Benchmark and Implications

The paper benchmarks its performance against a conventional FIFO-based approach prevalent in previous literature. The proposed approach demonstrates significant benefits, including reduced energy consumption and enhanced traffic flow management, which is particularly relevant for high-density traffic scenarios.

Conclusion and Future Work

The research establishes a robust framework for autonomous intersection management. The essential contribution pertains to the innovative convex relaxation and modeling accuracy enhancement, addressing both trajectory optimization and crossing order problems. Future work might explore incorporating dynamic traffic information and extending the framework to multiple intersection systems, enhancing adaptability to real-world urban environments. This paper represents a significant leap toward practical implementation of autonomous vehicular control in urban transportation systems.

For further details, refer to "A Convex Optimal Control Framework for Autonomous Vehicle Intersection Crossing" (2203.16870).