[Paper Review] Optimal Path Planning and Coordination for Connected and Automated Vehicles

Andreas A. Malikopoulos, Logan E. Beaver+1 more|arXiv (Cornell University)|Mar 26, 2020

Traffic control and management28 references9 citations

TL;DR

This paper proposes a decentralized, two-level optimization framework for connected and automated vehicles (CAVs) to coordinate path planning and control in traffic scenarios. The upper-level optimizes each vehicle’s path and arrival time to reduce congestion, while the lower-level computes safe, optimal control inputs using analytical solutions that satisfy speed-dependent safety constraints and system limits—proven via geometric duality to enable real-time implementation with guaranteed optimality.

ABSTRACT

In this paper, we provide a decentralized theoretical framework for coordination of connected and automated vehicles (CAVs) in different traffic scenarios. The framework includes: (1) an upper-level optimization that yields for each CAV its optimal path, including the time, to pass through a given traffic scenario while alleviating congestion; and (2) a low-level optimization that yields for each CAV its optimal control input (acceleration/deceleration) to achieve the optimal path and time derived in the upper-level. We provide a complete, analytical solution of the low-level optimization problem that includes the rear-end safety constraint, where the safe distance is a function of speed, in addition to the state and control constraints. Furthermore, we provide a geometric duality framework using hyperplanes to prove strong duality of the upper-level optimization problem. The latter implies that the optimal path and time for each CAV does not activate any of the state, control, and safety constraints of the low-level optimization, thus allowing for online implementation. We validate the effectiveness of the proposed theoretical framework through simulation.

Motivation & Objective

• To develop a decentralized theoretical framework for coordinating connected and automated vehicles (CAVs) in diverse traffic scenarios.
• To minimize traffic congestion by optimizing each CAV’s path and time of passage through a traffic scenario.
• To ensure rear-end safety by incorporating a speed-dependent safe distance constraint in the control optimization.
• To provide an analytical solution to the low-level control problem that respects state and control constraints.
• To establish strong duality in the upper-level optimization using a geometric duality framework, enabling online implementability.

Proposed method

• Formulates an upper-level optimization problem to determine the optimal path and time-of-arrival for each CAV to alleviate congestion.
• Develops a low-level optimization that computes optimal acceleration/deceleration inputs to track the upper-level path and time.
• Solves the low-level problem analytically, explicitly incorporating rear-end safety constraints with speed-dependent safe distance.
• Applies a geometric duality framework using hyperplanes to prove strong duality in the upper-level problem.
• Demonstrates that optimal solutions do not activate state, control, or safety constraints in the lower-level, enabling efficient online computation.
• Validates the framework through simulation to assess performance and feasibility in real-world traffic scenarios.

Experimental results

Research questions

• RQ1 How can connected and automated vehicles be coordinated to minimize congestion in shared traffic scenarios?
• RQ2 What analytical control strategy ensures safe, optimal vehicle trajectories while respecting speed-dependent safety distances?
• RQ3 Can strong duality be established in the path planning optimization to guarantee optimal solutions without constraint activation?
• RQ4 How can the proposed framework be implemented in real time despite dynamic traffic conditions and vehicle constraints?
• RQ5 What is the performance gain in terms of congestion reduction and safety compared to conventional coordination methods?

Key findings

• The proposed framework achieves optimal path and time selection for each CAV through a decentralized, two-level optimization structure.
• The low-level control problem admits a complete, analytical solution that satisfies all state, control, and rear-end safety constraints.
• The geometric duality framework proves strong duality in the upper-level problem, implying that optimal solutions do not bind any constraints.
• This duality ensures that the optimal path and time for each CAV are feasible and implementable in real time without constraint activation.
• Simulation results confirm the framework’s effectiveness in reducing congestion and maintaining safety across various traffic scenarios.
• The analytical solution enables online implementation due to the absence of active constraints in the optimal trajectory, ensuring computational efficiency.