Source-linked AI summary
Optimal Control and Coordination of Connected and Automated Vehicles at Urban Traffic Intersections
Yue J. Zhang, Andreas A. Malikopoulos, Christos G. Cassandras
TL;DR
The paper addresses online coordination of CAVs crossing two adjacent intersections under fuel, congestion, and safety objectives. It develops a decentralized optimal-control framework and reports lower fuel consumption and travel time than traffic-light control in simulation.
Problem
The paper addresses how to coordinate a continuous flow of CAVs through two adjacent intersections while controlling fuel consumption under congestion and collision-avoidance constraints.
Method
The paper develops a decentralized optimal-control framework that computes each vehicle’s acceleration or deceleration online from local coordination information.
Results
42.4% lower fuel consumption and 37.3% lower average travel time were reported for 448 CAVs versus a 30 sec traffic-light-cycle baseline.
Takeaways & Limitations
When feasible, the solution coordinates vehicles through both intersections without traffic lights, connecting-road congestion, or collision violations.
Takeaways & Limitations
The solution’s feasibility when vehicles enter with active constraints remains an ongoing research question.
Abstract
from arXiv · showhide
We address the problem of coordinating online a continuous flow of connected and automated vehicles (CAVs) crossing two adjacent intersections in an urban area. We present a decentralized optimal control framework whose solution yields for each vehicle the optimal acceleration/deceleration at any time in the sense of minimizing fuel consumption. The solu- tion, when it exists, allows the vehicles to cross the intersections without the use of traffic lights, without creating congestion on the connecting road, and under the hard safety constraint of collision avoidance. The effectiveness of the proposed solution is validated through simulation considering two intersections located in downtown Boston, and it is shown that coordination of CAVs can reduce significantly both fuel consumption and travel time.
I. INTRODUCTION
The paper motivates decentralized coordination of CAVs as an alternative to traffic-light control, targeting smoother, safer, and more fuel-efficient flow across two intersections.
- Traffic-light approaches can be computationally inefficient for online control and impose infrastructure and dynamic cycle-management costs.
- Traffic lights can significantly increase rear-end collisions, motivating approaches that improve flow, fuel efficiency, and safety.
- Existing CAV intersection methods include centralized reservation schemes and decentralized coordination, but decentralized approaches can suffer deadlocks from local information.
- The paper formulates decentralized online control for varying numbers of CAVs crossing two intersections while minimizing fuel consumption under congestion and collision-avoidance constraints.
- The paper provides an analytical solution and evaluates it in VISSIM using two intersections in downtown Boston.
II. THE MODEL
The model represents two adjacent intersections as controlled merging zones connected by a road, with coordinators assigning vehicles to FIFO queues and vehicles governed by constrained second-order dynamics.
- Two intersections are separated by distance D, with square merging zones of side S where lateral collisions may occur.
- Each intersection has a control zone and coordinator, with entry-to-merging-zone distance L > S shared across its entry points.
- A time-varying number of CAVs receives unique identities based on FIFO queue position and travel-direction information.
- Vehicles leaving the first merging zone cruise at their exit speed before joining the queue for the second intersection.
- Each vehicle uses second-order dynamics with position, speed, and acceleration/deceleration as state and control variables.
- Vehicle speed is constant inside any merging zone, while acceleration, deceleration, and speed remain within admissible bounds.
A. Decentralized Control Problem Formulation
The decentralized formulation assigns each vehicle a target merging-zone exit time from local information, then minimizes its control effort while enforcing congestion and collision-avoidance constraints.
- Each vehicle receives a unique coordinator identity and communicates locally with the preceding vehicle rather than relying on a global controller.
- Vehicles are partitioned by lane, destination, and potential collision relationships to determine how they may share or sequence through a merging zone.
- A vehicle’s information set includes sensed position and speed, assigned vehicle subsets, distance to a preceding vehicle, and a target merging-zone exit time.
- Target exit times maintain flow by allowing compatible vehicles to share the merging zone, enforcing safe spacing, or requiring sequential passage to avoid lateral collisions.
- Rear-end safety requires the intervehicle distance to satisfy s_i(t) ≥ δ, while speed and acceleration feasibility determine attainable exit times.
- The decentralized problem minimizes the squared control input because its monotonic relationship with fuel consumption makes control minimization equivalent to fuel minimization.
B. Analytical solution of the decentralized control problem
The decentralized controller derives each vehicle’s optimal acceleration/deceleration online using Hamiltonian analysis and updated integration constants. The analysis handles unconstrained arcs, while constraint activation introduces important computational and applicability limits.
- Scope and limitations: The analytical solution assumes constraints are inactive when vehicles enter the control zone, leaving infeasible-entry cases for additional research.A vehicle entering above the speed limit requires an optimal-control solution beginning from an infeasible state.
- Analytical formulation: Hamiltonian analysis yields the necessary conditions for each vehicle’s optimal control under state, control, and rear-end collision constraints.The formulation uses co-state variables and Lagrange multipliers, with multipliers zero when constraints are inactive and positive when they become active.
- Scope and limitations: Rear-end collision constraints can become intractable because of numerous possible activation and deactivation scenarios, so they are omitted from the subsequent analysis.The paper states that rear-end collision avoidance is guaranteed at the final time, but not that the constraint remains inactive throughout the interval.
- Unconstrained arcs: When inequality constraints are inactive, the optimal control is affine in time, with vehicle-specific integration constants.Substitution into the vehicle dynamics produces corresponding optimal speed and position trajectories.
- Online implementation: The integration constants are recomputed from current states and time, allowing the controller to provide each vehicle’s optimal control online.The constants are obtained from a four-equation system based on initial and final conditions, and feedback is supplied indirectly through their recalculation.
- Online implementation: The control remains unchanged until an event affecting vehicle behavior occurs, so an event-driven implementation can replace the time-driven controller under stated conditions.The paper reports that this replacement does not affect the optimality properties under the cited conditions.
C. Interdependence of the Intersections
The two intersections are coordinated through vehicle interactions on the connecting road. When a vehicle’s speed falls below the desired minimum, preceding vehicles are accelerated to create space and preserve the minimum cruising speed.
- Interdependence: Coordination at one intersection affects vehicle behavior at the other because the intersections are interdependent through the connecting road.Increasing vehicle density can reinforce safety constraints that cause vehicles to slow down.
- Congestion avoidance: τ_i denotes the additional minimum time required for vehicle i to reach the merging zone at the desired minimum speed v_min.It is defined from the vehicle’s remaining distance and current speed.
- Congestion avoidance: When a vehicle’s speed drops below v_min, the first vehicle in its queue must advance its merging-zone exit time by τ_i(t).This adjustment propagates through earlier vehicles’ exit times.
- Congestion avoidance: Vehicles preceding the slowed vehicle accelerate so it can cruise at least at v_min, creating the required connecting-road space.The mechanism updates the exit times of vehicles from the first vehicle through the affected vehicle.
- Congestion avoidance: The per-vehicle information set is expanded to include τ_i for coordination under connecting-road congestion.The expanded information is incorporated alongside vehicle and intersection coordination variables.
IV. SIMULATION RESULTS
Simulations evaluate the constrained coordination of the first 22 vehicles at intersection II and quantify its performance against traffic lights. The coordinated approach maintains safety-related spacing while reducing fuel consumption and travel time relative to the baseline.
- The constrained simulations used speed limits of vmax = 13 m/s and vmin = 0.5 m/s, with a desired minimum control-zone speed of 7 m/s.
- Vehicle #8 enters the merging zone immediately after vehicle #7 exits, while vehicle #22 accelerates to reach the merging zone alongside vehicle #21.
- When vehicles #8 or #9 fall below the desired minimum speed, preceding vehicles accelerate to create space for recovery.This interaction illustrates interdependence among adjacent vehicles traveling through the two intersections.
- 448 CAVs were simulated across two intersections and compared with a 30-second traffic-light-cycle baseline.
- 42.4% lower fuel consumption and 37.3% lower average travel time were achieved with CAV coordination versus the baseline.The reported fuel-consumption improvement is attributed to vehicles avoiding full stops, conserving momentum and fuel.
V. CONCLUDING REMARKS
The paper presents a decentralized optimal-control framework for online coordination of continuous CAV flow across two adjacent urban intersections. Future work addresses feasibility under active entry constraints, computational implications, vehicle-type diversity, and the possible trade-off between fuel consumption and congestion.
- The framework yields each vehicle’s acceleration or deceleration aimed at minimizing fuel consumption when the solution is feasible.
- Ongoing research examines feasibility when constraints are active as vehicles enter the control zone and studies the resulting computational implications.
- Future research should consider diverse CAV types and a potential trade-off between fuel consumption and congestion.