Source-linked AI summary
A Decentralized Energy-Optimal Control Framework for Connected Automated Vehicles at Signal-Free Intersections
Andreas A. Malikopoulos, Christos G. Cassandras, Yue J. Zhang
TL;DR
The paper addresses energy-efficient control of CAVs crossing urban intersections without explicit traffic signals while maintaining throughput and hard safety constraints. It uses throughput maximization to determine crossing times, then derives decentralized optimal controls with analytical feasibility conditions; simulations report lower fuel consumption and travel time than traffic lights. The framework assumes full penetration of identical CAVs with perfect information and excludes lane changes, turns, and pedestrians.
Problem
The paper addresses how to control CAVs crossing signal-free urban intersections while minimizing energy consumption under throughput and hard safety requirements.
Method
Throughput maximization first determines each vehicle’s crossing time, enabling decentralized energy-minimization problems with analytical solutions and feasible safety-constrained regions.
Results
46.6% fuel consumption improvement and 30.9% travel time improvement were obtained against a traffic-light baseline.
Takeaways & Limitations
Vehicles can conserve momentum and fuel while improving travel time by avoiding full stops and minimizing acceleration and deceleration inside the control zone.
Takeaways & Limitations
The framework assumes full penetration of identical CAVs with perfect information and excludes lane changing, turns, and pedestrians.
Abstract
from arXiv · showhide
We address the problem of optimally controlling connected and automated vehicles (CAVs) crossing an urban intersection without any explicit traffic signaling, so as to minimize energy consumption subject to a throughput maximization requirement. We show that the solution of the throughput maximization problem depends only on the hard safety constraints imposed on CAVs and its structure enables a decentralized optimal control problem formulation for energy minimization. We present a complete analytical solution of these decentralized problems and derive conditions under which feasible solutions satisfying all safety constraints always exist. The effectiveness of the proposed solution is illustrated through simulation which shows substantial dual benefits of the proposed decentralized framework by allowing CAVs to conserve momentum and fuel while also improving travel time.
1 Introduction
The paper motivates new control and optimization approaches for increasingly complex transportation networks, focusing on signal-free intersection control for CAVs. Its framework targets congestion, energy use, safety, and travel delays through tighter vehicle coordination and decentralized optimization.
- Transportation networks are increasingly complex cyber-physical systems integrating energy, transportation, cyber networks, and human interactions.
- 2014 congestion caused 6.9 billion additional vehicle-hours and 3.1 billion extra gallons of fuel in urban areas.
- Intersection bottlenecks motivate control mechanisms that expand capacity without changing existing road infrastructure.
- Autonomous highways can reduce congestion, energy use, emissions, and safety risks by increasing traffic flow through closer vehicle spacing.
- The paper optimally controls CAVs through signal-free urban intersections to minimize energy consumption subject to throughput maximization and hard safety constraints.
- Its first contribution connects throughput-based crossing times with a decentralized energy-minimization control problem and provides a complete analytical solution including state and control constraints.
2 Problem Formulation
The formulation models CAVs entering and crossing an unsignalized intersection while coordinating throughput, energy use, vehicle dynamics, and hard collision-avoidance constraints. It establishes a recursive throughput schedule that supports decentralized energy minimization under conditions guaranteeing safety feasibility.
- 2 Problem Formulation: The intersection model contains a Control Zone with communication support and a central Merging Zone where lateral collisions may occur.The coordinator communicates information but does not make decisions for individual CAVs.
- 2 Problem Formulation: The formulation assumes no lane changes or turns, with L denoting the distance from Control Zone entry to Merging Zone entry and S the Merging Zone side length.These geometric assumptions define the setting in which the control problems are formulated.
- 2 Problem Formulation: Vehicles are ordered in a queue and assigned Merging Zone entry times, while multiple scheduling policies can satisfy the required temporal ordering.The policy may preserve first-in-first-out order or update a vehicle’s queue position when it enters the Control Zone.
- 2.1 Vehicle Model, Constraints, and Assumptions: Each CAV is modeled with second-order longitudinal dynamics and position, speed, acceleration/deceleration, and state-control admissibility constraints.The model uses compact position-speed state spaces and bounds acceleration/deceleration and speed.
- 2.1 Vehicle Model, Constraints, and Assumptions: Neighbor sets distinguish same-road different-lane, same-lane, collision-conflicting, and other vehicles, supporting rear-end and lateral safety constraints.A predefined safe distance constrains vehicles in the same lane, while conflicting vehicles cannot occupy the Merging Zone simultaneously.
- 2.1 Vehicle Model, Constraints, and Assumptions: The assumptions include initially inactive constraints, constant speed inside the Merging Zone, and error-free local proximity sensing.The sensing assumption can be relaxed when measurement and communication uncertainty or delay is bounded.
- 2.2 Energy Minimization Problem Formulation: The energy objective minimizes a control-input cost, while the throughput schedule minimizes queue-clearing time and determines terminal times for the energy problems.The terminal entry time can be adjusted to trade off throughput emphasis against energy consumption.
- 2.2 Energy Minimization Problem Formulation: The throughput solution has a recursive structure based on safety and state-control constraints, enabling decentralized energy minimization and a nonempty feasible region of initial conditions.The stated feasible region guarantees that all safety constraints hold throughout the relevant interval under the paper’s conditions.
3 Decentralized Framework
The decentralized framework assigns each CAV local information and a target MZ-entry time, then solves sequential online optimal-control problems using Hamiltonian analysis. The analytical solution handles active state and control constraints, while feasibility conditions ensure rear-end safety under appropriate initial conditions.
- Decentralized optimization: The coordinator enables communication but does not make control decisions, allowing sequential decentralized problems to be solved online for each CAV.The decentralized formulation uses the L2-norm of the control input as a special case of the energy cost.
- Information structure: A coordinator assigns each CAV a unique identity, queue position, and positional relationship to the preceding vehicle.The identity is the triplet (w, i, j), where j maps the four positional subsets R_i(t), L_i(t), C_i(t), and O_i(t).
- Information structure: Each vehicle’s information set includes its position, speed, assigned queue subset, preceding-vehicle distance, and target time to enter the MZ.The target MZ-entry time is computed from the vehicle’s queue relationship and information received from the preceding vehicle.
- Safety feasibility: The rear-end safety constraint is omitted from the decentralized problem because the resulting solution is shown to satisfy it throughout the control and merging zones under suitable initial conditions.A nonempty feasible region of initial conditions exists, and the safety distance s_i(t) remains at least δ over the relevant interval.
- Analytical solution: Hamiltonian analysis yields analytical control, speed, and position trajectories, with constrained arcs pieced together whenever unconstrained solutions violate bounds.The method considers combinations of inactive, control-constrained, and state-constrained arcs, including speed limits and acceleration limits.
2. Control Constraint Active, u∗
The analytical controller is constructed from unconstrained and constrained trajectory arcs. Although the rear-end safety constraint can be violated by the unconstrained solution, a nonempty feasible initial-condition region guarantees safety under the decentralized control.
- Control and state constraints: When the unconstrained control reaches u_max, the solution transitions through arcs that may also activate the upper speed constraint v_i(t) = v_max.The corresponding speed and position trajectories are polynomial on the constrained segments and are matched at transition points.
- Control and state constraints: When the unconstrained control reaches u_min, the controller can activate the lower control bound and subsequently the lower speed constraint v_i(t) = v_min.On the lower-speed constrained arc, acceleration is zero and position evolves according to the vehicle dynamics.
- Arc transitions: Constraint arcs can later become inactive, after which Hamiltonian and costate continuity conditions determine the subsequent unconstrained trajectory.The same arc-piecing logic is applied when upper or lower state constraints are exited.
- Implementation: An event-driven implementation can preserve optimality because the control structure remains unchanged until an event occurs.This avoids repeatedly re-evaluating the optimal control on a time-driven schedule under the stated conditions.
- Safety feasibility: With δ = 10, the unconstrained optimal control can violate the rear-end safety constraint inside the control zone even when the constraint initially holds.The example identifies an interior violation by CAV 3, although the constraint is eventually satisfied.
- Safety feasibility: Theorem 2 establishes a nonempty feasible region of initial conditions under which the decentralized optimal control maintains the safety distance throughout the control and merging zones.Thus, feasibility depends on driving the CAV to an appropriate feasible initial point before applying the decentralized solution.
4 Simulation Results
Simulations evaluate coordination for 20 and 448 vehicles against fixed-time traffic lights. In the tandem-intersection study, the decentralized framework improves both fuel consumption and travel time.
- Study design: The evaluation includes case studies coordinating 20 vehicles with MATLAB and 448 vehicles with VISSIM, compared against fixed-time traffic lights.The simulations assess the proposed vehicle-coordination solution under single- and tandem-intersection settings.
- Results: 46.6% fuel consumption improvement and 30.9% travel time improvement are reported for the tandem-intersection comparison with traffic lights.The study assumes a Poisson arrival rate of λ = 450 veh/h per lane and does not consider coupling between the two intersections.
- Results: Fuel savings are attributed to avoiding full stops and using minimum acceleration/deceleration inside the control zone.These choices conserve momentum and reduce transient engine operation.
5 Concluding Remarks and Future Work
The framework provides a decentralized analytical solution for energy-efficient CAV control at signal-free intersections while satisfying throughput and safety requirements. The concluding discussion identifies assumptions and extensions concerning vehicle diversity, information quality, queueing, and intersection operations.
- The proposed framework minimizes energy consumption subject to throughput maximization and hard safety constraints at signal-free urban intersections.
- Its decentralized control structure depends on neighboring CAVs, admits a complete analytical solution, and has conditions guaranteeing feasible safety-compliant solutions.
- Limitations and extensions: The framework assumes full penetration of identical CAVs with perfect information and excludes lane changing, turns, and pedestrians.
- Limitations and extensions: The control structure remains unchanged until behavior-affecting events occur, supporting future event-driven controller development.
- Limitations and extensions: The first-in-first-out queue can become limiting in heavy traffic, motivating dynamic scheduling, mixed penetration studies, and analysis of information errors or delays.
A. Proof of Lemma 1
The proof of Lemma 1 determines the minimum attainable terminal time by examining which safety constraints can become active for each vehicle relationship. It reduces the calculation to several cases involving preceding, following, and conflicting vehicles.
- The proof minimizes each vehicle’s terminal time after fixing the first vehicle’s solution and then treats vehicles i = 2, . . . , N sequentially.
- Case analysis: When vehicle i −1 is in a following or opposing relationship, one safety constraint cannot activate, while another may couple i to a vehicle k in the preceding lane.
- Case analysis: When vehicle i −1 is in the preceding-lane set, the proof again identifies which constraint can activate and applies the corresponding terminal-time expression.
- Case analysis: When vehicle i −1 is a conflicting vehicle, the conflict-related safety constraint can become active and determines the applicable terminal-time case.
B. Proof of Theorem 1
The proof of Theorem 1 establishes lower bounds on terminal times by separating vehicle trajectories according to their entry conditions and whether they can reach the maximum speed. These bounds are combined with Lemma 1 to obtain the theorem’s result.
- The proof seeks a lower bound for vehicle i’s terminal time that is independent of constraints whose attainability is uncertain.
- Case analysis: The analysis distinguishes cases based on vehicle i’s initial time and whether it can reach vmax before reaching the merging zone.
- Case analysis: If vehicle i reaches vmax, the trajectory accelerates at umax, cruises at vmax, and then exits the merging zone at the corresponding terminal time.
- Case analysis: If vehicle i reaches the merging zone below vmax after accelerating at umax, the proof uses the corresponding exit-time characterization.
- The lower bound is combined with Lemma 1 to obtain the stated result, including the free variable tm∗1 dependent on A1.
C. Proof of Theorem 2
The proof establishes feasibility by analyzing whether state or control constraints are active and characterizing the resulting safety-separation conditions. It then shows that the feasible initial-condition region is always nonempty.
- Case analysis: The proof separates cases according to whether state or control constraints become active for either CAV over the control zone.Each active-constraint combination changes the trajectory expressions and feasibility analysis.
- Unconstrained case: When constraints are inactive, the inter-vehicle separation s_i(t; τ, υ) is analyzed through its cubic trajectory and stationary points.The minimum separation is located using ṡ_i(t; τ, υ) = 0 with s̈_i(t; τ, υ) ≥ 0, alongside endpoint checks.
- Active-constraint cases: For active constrained arcs, the same feasibility logic is applied piecewise, using the appropriate polynomial coefficients and evaluating separation at relevant times.The resulting feasible region consists of initial conditions satisfying an inequality of the form s_i(σ; τ, υ) − δ ≥ 0.
- Nonempty feasible region: A feasible initial condition can be obtained by choosing v_min < υ < v_max and τ = t_f_i, which gives s_i(τ) > S > δ.Therefore, at least one feasible point exists in the initial-condition space.
- Geometric interpretation: The feasible region is illustrated as the yellow portion of the (τ, υ) space, separated from the infeasible region by a generally nonlinear black boundary curve.The boundary shifts across the different constraint cases, while points to the right of the curve correspond to feasible entry times.