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Cooperative Decision Making of Connected Automated Vehicles at Multi-lane Merging Zone: A Coalitional Game Approach
Peng Hang, Chen Lv, Chao Huang, Yang Xing, Zhongxu Hu
TL;DR
Multi-lane CAV merging requires decisions that accommodate safety, comfort, efficiency, and differing driving preferences amid complex vehicle interactions. The paper combines motion prediction, MPC, and a coalitional game with driving-characteristic-aware costs and constraints. Testing reports feasible, reasonable decisions that adapt to different driving characteristics while addressing group and individual objectives.
Problem
Multi-lane merging creates safety, efficiency, comfort, and coordination challenges because vehicles interact under dynamic traffic conditions and have differing driving preferences.
Method
The paper combines a simplified vehicle-dynamics motion predictor, MPC, constrained safety-comfort-efficiency costs, driving characteristics, and four coalition types for cooperative CAV decisions.
Results
Testing shows the coalitional-game approach makes feasible and reasonable decisions, adapts to different driving characteristics, and accommodates both collective and individual vehicle objectives.
Takeaways & Limitations
Coalitional cooperation can reduce whole-group cost, while coalition selection must account for individual optimality when CAV driving characteristics differ.
Abstract
from arXiv · showhide
To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, a motion prediction module is established based on the simplified single-track vehicle model for enhancing the accuracy and reliability of the decision-making algorithm. Then, the cost function and constraints of the decision making are designed considering multiple performance indexes, i.e. the safety, comfort and efficiency. Besides, in order to realize human-like and personalized smart mobility, different driving characteristics are considered and embedded in the modeling process. Furthermore, four typical coalition models are defined for CAVS at the scenario of a multi-lane merging zone. Then, the coalitional game approach is formulated with model predictive control (MPC) to deal with decision making of CAVs at the defined scenario. Finally, testings are carried out in two cases considering different driving characteristics to evaluate the performance of the developed approach. The testing results show that the proposed coalitional game based method is able to make reasonable decisions and adapt to different driving characteristics for CAVs at the multi-lane merging zone. It guarantees the safety and efficiency of CAVs at the complex dynamic traffic condition, and simultaneously accommodates the objectives of individual vehicles, demonstrating the feasibility and effectiveness of the proposed approach.
I. INTRODUCTION
The paper addresses cooperative CAV decision making at multi-lane merging zones, where safety, comfort, efficiency, vehicle interactions, and differing driving preferences complicate merging. It proposes a coalitional-game framework that combines motion prediction, MPC, and driving-characteristic-aware decision making.
- I. INTRODUCTION: Multi-lane merging involves interacting safety, comfort, efficiency, and personalized driving objectives under complex dynamic traffic conditions.The paper highlights sudden deceleration, collision risk, delayed merging, and differing travel preferences as central challenges.
- I. INTRODUCTION: Existing studies mainly optimize longitudinal merging sequences, while multi-lane settings and lateral lane-change behavior are less fully addressed.The paper identifies a focus on single-lane main-road and on-ramp scenarios, with main-lane lane changes and lateral optimization often neglected.
- I. INTRODUCTION: The proposed coalitional-game framework coordinates CAVs at multi-lane merging zones while considering safety, comfort, efficiency, and individual vehicle objectives.The framework is designed for interactions and decision-making strategies among CAVs in the multi-lane merging scenario.
- I. INTRODUCTION: Motion prediction is integrated with MPC, and different driving characteristics produce multi-modal coalitions and personalized decision-making strategies.The contribution explicitly considers aggressive, moderate, and conservative driving behaviors within cooperative merging decisions.
B. Cooperative Decision-Making Framework for CAVs
The framework models CAV interactions using human-like driving characteristics, a single-track vehicle model, and a cost-constrained cooperative decision process. Motion prediction supplies vehicle states for decisions that balance safety, comfort, and efficiency.
- B. Cooperative Decision-Making Framework for CAVs: Aggressive, moderate, and conservative driving characteristics assign different priorities to efficiency, safety, and comfort in CAV decision making.Aggressive driving prioritizes travel efficiency, conservative driving prioritizes safety and comfort, and moderate driving lies between them.
- B. Cooperative Decision-Making Framework for CAVs: The framework predicts host and surrounding CAV motions, formulates constrained costs, solves cooperative decisions in the cloud, and sends commands to motion planning and control.The pipeline proceeds from predicted motion states to cost optimization, decision transmission, and execution by each vehicle’s motion controller.
- A. The Single-track Vehicle Model: A simplified single-track bicycle model represents CAV motion for prediction, reducing the complexity of the four-wheel vehicle model under a small steering-angle assumption.The model uses longitudinal and lateral vehicle dynamics, yaw motion, position, tire forces, and steering-related quantities.
- A. The Single-track Vehicle Model: The vehicle model neglects air and rolling resistance and uses a small-slip-angle assumption to obtain simplified longitudinal and lateral tire-force relationships.Cornering stiffness and front and rear tire slip angles support the lateral dynamics formulation.
B. Discrete Motion Prediction
The continuous single-track model is discretized into a time-varying linear system for MPC-based prediction. Predicted output sequences are assembled over prediction and control horizons, after which control increments are obtained for cooperative decision making.
- B. Discrete Motion Prediction: The single-track model is transformed into a time-varying linear system to support motion prediction over a finite horizon.The prediction uses time-indexed state, input, and output coefficient matrices across p = k, k + 1, ..., k + Np − 1.
- B. Discrete Motion Prediction: Discrete dynamics use a sampling interval to map vehicle states and controls into a new state-space representation with control increments.The discretization defines Ak, Bk, the sampling time, the control vector, and ∆u(k) for acceleration and steering changes.
- B. Discrete Motion Prediction: The predictive horizon Np exceeds the control horizon Nc, enabling predicted state vectors to be generated from known states, inputs, and coefficient matrices.The formulation recursively propagates states through the prediction horizon using the time-varying matrices.
- B. Discrete Motion Prediction: The predicted output sequence Y(k) stacks future outputs across the prediction horizon and is derived from the state-transition and input-response matrices.The stacked sequence includes y(k + 1|k) through y(k + Np|k), with matrix structures encoding their dependence on control increments.
- B. Discrete Motion Prediction: After motion prediction, the control-increment sequence ∆u is obtained by solving the cooperative decision-making problem.This links the prediction module to the subsequent coalition-based optimization stage.
IV. DECISION MAKING USING THE COALITION GAME APPROACH
The coalitional-game approach defines coalition types for CAVs in multi-lane merging and combines cost optimization with MPC under safety, comfort, and efficiency constraints. It computes predictive decision sequences for each coalition.
- IV. DECISION MAKING USING THE COALITION GAME APPROACH: The approach applies a coalitional game to CAV decision making at multi-lane merging zones.The method treats cooperative decision making as a game among relevant CAVs in the merging scenario.
- IV. DECISION MAKING USING THE COALITION GAME APPROACH: Four typical coalition types are proposed, and each coalition’s cost function considers safety, comfort, and efficiency.The coalition formulation is paired with constraints and MPC to represent multiple decision-making objectives.
- IV. DECISION MAKING USING THE COALITION GAME APPROACH: MPC computes the predictive decision-making sequence for each coalition while satisfying multiple constraints.The formulation explicitly includes safety constraints alongside the stated comfort and efficiency objectives.
A. Formulation of the Coalitional Game for CAVs
The paper formulates CAV merging as a coalitional game in which vehicles cooperate to reduce decision-making costs while satisfying individual rationality. It defines four coalition structures and rules for coalition formation and splitting.
- Individual rationality requires each member’s allocated cost to be no greater than its standalone cost, with allocation performed using the Shapley method.
- Coalitions may combine disjoint groups when the stated condition holds or split into smaller coalitions otherwise.
- The game includes direct and adjacent passive participants, while interactions with upstream or downstream coalitions remain future work.
- Coalitions minimize decision-making costs associated with safety, comfort, and efficiency through cooperation.
- The four structures are single-player, multi-player, grand, and grand coalitions containing a sub-coalition.
B. Cost Function for the Decision Making of an Individual CAV
Each CAV’s decision cost combines safety, ride comfort, and travel efficiency, with weighting coefficients representing different driving characteristics. The formulation captures longitudinal and lateral safety, lane keeping and changing, jerk, and velocity-related efficiency.
- The motion decisions involve acceleration control and lane changes, with surrounding acceleration, velocity, and position shared through V2V communication.
- The individual CAV cost function consists of safety, comfort, and efficiency terms weighted according to driving characteristics.The paper considers aggressive, moderate, and conservative weighting profiles.
- Safety cost includes longitudinal, lateral, lane-keeping, and lane-change components based on surrounding-vehicle relations and vehicle motion.
- The safety terms account for relative distance and, depending on lane conditions, relative velocity with surrounding vehicles.
- Ride comfort is represented through jerk, while travel efficiency is modeled as a function of the CAV’s longitudinal velocity.
C. Constraints of the Decision Making
The decision-making optimization imposes constraints for safety, comfort, acceleration, travel efficiency, trajectory curvature, and steering angle. These constraints are collected into a compact feasible-set representation.
- Decision making includes constraints covering safety, ride comfort, acceleration, and travel efficiency.
- Lane-change trajectories are constrained by curvature through the minimum turning radius Rmin.
- The front-wheel steering angle is also bounded during the maneuver.
- The individual constraints are expressed in a compact form for use in the decision-making optimization.
D. Decision Making with the Coalitional Game Approach
The coalitional-game decision problem is solved as a constrained MPC optimization using predicted motion and coalition-specific decision sequences. Four coalition strategies determine whether vehicles optimize separately, jointly, or through a sub-coalition.
- MPC uses predicted motion and constrained optimization to compute each coalition’s decision-making sequence.The decision sequence contains predicted control inputs over the control horizon.
- The single-player strategy optimizes three separate coalitions, whereas the multi-player strategy jointly optimizes V1 and V2 while leaving V3 separate.
- The grand-coalition strategy jointly optimizes V1, V2, and V3 as one coalition.
- The grand coalition with a sub-coalition treats V1 and V4 as one coordinated unit whose actions may differ by a time delay τ.
- The algorithm optimizes the resulting coalition structure and outputs the decision-making results, with the formulation extendable beyond four vehicles.
- Coalition formation uses sub-coalition rules based on spacing and matching driving-characteristic weights, then checks cost allocation to decide whether groups remain or split.
- The game-based problem becomes a closed-loop iterative multi-constraint optimization problem whose Nash equilibrium existence is guaranteed although uniqueness is not.
V. TESTING, VALIDATION AND DISCUSSION
Two testing cases were designed to verify the feasibility and effectiveness of the cooperative decision-making algorithms. The scenarios were implemented in MATLAB/Simulink using the listed decision-making parameters.
- Two testing cases evaluate the feasibility and effectiveness of the proposed cooperative decision-making algorithms.
- All driving scenarios were established and implemented on the MATLAB/Simulink platform.
- Table II provides the parameter settings used by the decision-making algorithm in the driving scenarios.
A. Case Study 1
Case Study 1 compares single-player and grand coalitions across moderate and aggressive driving-characteristic scenarios. The results show that grand cooperation reduces group cost when characteristics match, but may disadvantage an individual with different characteristics.
- Case Study 1: Case 1 compares the single-player and grand coalitions, representing noncooperative and fully cooperative forms for three CAVs.
- Case Study 1: The grand coalition reduces the sum cost and each CAV’s cost in Scenario A, but increases V1’s cost in Scenario B.Scenario A uses moderate characteristics for all CAVs, whereas Scenario B assigns V1 an aggressive mode and leaves V2 and V3 moderate.
- Case Study 1: The decision-making results are presented for Scenario A and Scenario B, while longitudinal paths and velocities provide corresponding motion outcomes.
- Case Study 1: V1’s velocity is smaller in the grand coalition than in the single-player coalition in Scenario B, increasing its travel-efficiency cost.
- Case Study 1: Because the grand coalition is not optimal for V1 in Scenario B, V1 does not join it.
- Case Study 1: The proposed algorithm has a mean computational time of about 0.06s per step in Case 1.The paper notes that future real-time experiments could improve computational efficiency through more efficient solvers and computing platforms.
B. Case Study 2
Case 2 shows that driving characteristics change coalition formation and the resulting cooperative maneuvers, while the algorithm maintains a mean computational time of about 0.07 s per step.
- B. Case Study 2: In Scenario A, all five CAVs form a grand coalition, with V1–V4 and V3–V5 as sub-coalitions; V2 slows and changes lanes to create safer merging space.
- B. Case Study 2: In Scenario B, aggressive V3 and V5 form a separate coalition, V3 does not yield, and V2 slows while V1 and V4 increase speed to preserve safe distance.
- B. Case Study 2: About 0.07 s per step is the mean computational time in Case 2, indicating potential for real-time applications.
- B. Case Study 2: In Scenario C, conservative V2 remains a single-player coalition and decreases speed in advance instead of changing lanes to assist V1 and V4.
- B. Case Study 2: Different driving characteristics produce different coalition formations and cooperative merging behaviors across Scenarios A–C.Scenario A forms a grand coalition; aggressive vehicles in Scenario B split into a separate coalition, while conservative behavior in Scenario C leaves V2 in a single-player coalition.
VI. CONCLUSION
The paper concludes that its coalitional-game framework provides cooperative multi-lane merging decisions that adapt to driving characteristics while balancing traffic-system safety with individual driving demands. It identifies mixed traffic with human-driven vehicles and CAVs as future work.
- VI. CONCLUSION: The approach produces feasible, reasonable, and adaptive coalition-based decisions for CAVs across different driving scenarios.
- VI. CONCLUSION: The testing results indicate that the method can ensure traffic-system safety while meeting personalized driving demands in complex merging zones.
- VI. CONCLUSION: Future work will address decision making in more complex traffic scenarios involving both human-driven vehicles and CAVs.