Cooperative Decision Making of Connected Automated Vehicles at Multi-lane Merging Zone: A Coalitional Game Approach

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.Source: A. Motivation · p. 1, A. Problem Formulation · p. 2
• 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.Source: B. Related Work · pp. 1–2
• 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.Source: C. Contribution · p. 2, A. Problem Formulation · p. 3
• 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.Source: C. Contribution · p. 2

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.Source: B. Cooperative Decision-Making… · p. 3
• 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.Source: B. Cooperative Decision-Making… · p. 3

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.Source: A. The Single-track Vehicle Model · p. 3
• 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.Source: A. The Single-track Vehicle Model · p. 3

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.Source: B. Discrete Motion Prediction · pp. 3–4
• 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.Source: B. Discrete Motion Prediction · p. 4
• 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.Source: B. Discrete Motion Prediction · p. 4
• 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.Source: B. Discrete Motion Prediction · pp. 3–4
• 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.Source: B. Discrete Motion Prediction · p. 4

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.Source: §IV · p. 4
• 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.Source: §IV · p. 4
• 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.Source: §IV · p. 4

• Individual rationality requires each member’s allocated cost to be no greater than its standalone cost, with allocation performed using the Shapley method.Source: A. Formulation of the Coalitional Game… · p. 4
• Coalitions may combine disjoint groups when the stated condition holds or split into smaller coalitions otherwise.Source: A. Formulation of the Coalitional Game… · p. 4
• The game includes direct and adjacent passive participants, while interactions with upstream or downstream coalitions remain future work.Source: A. Formulation of the Coalitional Game… · p. 5
• Coalitions minimize decision-making costs associated with safety, comfort, and efficiency through cooperation.Source: A. Formulation of the Coalitional Game… · pp. 4–5
• The four structures are single-player, multi-player, grand, and grand coalitions containing a sub-coalition.Source: A. Formulation of the Coalitional Game… · p. 5

• The motion decisions involve acceleration control and lane changes, with surrounding acceleration, velocity, and position shared through V2V communication.Source: B. Cost Function for the Decision… · p. 5
• 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.Source: B. Cost Function for the Decision… · p. 5
• Safety cost includes longitudinal, lateral, lane-keeping, and lane-change components based on surrounding-vehicle relations and vehicle motion.Source: B. Cost Function for the Decision… · pp. 5–6
• The safety terms account for relative distance and, depending on lane conditions, relative velocity with surrounding vehicles.Source: B. Cost Function for the Decision… · p. 6
• Ride comfort is represented through jerk, while travel efficiency is modeled as a function of the CAV’s longitudinal velocity.Source: B. Cost Function for the Decision… · p. 6

• Decision making includes constraints covering safety, ride comfort, acceleration, and travel efficiency.Source: C. Constraints of the Decision Making · pp. 6–7
• Lane-change trajectories are constrained by curvature through the minimum turning radius Rmin.Source: C. Constraints of the Decision Making · p. 7
• The front-wheel steering angle is also bounded during the maneuver.Source: C. Constraints of the Decision Making · p. 7
• The individual constraints are expressed in a compact form for use in the decision-making optimization.Source: C. Constraints of the Decision Making · p. 7

• 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.Source: D. Decision Making with the… · p. 7
• The single-player strategy optimizes three separate coalitions, whereas the multi-player strategy jointly optimizes V1 and V2 while leaving V3 separate.Source: D. Decision Making with the… · p. 7
• The grand-coalition strategy jointly optimizes V1, V2, and V3 as one coalition.Source: D. Decision Making with the… · p. 7
• The grand coalition with a sub-coalition treats V1 and V4 as one coordinated unit whose actions may differ by a time delay τ.Source: D. Decision Making with the… · pp. 7–8
• The algorithm optimizes the resulting coalition structure and outputs the decision-making results, with the formulation extendable beyond four vehicles.Source: D. Decision Making with the… · p. 8
• 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.Source: D. Decision Making with the… · p. 8
• The game-based problem becomes a closed-loop iterative multi-constraint optimization problem whose Nash equilibrium existence is guaranteed although uniqueness is not.Source: D. Decision Making with the… · p. 8

• Two testing cases evaluate the feasibility and effectiveness of the proposed cooperative decision-making algorithms.Source: §V · p. 8
• All driving scenarios were established and implemented on the MATLAB/Simulink platform.Source: §V · p. 8
• Table II provides the parameter settings used by the decision-making algorithm in the driving scenarios.Source: §V · p. 8

Case Study 1

• Case 1 compares the single-player and grand coalitions, representing noncooperative and fully cooperative forms for three CAVs.Source: A. Case Study 1 · pp. 8–9, Figure 4 · p. 9
• 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.Source: A. Case Study 1 · pp. 9–10, Table III · p. 10
• The decision-making results are presented for Scenario A and Scenario B, while longitudinal paths and velocities provide corresponding motion outcomes.Source: Figure 5 · p. 9, Figure 6 · p. 9, Figure 7 · p. 10
• V1’s velocity is smaller in the grand coalition than in the single-player coalition in Scenario B, increasing its travel-efficiency cost.Source: A. Case Study 1 · p. 9, Figure 7 · p. 10
• Because the grand coalition is not optimal for V1 in Scenario B, V1 does not join it.Source: A. Case Study 1 · p. 9
• 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.Source: A. Case Study 1 · p. 9, Figure 8 · p. 10

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.Source: B. Case Study 2 · p. 10
• 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.Source: B. Case Study 2 · p. 10
• About 0.07 s per step is the mean computational time in Case 2, indicating potential for real-time applications.Source: B. Case Study 2 · p. 10, Figure 14 · p. 11
• In Scenario C, conservative V2 remains a single-player coalition and decreases speed in advance instead of changing lanes to assist V1 and V4.Source: B. Case Study 2 · pp. 10–11
• 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.Source: B. Case Study 2 · pp. 10–11

VI. CONCLUSION

• The approach produces feasible, reasonable, and adaptive coalition-based decisions for CAVs across different driving scenarios.Source: §VI · p. 12
• The testing results indicate that the method can ensure traffic-system safety while meeting personalized driving demands in complex merging zones.Source: §VI · p. 12
• Future work will address decision making in more complex traffic scenarios involving both human-driven vehicles and CAVs.Source: §VI · p. 12