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An Integrated Framework of Decision Making and Motion Planning for Autonomous Vehicles Considering Social Behaviors
Peng Hang, Chen Lv, Chao Huang, Jiacheng Cai, Zhongxu Hu, Yang Xing
TL;DR
Autonomous-vehicle decision making and motion planning are often treated separately, while social interactions with surrounding vehicles are rarely modeled. This paper integrates both modules for lane changes using Stackelberg Game decision making, potential-field motion planning, and MPC, and tests the approach in three scenarios with different social behaviors. The reported tests show proper and safe decisions and planning across these interactions, demonstrating feasibility and effectiveness.
Problem
Social interactions with surrounding vehicles are rarely considered in autonomous-vehicle decision making, although driving styles and intentions affect AV decisions and planning.
Method
The paper integrates Stackelberg Game decision making with potential-field and MPC-based motion planning while modeling surrounding vehicles’ driving styles.
Results
Testing in three scenarios shows that the integrated approach addresses different social interactions and produces proper and safe AV decisions and planning.
Takeaways & Limitations
The integrated approach demonstrates feasibility and effectiveness for lane-change decision making and motion planning under different surrounding-vehicle social behaviors.
Abstract
from arXiv · showhide
This paper presents a novel integrated approach to deal with the decision making and motion planning for lane-change maneuvers of autonomous vehicle (AV) considering social behaviors of surrounding traffic occupants. Reflected by driving styles and intentions of surrounding vehicles, the social behaviors are taken into consideration during the modelling process. Then, the Stackelberg Game theory is applied to solve the decision-making, which is formulated as a non-cooperative game problem. Besides, potential field is adopted in the motion planning model, which uses different potential functions to describe surrounding vehicles with different behaviors and road constrains. Then, Model Predictive Control (MPC) is utilized to predict the state and trajectory of the autonomous vehicle. Finally, the decision-making and motion planning is then integrated into a constrained multi-objective optimization problem. Three testing scenarios considering different social behaviors of surrounding vehicles are carried out to validate the performance of the proposed approach. Testing results show that the integrated approach is able to address different social interactions with other traffic participants, and make proper and safe decisions and planning for autonomous vehicles, demonstrating its feasibility and effectiveness.
I. INTRODUCTION
The paper identifies gaps in separately designed decision making and motion planning, especially for socially interactive traffic, and proposes an integrated lane-change framework for AVs.
- Research gap: Social interactions are rarely incorporated into AV decision making, despite surrounding vehicles’ driving styles and intentions affecting AV decisions and planning.The paper motivates characterizing these behaviors to support more human-like interaction-aware decisions.
- Proposed direction: The proposed framework integrates decision making and motion planning for lane changes while modeling surrounding vehicles’ social behaviors.Lane change is selected as the target scenario because it is a typical highway action, with lateral and longitudinal choices influenced by obstacle-vehicle driving styles.
- Proposed direction: Stackelberg Game theory formulates decision making as a non-cooperative game, while potential fields and MPC support motion planning.The paper integrates the modules through common social-behavior features and uses MPC for motion-planning development.
- Research gap: Decision making and motion planning are highly correlated, but separate designs may produce infeasible paths, frequent braking, or sharp steering.The paper notes that overly narrow or broad planning constraints can respectively hinder feasible solutions or limit performance potential.
- Evaluation scope: The approach is evaluated across different driving scenarios and obstacle-vehicle behaviors to assess feasibility, effectiveness, and adaptivity.The stated assumptions restrict the study to behavior planning, straight lanes, lane changes, and obstacle-vehicle acceleration or deceleration.
III. DEVELOPMENT OF DECISION MAKING BASED ON STACKELBERG GAME THEORY
The decision-making module models lane changes as a non-cooperative Stackelberg Game between a host vehicle and an obstacle vehicle, with costs capturing safety, comfort, and efficiency.
- Game formulation: The lane-change problem is formulated as a non-cooperative game in which vehicles choose actions under complex traffic conditions.The modeling framework explicitly considers players, actions, and costs.
- Game formulation: The host vehicle is the leader, the obstacle vehicle is the follower, and their actions are lane change or lane keeping versus acceleration or deceleration.The host vehicle can change lanes or remain in its lane; the obstacle vehicle reacts longitudinally.
- Game formulation: Four interaction cases represent combinations of host and obstacle actions, with action costs related to safety, ride comfort, and travel efficiency.Both vehicles minimize their costs when selecting responses in the game.
- Host-vehicle cost: Host-vehicle safety costs depend on gaps and relative velocities to the vehicle ahead and obstacle vehicle, with lateral safety handled in motion planning.Lane velocity limits and vehicle-length safety coefficients also enter the cost formulation.
- Host-vehicle cost: The host vehicle’s cost combines longitudinal and lateral safety costs, ride-comfort costs based on acceleration, and travel-efficiency costs based on velocity.The total cost uses weighting coefficients for the three components, while the action includes changing left, no lane change, or changing right.
C. Cost Function of the Obstacle Vehicle
The obstacle-vehicle cost function aggregates safety, ride comfort, and travel efficiency under the assumption that obstacle vehicles do not change lanes.
- Obstacle-vehicle cost: Obstacle-vehicle driving-safety cost includes longitudinal and lateral components.The longitudinal component is written using gaps and relative velocities involving the obstacle vehicle and its vehicle ahead.
- Obstacle-vehicle cost: Under the no-lane-change assumption, the obstacle vehicle’s lateral safety cost is set equal to the host vehicle’s lateral safety cost.Only acceleration or deceleration actions are considered for obstacle vehicles.
- Obstacle-vehicle cost: Obstacle-vehicle ride-comfort cost depends only on longitudinal acceleration.The formulation uses a weighting coefficient for longitudinal acceleration.
- Obstacle-vehicle cost: Obstacle-vehicle travel-efficiency cost depends on its longitudinal velocity relative to the lane velocity limit.The velocity limit is defined for the lane associated with the obstacle vehicle’s action.
- Obstacle-vehicle cost: The total obstacle-vehicle cost integrates driving safety, ride comfort, and travel efficiency through corresponding weighting coefficients.Separate coefficients are specified for the three cost categories.
D. Decision Making using Stackelberg Game Theory
The lane-change decision is formulated as a bilevel, two-player Stackelberg Game, with the host vehicle leading and an obstacle vehicle responding. The formulation incorporates lane options, acceleration choices, and velocity and acceleration constraints, and is intended to be combined with motion planning.
- The host and one obstacle vehicle are modeled as a two-player Stackelberg Game and solved as a bilevel optimization problem.
- The optimization includes bounds on the host vehicle’s acceleration and constraints on velocity and acceleration.The acceleration boundaries are represented by lower and upper limits, while velocity and acceleration constraints are explicitly included.
- The host vehicle selects the lane-change decision and longitudinal acceleration, while the obstacle vehicle selects an optimal response to that decision.The host vehicle is the leader; the obstacle vehicle is the follower, and its action is selected given the host vehicle’s decision.
- On roads with more than two lanes, a middle-lane host may choose either adjacent lane, requiring both left and right obstacle vehicles to be considered.On two-lane roads or marginal lanes, only one lane-change option and one obstacle vehicle are considered.
- Because the decision problem is highly coupled with vehicle motion planning, the paper combines lane-change decision making with motion planning.
IV. MOTION PLANNING BASED ON POTENTIAL FIELD MODEL
The motion-planning approach combines a potential-field model with Model Predictive Control to plan the autonomous vehicle’s optimal path while representing interactions with surrounding obstacles.
- Potential fields model vehicle dynamics and interactions with surrounding obstacles, and are combined with MPC for autonomous-vehicle optimal path planning.
A. The Potential Field Model
The potential-field model assigns spatial potential values to obstacle vehicles and road boundaries, then combines these components into an integrated field for multi-vehicle, multilane environments. High values occur near obstacles and boundaries, while free space has low potential.
- Obstacle vehicle field: The obstacle-vehicle potential field is defined over geodetic position, with its value determined by obstacle location, maximum potential, directional convergence coefficients, velocity, and shape.The obstacle position is represented by its center-of-gravity coordinates; the maximum field value and convergence coefficients shape the field.
- Visualizations: The obstacle-vehicle field is illustrated as a 3D map, and the road field is illustrated for a three-lane road.
- Road field: The road potential field uses the road’s maximum potential, distance to the lane mark, a safety threshold, and vehicle width.
- Integrated field: The model combines potential fields from all obstacle vehicles and lane lines into one integrated function.The number of obstacle vehicles is m, and the number of lane lines is n.
- Integrated field: The resulting three-lane highway field has very large values near obstacles and road boundaries and very small values in free space.The paper illustrates this configuration with three vehicles on a three-lane highway.
B. The Motion Planning Model
The motion-planning model couples longitudinal planning with decision making and uses a simplified kinematic model for motion-planning design. Longitudinal planning concerns acceleration or velocity, while the model includes the host vehicle’s heading angle.
- Longitudinal motion planning concerns the autonomous vehicle’s acceleration or velocity and is coupled with the decision-making module.
- A simplified kinematic model is proposed for motion-planning design, with the host vehicle’s heading angle identified in the model description.
C. Prediction of the Planned Path
The planned-path predictor discretizes the vehicle model, uses MPC over prediction and control horizons, and repeatedly solves a constrained cost-minimization problem. Its output combines potential-field tracking, lane-center error, and control-variation penalties.
- Model prediction: The vehicle dynamics are discretized with sampling time ΔT, while the output vector contains the integrated potential-field value at the vehicle position.The output is defined as y(k)=g(x(k),u(k))=[P(X_hv(k),Y_hv(k)),δ_hv(k)].
- Model prediction: MPC predicts multiple future states and outputs using a prediction horizon N_p and a shorter control horizon N_c, with N_p>N_c.The method defines output and control sequences over these horizons before optimizing the motion-planning cost.
- Optimization objective: The motion-planning cost penalizes output error, lateral distance from the lane centerline, and control-input variation.Q_1 and Q_2 weight output-related terms, while R weights control-input variation.
- Optimization objective: Motion planning is formulated as a constrained optimization problem with bounded control inputs and system-state and output constraints.The optimized control sequence is selected subject to minimum and maximum control-vector values.
- Receding-horizon update: After optimization, the controller applies the optimal sequence and restarts the problem at the next time step with an updated state and shifted horizon.This receding-horizon update repeatedly predicts the planned path using the newly estimated state.
V. INTEGRATED SOLUTION CONSIDERING DISTINGUISHED SOCIAL BEHAVIORS
The integrated solution represents surrounding vehicles through three driving styles and incorporates their distinct priorities into decision-making. Aggressive, cautious, and normal styles differ mainly in emphasis on efficiency, safety, and an intermediate balance.
- Driving-style representation: The model defines aggressive, normal, and cautious driving styles as distinct social behaviors of obstacle vehicles.These styles are used to represent differing behavior during decision-making and planning.
- Driving-style representation: Aggressive drivers prioritize travel efficiency, cautious drivers prioritize safety, and normal drivers occupy an intermediate position.The paper assigns these behavioral priorities explicitly in the decision-making problem.
- Decision-model weighting: Driving styles are associated with driving safety, ride comfort, and travel efficiency through different weighting-coefficient settings.The coefficient selections for the three styles are listed in Table II.
B. Motion Planning Considering Different Social Behaviors of Obstacle Vehicles
The motion-planning system maps obstacle-vehicle driving styles to different potential-field distributions and couples its outputs with decision making in a closed-loop optimization. Testing scenarios then examine how these social behaviors alter lane-change decisions and planning.
- Socially differentiated potential fields: Potential-field models represent aggressive, normal, and cautious obstacle vehicles with different spatial distributions despite equal velocity.The aggressive model extends most broadly along the vehicle’s motion direction, while the cautious model has the smallest distribution.
- Integrated closed loop: Decision-making outputs feed the motion-planning system, whose generated motion states return as feedback in a closed-loop iterative optimization.The integrated computation is solved as a multi-constraint optimization using an evolutionary algorithm.
- Testing scenarios: The evaluation uses three scenarios: two two-lane highway cases and one three-lane highway case.These cases are used to validate the integrated decision-making and path-planning approach.
- Testing scenarios: In Case 1, an aggressive adjacent vehicle accelerates to block the host vehicle, whereas normal and cautious behavior leaves increasing space for a lane change.The cautious case permits the earliest lane-change execution because the obstacle vehicle accelerates less.
B. Testing Case 2
Case 2 evaluates a second lane change after the host vehicle encounters a slower vehicle, while Case 3 evaluates lane selection on a three-lane highway under differing obstacle-vehicle styles. Across these tests, the integrated method changes its maneuver according to surrounding behavior and lane cost.
- Testing Case 2: Case 2 adds a slower vehicle ahead after the initial lane change, requiring the host vehicle to choose between following and overtaking.The decision-making process must also account for the behavior of the vehicle that becomes the new obstacle.
- Testing Case 2: An aggressive V1 accelerates to prevent the second lane change, while normal V1 gives way and cautious V1 enables completion in less time and distance.With normal V1, the host vehicle completes the double lane change at 320 m.
- Testing Case 3: Case 3 evaluates a more complex three-lane highway with multiple obstacle vehicles occupying adjacent lanes.The initial configuration includes the host vehicle and V1 in the middle lane, with V2 and V4 on the adjacent lanes.
- Testing Case 3: When both adjacent vehicles are aggressive, the host vehicle follows and slows; when V4 is normal, it gives way and permits a safe lane change.When both are normal, the host vehicle selects the left lane because it has the smaller generated cost.
- Testing Case 2: The paper concludes that the integrated method supports reasonable decisions and safe path planning under varied surrounding social behaviors.The conclusion describes the approach as feasible and effective across the tested cases.