Trajectory planning and tracking control for autonomous lane change maneuver based on the cooperative vehicle infrastructure system

doi:10.1016/j.eswa.2015.03.022

Expert Systems with Applications

Volume 42, Issue 14, 15 August 2015, Pages 5932-5946

https://doi.org/10.1016/j.eswa.2015.03.022 Get rights and content

Highlights

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Autonomous lane change maneuver was developed using cooperative strategy.
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Proposed system can be potential to prevent lane change crashes and thus reducing injuries and fatalities.
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A trajectory planning method based on polynomial was developed.
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A trajectory tracking controller with global convergence ability was designed.
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Simulations and experimental results were presented to validate the method.

Abstract

Lane change maneuver is one of the most conventional behaviors in driving. Unsafe lane change maneuvers are key factor for traffic accidents and traffic congestion. For drivers’ safety, comfort and convenience, advanced driver assistance systems (ADAS) are presented. The main problem discussed in this paper is the development of an autonomous lane change system. The system can be extended applied in intelligent vehicles in future. It solves two crucial issues – trajectory planning and trajectory tracking. Polynomial method was adopted for describing the trajectory planning issue. Movement of a host vehicle was abstracted into time functions. Moreover, collision detection was mapped into a parameter space by adopting infinite dynamic circles. The second issue was described by backstepping principle. According to the Lyapunov function, a tracking controller with global convergence property was verified. Both the simulations and the experimental results demonstrate the feasibility and effectiveness of the designed method for autonomous lane change.

Introduction

Lane change maneuvers are one of the most conventional behaviors in driving. It is defined transfer of a host vehicle from the current lane to the next adjacent lane. To perform a lane change, drivers have to collect a large amount of information, such as velocity and distance between the host vehicle and vehicles in the target lane, traffic flow and road traffic environment information related to facilities. The decision of lane change is made on condition that the safe gap between vehicles is satisfied according to human driver experience. Actually, the process of a lane change involves environmental information collection and analysis, opportunity judgment, trajectory generation, collision detection, conflict processing and etc. According to past research, lane change and lane merge maneuvers account for approximately 5% of total crashes and as high as 7% of total crash fatalities (Habel and Schreckenberg, 2014, Rodemerk et al., 2012). At present, traffic accidents related to lane change on highway account for a considerable proportion. From the Netherlands’s transportation statistics, 12.6% of all traffic accident are caused by lane change (Bax, Leroy, & Hagenzieker, 2014). In Canada, 9.8% of crash fatalities result from lane change (Amin, Zareie, & Amador-Jiménez, 2014). In the United States, from 1994 to 2005, there were 13,939 traffic accidents caused by lane change and 24,565 killed (Kretschmer, Neubeck, & Wiedemann, 2005).

In developing countries such as India, Brazil and China, the problem gets worse. In China, traffic accidents caused by lane change are on the rise. Depending on the report from the China’s Highway Traffic Safety Administration, massive traffic accidents caused by lane change are outstanding. Especially, more than 60% of the traffic accidents on the freeway are related to lane change (Li, Wu, Xu, & Lin, 2014). It is obvious that traffic accidents caused by lane change occur frequently. Thereby, how to improve safety for lane change has become an urgent issue to be dealt with.

Recently, traffic safety administration agencies and automobile companies focus more on reducing the number of lane change crashes. Traffic safety administration agencies are actively finding a solution to the issue that can regulate driving behavior by encouraging safer driving actions. For instance, through public advertisement or publicity board, the serious consequences in lane change crashes are emphasized. Also, notes on lane change safety are repeated. Some agencies in China use large variable message board (VMB) for freeways to remind drivers to reduce the number of lane change in accident high-risk or heavy-traffic areas.

On the other hand, the automobile companies have an urgent interest in utilizing high technology to provide lane change assistance for drivers. With the increase in the wide application of sensor technology in automobiles, advanced driver assistance systems (ADAS) have been implemented in recent years. The development of ADAS to aid in driving-related tasks has a crucial role to play in the automotive field. For more lane change safety, the lane change assistance system will become one of the most significant parts of the ADAS.

As discussed above, ADAS are developed to assist human drivers. One of the main objectives of the technology has been to increases driver awareness by providing useful information. Over the last years, ADAS have obtained a large number of research achievements. There are some examples of lane detection and lane keeping assistance (LKA) (He et al., 2013, Lefevre et al., 2014, Son et al., 2015), and obstacles detection and avoidance in the vehicle’s path such as either vehicles (Hassannejad, Medici, Cardarelli, & Cerri, 2015) or pedestrians detection (Alahi et al., 2014, Sermanet et al., 2013), adaptive cruise control (ACC), stop&go, autonomous parking or other elements, like traffic lights on roads (Diaz-Cabrera, Cerri, & Medici, 2015). ADAS are on-board vehicle systems which concentrate on the driving process. Of all examples, LKA and ACC are becoming the highest potential technologies in ADAS. The former was regarded as an extension of cruise control (CC). Drivers can set a specified driving velocity in advance with CC in which the vehicle is capable of following a leading car on freeways by controlling the throttle and brake pedals, i.e., longitudinal control. On the other hand, in essence, LKA, which remains one of the toughest challenges in the development of ADAS, is lateral control for vehicle. It is designed to alert the driver when the system detects that the vehicle is about to deviate from a lane. Complete lateral vehicle control has still to be addressed by the automotive companies.

Compared with the achievements achieved in ADAS, the research on lane change safety lags behind. In all maneuvers, lane change is one of the most complexes since both lateral and longitudinal control need to be considered. Drivers have to consider several factors affecting safety. These factors include, speed and position of the subject vehicle and vehicles in the target lane, geometric characteristics of the road, vehicle characteristics, and others. Due to the significance of the lane change safety, recent literature has been devoted to four main aspects of lane change, i. e., lane change warning, lane change behavior, lane changing trajectory planning and lane change control.

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Lane change warning

According to the ISO Standard 17387, Lane Change Decision Aid System (LCDAS) consist of three different types of warning systems – Blind Spot Warning (BSW), Vehicle Proximity Warning (VPW), and lane change warning (LCW). In BSW systems, there is a warning message triggered in case that any obstacles intervene into drivers’ blind spots or areas. VPW systems are capable of recognizing approaching vehicles from behind in adjacent lanes. LCW systems are considered as a hybrid system, which has the function of both BSW systems and VPW systems. Based on the Standard, some studies have been conducted. For instance, in Shiller, Prasanna, and Salinger (2008), a collision warning approach due to neighboring traffic is presented. Based on the concept of velocity obstacles, it designed to alert the driver of a potential front collision and against attempting a dangerous lane change maneuver. To avoid false alarms in lane changes, prediction of a lane-change maneuver is needed. In Schmidt, Beggiato, Hoffmann, and Krems (2014), obtained early predictors by analyzing 3111 lane changes with regard to speed, secondary task engagement, turn signal usage, and steering wheel angle. Tomar et al. proposed a strategy for warning and intervention to assist the driver in a lane change maneuver (Tomar, Verma, Kushwah, & Tomar, 2013). The strategy consists of a relative motion estimator and supervisor. To assess the threat in a lane change situation, vehicle sensor information and rear-side radar sensor information have been combined in the relative motion estimator. In our work, we have not considered this approach, since our technique, which is not only warning for lane change, focus on how to accomplish autonomous lane change.

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Lane change behavior

Many research works like (Guo et al., 2013, Zheng et al., 2014) have been conducted in lane change behavior. These studies show that the drivers’ decision to change lanes is associated with driver characteristics, driver attitudes (such as aggressive behavior) and depends on many factors. In Gipps (1986) designed a lane changing model that was implemented in a microscopic traffic simulator. In a recent study Hou, Edara, and Sun (2015), have developed a genetic fuzzy model to predict merging behavior of drivers at lane drops. Xiaorui and Hongxu (2013) established a lane change model integrated with the car following behavior. The model considers kinematic behavior of the lane-changing vehicle in the case of acceleration. In Zheng, Ahn, Chen, and Laval (2013) presented a method to explore diverse components of lane changes impacts- anticipation process, relaxation process and change in driver characteristics induced by lane changes. Laval and Daganzo (2006) proposed a model to consider the drop in discharge rate at bottlenecks due to lane-change maneuvers. It provides simulations that appear to replicate empirical results observed from fixed-point detectors in their studies. These models stated above have been proposed to acquire the accurate way to describe a lane change maneuver. However, none of them were designed for use in a real-time lane changing assistance system that advises drivers of when it is safe or unsafe to merge.

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Lane changing trajectory planning

A predefined trajectory must be presented to track during the lane change maneuver. Accordingly, trajectory planning is an extremely significant issue in the topic of autonomous lane change maneuver. Its main aim is to generate a trajectory from current lane to goal lane that satisfies some limitations or objectives, like acceleration, joint jerk, minimization of time interval, vibration, collision avoidance criteria or other dynamic constraints.

There are numerous experiences in lane changing trajectory planning. Classical trajectory planning strategies, such as road map, cell decomposition and potential field methods are frequently mentioned in robot field. Nevertheless, they have the possibility of getting stuck in local minima. Furthermore, it takes an extremely long time to reach global minima in the case of too many parameters. Actually, trajectory planning for a lane change is always simple. The existing methods are on various types of curves – circular (Kim, Oh, Suk, & Tsourdos, 2014), harmonic (Zhang, Chen, & Shen, 2013), polynomial (Rossi & Savino, 2013) and line segments (Vale, Fonte, Valente, & Ribeiro, 2014). In Ioannou (2013), lane change patterns of each driver are modeled with a hidden Markov model (HMM). From the HMM, vehicle trajectories are selected in a maximum likelihood criterion at random lane-changing time and state duration. On the other hand, the trapezoidal acceleration curve trajectory was proposed to generate the least possible lateral acceleration for lane changes (Soudbakhsh, Eskandarian, & Chichka, 2013). In Soudbakhsh et al. (2013), three different path planning methods- state lattice, predictive constraint-based planning and spline based on search tree -are evaluated. In Hidalgo-Martínez, Sanmiguel-Rojas, and Burgos (2014), a path planner based Bézier curve which enables the anti-collision behavior of vehicle is presented.

In spite of these developments, the latest trends have been focused on planning based on cooperative technologies (Behere et al., 2013, Pérez et al., 2013). In our work, in the framework of cooperative technologies, a trajectory planner based the polynomial for lane change maneuver was presented since the polynomial curve has the advantage of continuous curvature and simplicity. Moreover, the algorithm does not consume much computation time.

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Lane change control

To accomplish the autonomous lane change, a controller should be developed to track the predefined trajectories according to the vehicle states and road information. Many different controlling algorithms for trajectory tracking have been proposed in prior studies. Bayar (2013) designed a traditional PID controller for trajectory tracking, not only because of its simple structure and easy implementation but also because of its acceptable tracking performance. However, the controller is not satisfactory for applications that require high tracking accuracy. Guo, Ge, Yue, and Zhao (2014) reported the trajectory tracking controller of closed-loop control structure is derived using integral backstepping method to construct a new virtual variable. The Lyapunov theory is utilized to analyze the stability of the proposed tracking controller. In Du, Wang, and Chan (2014), a model predictive controller is calculated by reducing the complexity of the system model. The predictive controller allows full control of acceleration/deceleration as well as providing a decision variable regarding preferred lane at each time instance. In Berntorp, Olofsson, Lundahl, and Nielsen (2014), an optimal trajectory based on minimization of yaw acceleration was derived, and the simulation and comparative analysis were also done with different speed values. Ying, Mei, Song, and Liu (2014) studied the longitudinal and lateral coupling control for vehicle platoon lane changing by sliding mode method. In Ren, Zhang, and Wang (2014), a two-layer nonlinear adaptive steering controller is designed that allows tracking the desired trajectories. The adaptive controller is capable of dealing with parameter uncertainties with its self-organizing ability. However, this entails a high computational cost. And more importantly, in spite of the fact that the above controller can track the predefined trajectories, both passengers’ comfort and vehicles’ characteristics are ignored.

The main contribution of this paper is to develop a trajectory planning algorithm for autonomous lane change. It is based on polynomials because polynomial curve has the advantage of continuous curvature and simplicity. Another important advantage of the method over other methods is that it yields much safer trajectories with a lower computational cost. In addition, collision detection strategies are taken into account in this planner. Collision-free trajectories can be generated easily by mapping the obstacles into a parameter space.

As an additional contribution, a study is presented in the development of the tracking controller for trajectories for lane change maneuver. It is designed by using the backstepping method. The convergence of the controller is proven by the Lyapunov stability theory. The controller considers not only passengers’ comfort, but vehicles’ characteristics.

We tested our proposed the trajectory planning algorithm and the tracking controller for trajectories to verify their performance. This study includes simulation and experimental analyses.

The remainder of the paper is organized as follows. Section 2 describes the kinematics model for a lane change. The collaborative strategy for a lane change is discussed in Section 3. Section 4 introduces trajectory representation and generation for the lane change scenario. Section 4.1 presents a trajectory generation method for the case without a front vehicle. Section 4.2 describes the trajectory generation algorithm with a front vehicle. Section 5 introduces tracking control of reference trajectories. Section 6 shows the simulation and experimental results and provides information about the experimental platform. Conclusions are presented in Section 7 that indicate future directions for the research.

Section snippets

Vehicle kinematics and tracking error model

This work deals with the trajectory tracking problems of the kinematic car-like model shown in Fig. 1, with a nonholonomic constraint that restricts the wheels to roll with no slip. The vector $p_{c} = (x_{c}, y_{c}, θ_{c}, δ_{c})$ denotes the configuration of the vehicle, where $(x_{c}, y_{c})$ is the location of the midpoint of the rear axle, $θ_{c}$ is the angle between the $x$ -axis and a reference line on the vehicle frame and $δ_{c}$ is the steering angle. The subscript c stands for ‘current’.

Let $u_{c} = (v_{c} ω_{c})$ be a controlling vector. The

Collaborative strategy for lane change

The environmental information collected from a single vehicle is ultimately quite limited. Therefore, the latest trends have been dedicated to vehicle–vehicle-infrastructure communication (V2X). Using V2X techniques, cooperative trajectory planning can be performed for a lane change. In such a mechanisms, the state messages between vehicles, including information about coordinate position, velocity, and posture, can be broadcasted. For each vehicle, there is one local trajectory planner

Trajectory representation and generation for the lane change scenario

To seek a feasible trajectory and to keep the vehicle running smoothly in a lane change scenario, we introduced some basic principles for the trajectory planning (Feng, Rongben, & Ronghui, 2008):

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The trajectory is continuous.
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The first derivative and second derivative of the trajectory are continuous and also bounded.
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The trajectory can be generated easily and quickly.
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The trajectory should be reasonable and possible to execute.
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The trajectory should avoid rough output from the lane change

Trajectory generation

As shown in Fig. 5, by analyzing the area between vehicles $C_{0}$ and $C_{3}$ , the longitudinal displacements of vehicles $C_{3}$ and $C_{0}$ during the lane change can be determined using Eqs. (9), (10). $S_{C 3}^{1} = v_{C 3} \cdot t_{lc}$ $S_{C 0}^{1} = len + SS + v_{C 3} \cdot t_{lc} - Δ_{1} - len$ The trajectory planning method for a vehicle with one front vehicle is based on Section 4.2 mentioned above. If we increase the order of one of the polynomials, the trajectory will be changed, which is useful for giving more freedom to generate a collision-free trajectory. $\{\begin{matrix} f (x, \end{matrix}$

Calculation of ‘distance to obstacle‘

By analyzing Eqs. (14), (15), (16), (17), (18), (19), we find out that 13 parameters are undetermined in matrix A. However, the initial and target conditions of the vehicle only provide 12 equations. Hence, the obstacle avoidance algorithms should work cooperatively with trajectory generators. We have to introduce the ‘distance to obstacle’ to solve the indeterminate equation.

There are numerous approaches to calculating the distances to obstacles (Wang et al., 2013, You et al., 2013). Most of

Collision avoidance

As shown in Fig. 8, we choose a dynamic circle with a diameter equal to the width of the vehicle, and we construct the region by using the circle to sweep along the vehicle length. Hence, a vehicle can be represented by an infinite number of circles.

The centers of the dynamic circles are given by Eq. (22). $\{\begin{matrix} x = x_{r} + u_{x} (x_{f} - x_{r}) \\ y = y_{r} + u_{y} (y_{f} - y_{r}) \end{matrix}$ In this equation, $u_{x} \in [0, 1], u_{y} \in [0, 1], x_{r}, x_{f}, y_{r}$ and $y_{f}$ are the lateral coordinate of the rear dynamic circle, the lateral coordinate of the front dynamic circle, the

Tracking control of the reference trajectory of the vehicle

According to the kinematics model for a lane change and the control law design based on the backstepping method (Attia et al., 2014, Takemura et al., 2011, You et al., 2008), the error component $x_{e}$ is regarded as a virtual control input, and the new virtual variables are denoted by Eq. (29). ${\hat{x}}_{e} = x_{e} - a_{1} f (k ω_{c}) y_{e}$ where $f (k ω_{c})$ is the hyperbolic tangent function, and $a_{1} f (k ω_{c}) y_{e}$ is virtual feedback of controller. Let control input $u_{c}$ make ${\hat{x}}_{e} \to 0$ , the new virtual control input is defined in Eq. (31). $\forall a_{1} \in (0,)$

Experimental results

To validate the correctness and effectiveness of the control algorithm, a simulation was performed for a 4-wheeled vehicle in MATLAB/Simulink. It is more meaningful to select the parameters of the control law. In particular, parameter k influences the smoothness of the hyperbolic tangent function. Larger values of k cause $f^{'} (k ω_{c})$ converge to zero faster. The control parameters were selected as $(a_{1}, a_{x}, a_{y}, a_{0}, k) = (1.5, 2.5, 0.2, 2.5, 6.8)$ . The following figures represent the simulation results of the two

Conclusions

Lane change maneuvers are one of the most conventional behaviors in driving. Unsafe lane change maneuvers could result in road traffic accidents and the following congestion and delay. The main issue discussed in this paper is the development of a lane change assistance system. The system contains two core modules – trajectory planning and trajectory tracking. The former is based on the characteristics of polynomials. It abstracts the lateral and longitudinal movement of the host vehicle as

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Granted Nos.: 51408237, 51108192 and 51208500), Chinese Postdoctoral Science Foundation (The Granted Nos.: 2012M521824 and 2013T60904), and the Fundamental Research Funds for the Central University of China (Granted No.: 2014ZG0029). The first author would like to appreciate Dr. Ronghui Zhang and the anonymous reviewers for their valuable comments on the earlier versions of the paper.

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Trajectory planning and tracking control for autonomous lane change maneuver based on the cooperative vehicle infrastructure system

Highlights

Abstract

Introduction

Section snippets

Vehicle kinematics and tracking error model

Collaborative strategy for lane change

Trajectory representation and generation for the lane change scenario

Trajectory generation

Calculation of ‘distance to obstacle‘

Collision avoidance

Tracking control of the reference trajectory of the vehicle

Experimental results

Conclusions

Acknowledgments

Transportation Research Part C: Emerging Technologies

Transportation Research Part D: Transport and Environment

Transportation Research Part F: Traffic Psychology and Behaviour

Journal of Systems Architecture

Expert Systems With Applications

Transportation Research Part B: Methodological

Procedia – Social and Behavioral Sciences

Expert Systems with Applications

Mechanism and Machine Theory

Control Engineering Practice

Transportation Research Part B: Methodological

Expert Systems with Applications

Robotics And Computer-Integrated Manufacturing

Robotics and Autonomous Systems

Expert Systems with Applications

Robotics and Autonomous Systems

Procedia – Social and Behavioral Sciences

Chinese Journal of Aeronautics

Transportation Research Part C: Emerging Technologies

Simulation Modelling Practice and Theory

Combined longitudinal and lateral control for automated vehicle guidance

Vehicle System Dynamics

Long distance autonomous trajectory tracking for an orchard vehicle

Industrial Robot: An International Journal

Models and methodology for optimal trajectory generation in safety-critical road-vehicle manoeuvres

Vehicle System Dynamics