Design and validation of minimal jerk lane changing manoeuvre for adaptive cruise control in electric vehicles

Abstract

Vehicle stability largely depends on the driving conditions and the driver. In Autonomous vehicles the stability of the vehicle is an important factor and is directly related to safety. When performing the steering manoeuvres during overtaking or during turns, the autonomous features should ensure that the vehicle remains stable. This work focuses on design and development of a steering manoeuvre that ensures smooth operation during overtaking and turns. The model will be implemented along with Adaptive Cruise Control and Anti-Lock Braking mechanism. The validation of the model is performed in IPG CarMaker software. The software is linked with Matlab/Simulink which enables to operate the model at the backend to perform the validation of the safety and stability features.

Article Highlights

Proposes a minimal jerk-based lane-changing maneuver for smoother Adaptive Cruise Control in EVs.

Integrates real-time optimization for dynamic driving conditions using MATLAB/Simulink and IPG CarMaker.

Combines minimal jerk control, Adaptive Cruise Control, and ABS to enhance safety and skid prevention.

Introduction

Autonomous vehicles have gradually gained space and generated sufficient research interest in the automotive sector. There have been several features incorporated for driver assistance. However, they all come in varying degrees of autonomy [1]. The adaptive cruise control (ACC) is a feature predominantly used for driver assistance. It ensures a substantial part of the driver’s tasks is assigned automatically. ACC comes with several functionalities like adjusting the speed of the vehicle with respect to the surrounding traffic, automatic acceleration and deceleration, target selection and longitudinal control. For an autonomous vehicle, the concept of vehicle following and its consequences on traffic flow and density has been an active area of research [2]. In a deeply congested network, even with multiple lanes and corridors, the traditional driving mechanism by a human is characterised by reaction times, delays, errors that adversely impact the traffic flow. A way of eliminating these tendencies is the replacement of the human driver with computers, control system and other enabling accessories like sensors, indicators, cameras, lasers, and radar equipment etc. Sensory technologies are primarily employed for detecting and cautioning the driver about collisions. ACC systems are designed in such a way that they help the vehicles to maintain a safe distance from the leader vehicle while ensuring the speed limit. The main objective is to visualise the closeness of one vehicle with respect to the other and to maximise the spatial awareness which in turn would maximise the traffic flow. ACC forms the crux of vehicle intelligence. It can be classified mainly into three types as shown in Fig. 1.

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Fig. 1

Classification of ACC

Several methods employing computational intelligence [3, 4–5] are employed for solving the traffic safety issue with respect to self-driving vehicles. ACC is an important subset of Advanced Driver Assistance Systems (ADAS) which helps the human driver for manoeuvres during driving and parking. The sensors retrieve the information from the environment while the control algorithms are used to regulate the vehicle [6]. In the automotive market, ADAS, apart from ACC also caters to emergency braking, lane keeping assistant (LKA) etc. For the parameters like fault tolerance [7], road safety and geometry [8, 9], fuel efficiency, signal intersection and traffic flow [10], there are many optimization-based ACCs which have been designed, conceptualised, and developed. The connectivity also ensures that the ADAS leverages Vehicle-to-Vehicle (V2V) [11] and Vehicle-to-Infrastructure (V2I) communication for further improved performance. In [12], the authors present the design of an ACC controller incorporating the information related to gradeability of road, by means of a grade map, to predict the longitudinal dynamics of the vehicle. The proposed controller also smoothly and automatically transitions between distance and velocity tracking. The preview of the road grade as well as the future state trajectory of the leading vehicle is transmitted through V2V communication.

A flexible eco-cruising strategy is proposed by [13] for connected and automated vehicles Here, both driving lane planning and speed optimization are considered. The authors have designed a hierarchical control framework in which the driving lane sequence is planned by the first layer and the vehicle’s speed is optimised by the second layer for energy efficiency. The third layer then regulates the speed and yaw angle and optimises the driving trajectory. The authors of [14] propose an event-driven energy-efficient driving control strategy for connected electric vehicles in urban traffic. A model predictive control approach is utilised to optimise the vehicle’s speed and energy consumption when subjected to traffic events such as traffic lights and other vehicles. It is observed that there is a significant reduction in energy consumption as compared to traditional driving strategies. In [15], an overtaking-enabled eco-approach control strategy is proposed for connected and automated vehicles at intersections having signals. This strategy ensures slower vehicles are overtaken by vehicles behind them for improvement of fuel efficiency and reduction of travel time as compared to traditional traffic control strategies. The authors of [16] discuss the implementation of a distributed integrated control architecture for active front steering (AFS) and direct yaw control (DYC) systems in distributed drive electric vehicles. A multi-agent system approach is utilised for the control and coordination of the AFS and DYC systems for improving the vehicle stability and handling performance. It is observed that the vehicle stability and handling performance are better as compared to traditional control architectures.

The impact of Adaptive Cruise Control (ACC) and Lane Keeping Systems (LKS) is analysed in [17] on driving behaviour, particularly focusing on speeding and reduced time gaps. It was found that while ACC and LKS have certain positive impacts on driving, there is also a possibility of display of certain riskier behaviours like increase in speed and reducing time gaps. A comprehensive review of vehicle lane change research is provided in [18]. Several parameters are covered in this study which includes lane change manoeuvre planning, execution, and safety. The various techniques and algorithms used for lane change decision-making and control are also discussed along with the challenges encountered and future directions in this field. A novel model for predicting driver lane change behaviour is proposed in [19] for Cooperative Adaptive Cruise Control (CACC) systems. Machine learning techniques are utilised to analyse several parameters like vehicle speed, relative distance, and lane curvature for accurate prediction of lane change intentions. The objective is to enhance the safety and efficiency of CACC systems.

Additionally, several works [20, 21–22] discuss advanced adaptive cruise control strategiesfor enhancing safety and comfort. This includes the design of a variable weight approach adapting to the leading vehicle’s lane changes. A multi-mode system appraoch with emergency lane-changing capabilities. A Hidden Markov Model strategy for accurate prediction of lane changes, allowing for proactive responses. The purpose is to enhance the overall driving experience and reduce the risk of accidents.

There can be many complex driving scenarios encountered by a connected and autonomous vehicle particularly in vehicle following mode. Cut-in scenario is one such challenging situation faced during lane change for the ACC systems. During manoeuvring to change the lane [23], the host vehicle (with an ACC system) needs to follow the trajectory of the cut-in vehicle [24]. In the event of late or excessive braking, this would in turn affect the trajectory to be followed for the cut-in vehicle and would compromise the driving safety and comfort. Therefore, some investigators came up with the ACC for cut-in scenarios incorporating the Model Predictive Control (MPC) algorithm [25, 26]. Quantifying the cut-in possibility of a vehicle and considering it as a reference, the MPC algorithm [27] (considering the driving safety and comfort) realises co-ordinated control of the host vehicle and the cut-in vehicle [28, 29–30]. Apart from this, however, there are several other challenges and limitations associated with the ACC for connected and autonomous vehicles which are summarised in Table 1.

Table 1. Limitations and challenges faced by ADAS-ACC [31, 32]

Limitations/Challenges	Description
Accuracy and Inconsistency	Some of the systems may not function well in dim-light, low visibility and bad weather conditions., as the sensors would not be able to detect and track objects accurately, which may in turn lead to false alarms or even missed warnings. Sensors may also not be able to detect fast and small objects. Layers of dust on the sensor or modification in the vehicle may also affect the functioning
Processor requirements	Enormous amounts of vehicle data need to be processed under different conditions and time stamp. Data processing may be compromised in the event of a sensor error. Therefore, it is imperative to employ a powerful processor with a high processing power
Algorithm requirements for ADAS	The error in the algorithm logic (since they mainly rely on a set of rules) can severely compromise the functionality of the ADAS technology
Global positioning system (GPS) and mapping	GPS systems are affected sometimes by the constantly changing landscape which in turn would affect ACC and automated parking. Again, if the mapping data is not constantly updated, this would again impact the GPS
Over reliance of driver on ADAS	There is a prevailing confusion between automated driving and autonomous vehicles which in turn convinced many drivers that the vehicle can drive on its own. Too much attention to the technology would deflect attention from the road and lead to damage

Keeping these constraints in mind, our proposed work focusses on the design and validation of a manoeuvring mechanism for lane change with minimal jerk for ACC in electric vehicles. The main objective of this work is to:

• Ensure smooth operation and stability during overtaking and turning

• ACC and Anti-lock braking mechanism

• Real-time validation in IPG CarMaker environment

This work presents an innovative approach to autonomous overtaking maneuvers, focusing on the minimization of lateral jerk to significantly enhance both passenger comfort and vehicle stability. While traditional trajectory planning for autonomous vehicles emphasizes safety, efficiency, and timely maneuver execution, it often overlooks the effects of lateral jerk. Lateral jerk refers to the rapid changes in lateral acceleration, which can lead to sudden, uncomfortable movements for passengers and pose a potential risk to vehicle stability, particularly during complex maneuvers like overtaking. By targeting the reduction of lateral jerk, this research fills a crucial gap in the optimization of vehicle control strategies, offering a smoother, more stable driving experience.

The proposed method introduces an optimization framework that minimizes the square of the lateral jerk, effectively reducing the abruptness of lateral movements without compromising the primary objectives of overtaking, such as safety and efficiency. This is achieved through a quadratic programming (QP) approach, which allows for the computation of control inputs that balance the need for smooth lateral movements with the requirement to meet critical safety constraints. These constraints include maintaining adequate distances from surrounding vehicles and ensuring that the vehicle remains within lane boundaries during the overtaking process. By integrating comfort and safety considerations in real-time decision-making, this approach presents a more holistic strategy for autonomous overtaking, making it a notable contribution to the field. The proposed optimization process is integrated within a Stateflow modeling environment, which plays a pivotal role in adapting the control strategy to the constantly changing dynamics of the surrounding environment. This model-driven approach uses state-based logic to facilitate quick, real-time adjustments based on new sensor inputs and changes in the traffic situation.

The use of Stateflow not only ensures the efficient management of decision-making but also enhances the system’s adaptability across a wide range of driving conditions, such as varying traffic densities, road types, and weather conditions. This enables the autonomous vehicle to perform overtaking maneuvers safely and comfortably under diverse circumstances.The ability to continuously modify control inputs based on updated environmental data ensures that the autonomous system can perform overtaking maneuvers in a manner that maximizes both safety and comfort. Furthermore, this approach can be generalized to a variety of scenarios beyond overtaking, offering potential benefits in other maneuver types, such as lane-keeping and merging. By introducing real-time adaptability through a Stateflow-based approach, this work represents a significant advancement in autonomous vehicle trajectory planning, focusing on the overall passenger experience and vehicle stability, areas that have often been secondary to traditional safety and efficiency measures.

The paper is organised as follows: Sect. 1 details the motivation and background of the proposed work. Section 2 focusses on the mathematical foundation for ACC along with the implemented model and the simulation results. Section 3 provides the mathematical foundation and results for ABS. Section 4 showcases the lateral jerk control for trajectory creation with ACC. Section 5 presents the validated real-time results for the proposed system using the IPG CarMaker simulation tool, followed by discussion and conclusion.

Methods: adaptive cruise control

The model will enable to evaluate the overall performance of the ADAS and the impact of different ACC strategies on the traffic flow. The simulation model will consist of a number of elements including Vehicle Dynamics allowing the model to include the dynamics of the AVs, including acceleration, deceleration, Traffic Flow Model which will include the traffic flow equations to define the movement of vehicles in the network, ACC Controller which will include the algorithms that control the ACC of the AVs, such as the adaptive cruise control strategy, velocity profiles and acceleration limits. The model is developed in MATLAB SIMULINK.

The MATLAB/Simulink model is used to develop an Electric Vehicle model. The Electric Vehicle is modelled as the transfer function G(s):

1

$$G(s)=\frac{1}{s(0.5s+1)}$$which approximates the dynamics of the throttle body and vehicle inertia, as shown in Fig. 2.

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Fig. 2

Electric Vehicle Model

The ADAS in the ego vehicle decides which mode to use based on the forward collusion warning (FCW) system data. If the case is such that the leader vehicle is under the satisfactory case or below, the ACC system switches from Free Drive Mode to Vehicle Follow Mode. If the leader vehicle is far away, then the ACC system switches from Vehicle Follow Mode to Free Drive Mode. The representation of the ACC system is shown in Fig. 3.

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Fig. 3

Adaptive Cruise Control Mode

The following rules are used to determine the ACC system operating mode:

• If $d_{\mathit{ref}}\ge d_{\mathit{safe}}$, then Vehicle Follow mode is active, where $d_{\mathit{ref}}$ is the relative distance and $d_{\mathit{safe}}$ is the safe distance. The control goal is to track the driver-set velocity, 

• If $d_{\mathit{ref}}<d_{\mathit{safe}}$, then Free Drive mode is activated. The control goal is to maintain the safe distance, $d_{\mathit{safe}}$.

The model implemented in MATLAB is shown in Fig. 4. The leader vehicle is provided with an initial constant speed of 20 m/s. The ego vehicle is moving at a speed of 30 m/s at a distance of 100 m behind the leader vehicle. The Adaptive Cruise Controller should be able to regulate the speed of the ego vehicle such that a safe distance between the two vehicles is maintained and the ego vehicle speed reduces and matches the leader vehicle speed as it approaches the leader vehicle. A Model Predictive Controller is used to perform the regulation of the Ego vehicle drivetrain with respect to the leader vehicle operation.

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Fig. 4

Implemented model of ACC between Leader vehicle and Ego vehicle

As shown in Fig. 5, the leader vehicle speed is seen to be at constant 20 m/s while the ego vehicle could be seen to adjust its speed from 30 m/s to 20 m/s as the relative distance between the two vehicles reduces. The ego vehicle then maintains the constant speed of 20 m/s as it follows the leader vehicle.

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Fig. 5

Speed Characteristics of Leader vehicle and the response of Ego vehicle with ACC

The ego vehicle response after the implementation of ACC is seen in Fig. 6. The speed and the position characteristics of the ego vehicle is seen. The ego vehicle can be seen to move from Free drive mode to Vehicle Following mode.

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Fig. 6

Speed Characteristics & Position Characteristics of Ego vehicle with ACC

The relative distance between the ego vehicle and the leader vehicle is found to reduce as the ego vehicle approaches the leader vehicle at a speed of 30 m/s. This can be seen in Fig. 7. As the ego vehicle approaches the leader vehicle and the ACC is activated the distance between the vehicles is maintained to be around 40 m.

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Fig. 7

Relative distance between the Leader vehicle & Ego vehicle with ACC

The state flow model developed is seen in Fig. 8. The Free drive mode is activated when there is no vehicle in front of the Ego vehicle. In such scenarios the vehicle is free to accelerate and move forward. The Vehicle following mode has the Model Predictive Controller implementing the Adaptive Cruise Control. In such a scenario the Vehicle would be following as per the requirements of avoiding accident with the Leader vehicle. In case of some urgent braking requirement in the Ego vehicle, the Emergency Brake Mode is implemented. The Emergency Brake mode will have the Anti-Lock Braking System implemented to ensure safety of the ego vehicle.

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Fig. 8

State flow model for the Ego vehicle with ACC

The matrix concatenation module is used to convert the Simulink signal to 2-D parameters required for the driving control implemented by the Embedded –C Controller, as seen in Fig. 9.

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Fig. 9

ACC model implemented with 2-D visualization

The representation of the leader vehicle and the ego vehicle is shown in the Fig. 10. The red colour car represents the leader vehicle while the blue car represents the ego vehicle.

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Fig. 10

2-D visualization of the Ego vehicle implementing ACC with Leader vehicle

Anti-lock braking system

The primary goal of ABS is to avoid skidding, which occurs when locked wheels from heavy braking cause a loss of steering and control. Many modern cars are now equipped with these technologies. This is not meant to shorten stopping distances; rather, it is intended to allow more steering in emergency situations. With ABS, the speed sensors monitor the wheels’ reducing rotation as you apply the brakes. The electric control unit receives a signal from the brakes just before they are going to stop rotating electronic control unit (ECU). Through valves and pumps, the ECU partially releases the brake pads from the wheels, allowing the wheel to continue turning. With ABS, the wheels may keep turning as you apply strong braking, giving you control of the vehicle. When all crash severity levels and types are included, a meta-analysis of research studies demonstrates that ABS provides a relatively minor but statistically significant reduction in the number of crashes [33].

The anti-lock braking system is implemented to enable the deceleration of the ego vehicle from its vehicle follow mode at the speed of 35 kmph to zero in case the leader vehicle comes to sudden halt. The desired slip is to be maintained at 0.2. The relative slip ($R_s)$ is given by

2

$$R_s=1-(\frac{V_v}{V_w})$$

The wheel angular velocity and the vehicular angular velocity is monitored and the relative slip is calculated. The coefficient of friction changes as the wheel slip changes. To enable this a look up table is added so that for wheel slips are mapped to the coefficient of friction. The tyre torque is obtained using the coefficient of friction and is given by,

3

$$\text{Tyre Torque}({\tau }_t)=\mu \ast \text{N}\ast \text{R}$$where $\mu$—coefficient of friction, N- Normal force acting on the wheel = $\frac{m\ast g}{4}$, R- wheel radius.

The relative slip and the tyre torque is used to determine the wheel speed. To implement this a Bang-Bang Controller is used. The Bang-Bang controller provides,

4

$$\text{output}=\left\{\begin{array}{c}1,iftheinput>0\\ -1,iftheinput<0\end{array}\right)$$

The braking is done using hydraulic braking in the vehicle which involves a hydraulic lag in the implementation of the braking system. This is represented by a transfer function.

5

$$\text{Hydraulic lag},\text{Transfer Function}=\frac{100}{0.1s+1}$$

The hydraulic lag when integrated over time provides the braking torque.

6

$$\text{Braking torque},({\tau }_b)=\int \frac{100}{0.1s+1}$$

The difference between the braking torque and the tyre torque provides the deceleration of the vehicle.

7

$$\text{Deceleration}(\text{d})=\frac{{\tau }_b-{\tau }_t}{I}$$where I represents the moment of Inertia.

The integration of the deceleration provides the wheel speed of the vehicle.

8

$$n_w=\int \frac{{\tau }_b-{\tau }_t}{I}$$

Equivalent vehicle angular acceleration,

9

$$a_v=\frac{\tau _{t\ast m}^{}}{R}$$

Equivalent vehicle angular velocity,

10

$$v_v=\int \frac{\tau _{t\ast m}^{}}{R}$$

The stopping distance is determined from the Equivalent vehicle angular velocity. The vehicle actual slip,$R_s$ is determined as per Eq. (5). The responses can be seen in Fig. 11a–c. Figure 11b shows clearly the ABS in action with pulsated braking ensuring wheel locking is avoided.

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Fig. 11

a: Vehicle velocity reduction with ABS implementation. b Wheel velocity reduction with ABS implementation. c Stopping distance with ABS implementation

Minimum lateral jerk trajectory creation

The Lateral Jerk controls the stability of the vehicle and the comfort offered to the passengers. Lateral Jerk is obtained as a derivative of acceleration [34].

11

$$\stackrel{⃛}{d}\left(t\right)=\frac{d^{3}d\left(t\right)}{d{t}^3}$$

The lateral jerk is useful to generate lane changing decisions. The lateral trajectory has to be such that the square of the lateral jerk is minimized.

12

$$H\left(d\left(t\right)\right)=\frac{1}{2}\underset{t_i}{\overset{t_f}{\int }}\stackrel{⃛}{d}{\left(t\right)}^{2}dt$$where $H\left(d,\left(t\right)\right)$, is the cost function that has to be minimized and $t_{i}and{t}_f$ denotes the lane changing start and end time, respectively. To optimally ensure that the minimum jerk trajectory is obtained, the sixth derivative of the lateral displacement, $d^{\left(6\right)}=0.$ This would mean that a six coefficient equation has to be used to represent the lateral displacement.

13

$$\left[\begin{array}{c}d(t)\\ \dot{d}(t)\\ \ddot{d}(t)\end{array}\right]=\left[\begin{array}{c}{a}_0\\ a_1\\ {2a}_2\end{array},\begin{array}{c}{a}_1\\ {2a}_2\\ {6a}_3\end{array},\begin{array}{c}{a}_2\\ {3a}_3\\ {12a}_4\end{array},\begin{array}{c}{a}_3\\ {4a}_4\\ {20a}_5\end{array},\begin{array}{c}{a}_4\\ {5a}_5\\ 0\end{array},\begin{array}{c}{a}_5\\ 0\\ 0\end{array}\right]\left[\begin{array}{c}1\\ t\\ \begin{array}{c}{t}^2\\ t^3\\ \begin{array}{c}{t}^4\\ t^5\end{array}\end{array}\end{array}\right]$$

The boundary conditions includes—Maintain Safe Distance, Smooth Trajectory and Lane Boundaries, which are used control the trajectory [35, 36–37].

To showcase the Lateral Jerk Control a third vehicle is introduced which now acts as the ego vehicle. The ego vehicle then overtakes the two vehicles and moves forward. During the overtaking the ego vehicle has to perform minimum lateral jerk control. Figure 12a shows the Lateral Jerk Control mechanism implemented along with Adaptive Cruise Control. The Lateral Jerk Controller is regulating the steering controller and the powertrain of Vehicle -3, ego vehicle. Initialising the ego vehicle’s state, including its position, velocity, and other relevant control parameters, is the first step in the optimisation process for minimal jerk control in an autonomous overtaking manoeuvre. In order to evaluate potential dangers and limitations, the system then identifies nearby vehicles and estimates their relative positions and velocities. The risk of the overtaking manoeuvre is then assessed by a feasibility check that looks at longitudinal and lateral distances as well as variation in speed with the nearby vehicles. A smooth and stable transition during the overtaking process is ensured by formulating the objective function with the primary purpose of minimising the square of the lateral jerk. To do this, specific constraints are established, such as maintaining a safe distance from other cars, staying inside lane lines, and making sure the vehicle’s trajectory is as smooth as required. Once the objective and constraints are established, the objective function and these safety-related restrictions are combined to create a quadratic programming (QP) problem. The best control inputs that reduce lateral jerk while meeting safety requirements are obtained by solving this QP issue. The ego vehicle is then guided through the overtaking manoeuvre by an updated optimised trajectory. The ego vehicle executes this trajectory in real time, which allows it to execute the overtaking manoeuvre with the least amount of lateral jerk. After the overtaking is finished, the vehicle returns to a straight line, holding its new position and driving normally again. With few sudden changes in lateral motion, this methodical approach guarantees a safe and comfortable manoeuvre. Figure 13, shows the lane changing manoeuvre of the ego vehicle and occupying the left lane to overtake the vehicles in front.

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Fig. 12

a Lateral Jerk Control with ACC in Matlab, b flow chart for minimal lateral jerk control

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Fig. 13

Minimum Lateral Jerk and Lane Changing manoeuvre

The proposed minimal jerk lane-changing maneuver ensures vehicle stability by specifically targeting the reduction of lateral jerk, which is the rapid change in lateral acceleration. Traditional lane-changing methods often prioritize efficiency and safety, but they may overlook the impact of abrupt lateral movements on vehicle stability. These abrupt changes can destabilize the vehicle, especially during complex maneuvers or at high speeds. By minimizing lateral jerk, the proposed method ensures smoother transitions between lanes. This smoothness reduces the likelihood of sudden or sharp lateral movements that can lead to destabilization, especially in situations where the road is narrow or the vehicle’s speed is high. The optimization framework employed in this approach seeks to minimize the square of lateral jerk, effectively reducing the intensity and frequency of lateral forces exerted on the vehicle there by improving its stability.

Results and discussions

The IPG CarMaker is a simulation software which supports creation of real time scenarios in a virtual environment. MATLAB/Simulink is integrated with IPG CarMaker for model validation through a co-simulation interface, allowing for seamless interaction between the two platforms. This integration enables the use of MATLAB/Simulink’s advanced modeling and control design capabilities in conjunction with IPG CarMaker’s realistic vehicle dynamics simulation environment. IPG CarMaker has MATLAB running at the back end which ensures the flexibility in modelling and integration. The subsystem models created for Minimum Lateral Jerk Control, Adaptive Cruise Control and Anti-Lock braking system is integrated at the back end of the IPG CarMaker model. This enables the virtual vehicle model to perform the required regulations using the created subsystems. During validation in IPG CarMaker, several key safety and stability metrics were considered to ensure the effectiveness of the proposed minimal jerk lane-changing maneuver. The specific metrics evaluated include Lateral Jerk, Vehicle Stability (Yaw rate and roll angel), Lateral Acceleration, Safety Distance (minimum safety distance), Lane Boundary Adherence, Speed Control and Handling, Comfort Metrics (Passenger comfort, side-slip angle, ensuring the maneuver remains smooth and does not induce discomfort or nausea due to sudden movements. These metrics were evaluated during the simulation in IPG CarMaker to validate that the proposed minimal jerk lane-changing maneuver provides a smooth, stable, and safe transition between lanes, ensuring the vehicle remains within the desired operational limits while maintaining comfort and safety for passengers.

The model created in IPG CarMaker is shown in Fig. 14. The IPG CarMaker interface has the representation of different control signals required for the regulation of the vehicle shown. These control signals are utilized as inputs to the four subsystems created. The vehicle steering angle is provided as the input to the Lateral Jerk Control subsystem. The steering angle signal provides information on the lateral motion of the vehicle and thereby the smooth trajectory in the lateral direction can be obtained using the Lateral Jerk Control subsystem. The Adaptive Cruise Control subsystem takes the sensor data as the input. The sensor used in IPG CarMaker is an Object detection sensor. This sensor data is given to the ACC subsystem which implements the three operating modes identified, namely, Vehicle Following Mode, Free Driving Mode and Emergency Braking, if required. During the Emergency Braking or any braking condition, as per the input data from the sensor, Anti-Lock braking is to be implemented. This would ensure that the wheel locking is avoided. This is taken care by the ABS subsystem. During the lateral motion of the vehicle for overtaking, an indicator control is introduced. When the vehicle is overtaking the indicator turns on and provides indication to the following vehicle about its intended overtaking manoeuvre.

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Fig. 14

Minimum Lateral Jerk and Lane Changing Maneuver

The overtaking indicator operation is as shown in Fig. 15. The control is based on the steering angle. If the steering angle is rotated for more than 30% of the steering angle, it is a signal to the subsystem that the vehicle is planning to change lanes or overtake and so the indicator has to turn on, either towards the left or to the right.

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Fig. 15

Lane Changing Indicator Subsystem implemented

The implementation of the system in IPG CarMaker can be found in Fig. 16. The ego vehicle modelled is found to be moving with its Object Detection sensor ON. The ego vehicle is currently moving in Free Driving Mode as seen in Fig. 16a.

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Fig. 16

a Free Driving Mode in IPG CarMaker. b ACC turned on and ego vehicle enters Vehicle Following mode in IPG CarMaker. c Ego vehicle implements indicator control & Lateral Jerk Control in IPG CarMaker. d Ego vehicle enters Free Driving Mode, Indicator Control & Lateral Jerk Control in IPG CarMaker

As the ego vehicle approaches a truck in the front, it moves into the ACC mode and starts the Vehicle Following Mode. For this to happen the ego vehicle has to reduce its speed and maintain a constant distance from the vehicle in the front. As seen in Fig. 16b, the ego vehicle velocity has dropped from 106 kmph to 50.9 kmph. The ego vehicle then decides to overtake the truck in front of it. The controller initialises the indicator towards the left and the Minimum Lateral Jerk Trajectory controller is initialised along with the indicator subsystem. As seen in Fig. 16c, the ego vehicle changes lane after the left indicator is turned on. During the overtaking manoeuvre the ego vehicle has its velocity dropping to 47.6 kmph, which then increases for overtaking as the vehicle has moved to Free Driving Mode. Once the ego vehicle overtakes the truck, the ego vehicle again changes track to its right track using the Lateral Jerk manoeuvre. But during this manoeuvre the right indicator is turned on and the ego vehicle accelerates to a speed of 111.4 kmph. Since no other sensor is used to detect and ensure that the ego vehicle has overtaken the truck, the decision to change lane is made as time based in this model.

Figure 17, shows the responses of the ego vehicle motion in the IPG CarMaker environment. For a set of manoeuvres defined the ego vehicle is following the same. The vehicle uses the Object detection sensor to gather the information about obstacles in front of the vehicle. The steering angle variation, the braking characteristics and the accelerator variation characteristics shows the response of the vehicle for the defined path and the manoeuvre control implemented.

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Fig. 17

Steering Angle variation, Breaking Characteristics and Accelerator variation for a Driving Manoeuvre in IPG CarMaker

The ego vehicle while implementing the Minimum Jerk Control approach would ensure the stability of the vehicle and the roll angle of the vehicle is minimized. The Roll angle response of the ego vehicle is seen in the Fig. 18, shows that the ego vehicle has minimum roll angle with a maximum of 4.5° in the left direction and a maximum of 6.8° in the right direction.

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Fig. 18

Roll angle response of the ego vehicle in IPG CarMaker

Conclusion

The primary concerns in autonomous vehicles are safety and stability of the vehicle. Safety of the vehicle in terms of avoidance of accidence and stability in terms of reduced jerk and roll over in vehicles. This work concentrates on both the safety and stability aspects of the autonomous vehicle. For safety the ego vehicle is made to implement Adaptive Cruise Control during driving. This would have the ego vehicle implementing the vehicle follow mode thereby matching the speed of the vehicle is front and also maintaining a constant distance from the vehicle is front. The ego vehicle was observed to stabilize and maintain a relative distance of 40 m. When the vehicle ahead executes sudden braking, the ego vehicle activates Anti-Lock Braking, ensuring safe and stable deceleration. The slip is consistently maintained at the target value of 0.2. When the vehicle wants to overtake the vehicle is front, it implements an overtaking manoeuvre. This overtaking manoeuvre is supported by a Minimum Jerk trajectory approach. This ensures that the ego vehicle overtakes the vehicle in front with minimum jerk or roll over. The modelling is performed in Matalb and validated through the IPG CarMaker software.

Acknowledgements

Not applicable.

Author contributions

All authors contributed to the conception and implementation of the research. The simulation studies and analysis were carried out by Parag Jose Chacko and Mohan Krishna S. Haneesh K.M. was responsible for the analysis and interpretation of the results. The research was supervised by Febin Daya J.L. and Albert Alexander Stonier. The manuscript was written by Parag Jose Chacko, with all authors reviewing and approving the final version.

Funding

No funding was received for conducting this study.

Availability of data and materials

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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