A two-layer approach for vehicular flocking in lane-free environment
M. Rostami-Shahrbabakia,*, S. Weikla, M. Akbarzadehb, K. BogenbergeraaChair of Traffic Engineering and Control, Technical University of Munich, Munich, Germany
majid.rostami@tum.de, simone.weikl@tum.de, Klaus.bogenberger@tum.deb
Department of Transportation Engineering, Isfahan University of Technology, Isfahan, Iranmakbarzadeh@iut.ac.ir* Corresponding author

Extended abstract submitted for presentation at the 11th Triennial Symposium on
Transportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island
January 15, 2022
Keywords: Connected and automated vehicle, Flocking, Lane-free traffic, Traffic control

1

INTRODUCTION

While traffic lanes were initially introduced as essential instruments for simplifying driving tasks forhuman drivers and increasing traffic safety, their necessity with the emergence and advancement ofconnected and automated vehicles (CAVs) has to be questioned (Papageorgiou et al., 2021). CAVs areequipped with highly precise sensors and smart technologies for fast and reliable vehicle-to-vehicle(V2V) and vehicle-to-infrastructure (V2I) communication which allow them to make fast decisions
based on control and management strategies in order to avoid collisions, efficiently move forward andalso cooperate with other vehicles. Papageorgiou et al. (2021) introduced a novel paradigm for freeway
traffic, called the TrafficFluid concept, based on two combined principles: "Lane-free traffic" and"Nudging". Within lane-free traffic, vehicles are not limited to traffic lanes but can use the whole roadwidth, allowing for an increase in the efficiency of traffic operations. Nudging describes the effect ofvehicles in front moving in a specific direction as they sense the presence of other vehicles with a higher
desired speed. As one of the subjects to be investigated further for the lane-free-environment,
Papageorgiou et al. (2021) mention “the possibilities and impact of vehicle platoons within the lane-freeenvironment”.
In lane-based traffic, platoons are formed by CAVs that are grouped in a line along one lane with a very
short headway resulting in fuel saving, improved safety and increased highway capacity (Kavathekar
and Chen, 2011). In lane-free traffic, vehicles can be grouped not only longitudinally but also laterally
across the whole road width. We introduce platooning in lane-free traffic as "vehicular flocking" byanalogy to the phenomenon of collective behavior of self-acting individuals observed in some natural
species like birds, fish or ants. Numerous studies have addressed flocking for animals (Hemelrijk and
Hildenbrandt, 2012), multi-agent systems (Olfati-Saber, 2006), autonomous flying robots (Virágh et al.,2014), and conventional lane-based traffic (Wang and Chen, 2021). According to (Reynolds, 1987), thisbehavior is produced by three basic, simple rules of interaction: collision avoidance, velocity matchingwith flockmates and flock centering (based on the desire to stay close to nearby flockmates).
Based on these principles, this study develops an approach based on virtual forces that extends theconcept of lane-free traffic by vehicular flocking. A framework in MATLAB is developed to test the
proposed methodology that shows first promising results.

2

METHODOLOGY

The developed decentralized approach for vehicular flocking is based on two layers, i.e., the tactical andoperational layers. In the tactical layer, the control mode definition and vehicle matching, are carriedout. In contrast, the operational layer takes care of the calculation of the inter-vehicle forces and vehicle
movement based on the defined motion dynamics. In the following, the two proposed layers are
explained in detail.
TRISTAN XI Symposium

Original abstract submittal

M. Rostami-Shahrbabaki, S. Weikl, M. Akbarzadeh and K. Bogenberger

2.1

2

Tactical layer

Three control modes, i.e., cruise mode, catch-up mode, and flock mode, are designed for the movementof vehicles. There are three common goals in each control mode; first, the ego vehicle should drive as
closely as possible to its target speed; second, the ego vehicle should avoid collisions with obstacles,e.g., other vehicles; and third, the ego vehicle should remain within the road boundaries. The target speedof each vehicle is its desired speed in the cruise mode, the leading vehicle's speed in the catch-up phaseand the flock target speed in the flock mode.
Vehicles start their journey in cruise mode. Following the flocking command, which may be triggered
externally, e.g., from the road traffic management system, or internally, e.g., by a passenger's command,the ego vehicle goes to the catch-up mode. In the catch-up phase, the ego vehicle searches for anothervehicle in front which is either in the catch-up or in the flock mode, adjusts its target speed based on thecurrent speed of that vehicle and tries to reduce their longitudinal space-gap. Both vehicles go to theflock mode once their longitudinal space-gap is shorter than a defined gap. Inspired by natural flocking,a flock target speed is defined as the average desired speed of all the vehicles in the flock, i.e., flockmates. The flock's shape is defined solely based on the flock repulsion and attraction forces that lead toa self-organized flock. Such forces are calculated in the operational layer and are elaborated in the next
section. Once the flocking command is released, the vehicle switches back to the cruise mode.

2.2

Operational layer

The vehicle dynamics and force definitions for the individual and group movements of vehicles aredescribed in this section. In this work, the double integrator model for vehicle dynamics and theapproaches proposed in (Papageorgiou et al., 2021; Yanumula et al., 2021), with some modification, areused to achieve the mentioned three primary goals for individual movement of vehicles. Compared to(Yanumula et al., 2021), a new third term, as shown in (1), is added to the calculation of the 𝑥 axis of
the ellipse for repulsive and nudging forces. This term considers the relative speeds of vehicles andinduces lower space-gaps when two vehicles are driving at the same speed, e.g., in a flock.
𝑗𝑑𝑥 (𝑘) = 𝑠𝑥 (𝑙 𝑖 + 𝑙 𝑗 ) + 𝑡1,𝑥 (𝑣 𝑖 (𝑘) + 𝑣 𝑗 (𝑘)) + 𝑡2,𝑥 |𝑣 𝑖 (𝑘) − 𝑣 𝑗 (𝑘)|(1)where 𝑘 = 0,1, … is the discrete time index, 𝑠𝑥 is safety factors, 𝑙 is vehicle's length, 𝑡1,𝑥 and 𝑡2,𝑥 aretime gaps, and 𝑣 𝑖 and 𝑣 𝑗 are the longitudinal speeds of vehicle 𝑖 and 𝑗, respectively. In addition, in thiswork, the potential fields are placed symmetrically around each vehicle. When the ego vehicle goes tothe catch-up phase, and there is another vehicle 𝑗 in catch-up or flock mode in front, the target speed ofthe ego vehicle is adjusted based on the leading vehicle's speed. Note that we use a smoothing function
to prevent abrupt changes in the target speed of vehicles when they switch to another control mode. In
this mode, the ego vehicle 𝑖 has one additional catch-up force (2), using a PI-controller, aiming toapproach the leading vehicle 𝑗 longitudinally.
𝑗𝑓𝑥𝑐ℎ (𝑘) = 𝑓𝑥𝑐ℎ (𝑘 − 1) + 𝑘𝑥𝑐ℎ,𝑃 (𝑒(𝑘) − 𝑒(𝑘 − 1)) + 𝑘𝑥𝑐ℎ,𝐼 𝑒(𝑘), where 𝑒(𝑘) = 𝑑𝑐ℎ − [𝑥𝑥 (𝑘) − 𝑥𝑥𝑖 (𝑘)](2)where 𝑘 𝑐ℎ s are controller gains, 𝑥𝑥 is the vehicle's longitudinal location, and 𝑑𝑐ℎ is the desired spacegap between the ego and the leader vehicles in the catch-up phase. Once the desired space-gap is attained,
the vehicles go into the flock mode. The proposed flocking algorithm leads to a self-organized flockwith no leader. Three ellipses, which create a related potential force, are assumed for each vehicle in theflock, as shown in Figure 1. The safety force provides the minimum safety gaps between the vehicles
using repulsive and nudging forces, however, with shorter time gaps. The flock attraction ensures theflock centering attitude and allows the flockmates to drive close to each other. The role of the flock
repulsion is to enable different forms of the flock. The size and shape of repulsion and attraction zones
which shape the flock structure are design issues and can be fixed or adaptive based on the road geometryor traffic condition.
As shown in Figure 1.a, each vehicle 𝑗 receives a flock repulsion or attraction force based on its relative
distance to the vehicle 𝑖. The definition of the flock repulsion force is straightforward and is similar tosafety force with the difference that the ellipsoid axes do not change with the vehicles' speed. The
definition of the flock attraction force is a bit tricky and different since it takes its highest value at theattraction ellipse and decreases as the vehicle 𝑗 approaches vehicle 𝑖.

TRISTAN XI Symposium

Original abstract submittal

M. Rostami-Shahrbabaki, S. Weikl, M. Akbarzadeh and K. Bogenberger

a- Flock attraction force depends on the relative
location of the vehicles

3b- An example of flock attraction and repulsion forces forvehicle 𝑗 at two different positions

Figure 1. The flock repulsion and attraction zone and forces induced from vehicle 𝒊With the proposed approach, there is a balanced zone around each vehicle in which no flock repulsion
or attraction applies to other vehicles. Therefore, the flock's vehicles are automatically situated inlocations where the overall attraction and repulsion forces are zero or cancel each other. The attraction
force definition is illustrated in Figure 1.a. For any vehicle 𝑗 in the attraction zone of vehicle 𝑖, a directline connecting two vehicle centers is drawn. The cross points of this line with the repulsion andattraction ellipses are marked with 𝐴 and 𝐵, respectively. The flock attraction force 𝐹 𝑎𝑡 for the vehicle
𝑗 applied from vehicle 𝑖 is calculated as follows:
2 6
2
𝑗
𝑗
𝑥
(𝑘)−𝐵
(𝑘)
𝑥
(𝑘)−𝐵
(𝑘)
𝑦
𝑦
𝑥
𝑥
𝐹 𝑎𝑡 (𝑖, 𝑗, 𝑘) = 1⁄([(𝐵 (𝑘)−𝐴 (𝑘)) + (𝐵 (𝑘)−𝐴 (𝑘)) ] + 1)
𝑥
𝑥
𝑦
𝑦

(3)

In Figure 1.b, an example of repulsion and attraction functions for vehicle 𝑗 at two different locations is
illustrated. When the vehicle 𝑗 is affected by the attraction function, it is, thus, pushed towards vehicle
𝑖. The vehicle is pushed away from vehicle 𝑖 due to the flock repulsion function. The effect of attraction
and repulsion forces lead the vehicle 𝑗 towards the neutral area between the two functions.

3

SIMULATION RESULTS

To test the proposed methodology, a simulation framework in MATLAB is developed. A highway ringroad with 1 km length and 10.2 m width is assumed. Vehicle parameters such as desired speed,
dimensions, and willingness to form a flock are assigned at the initial phase, as well as their initial lateraland longitudinal locations. The flocking command is time-triggered and sent to those vehicles willingto join the flock. The flock command is also released at a pre-defined time, and flock vehicles switch tothe cruise mode afterwards. Two scenarios are designed. In the first scenario, the simulation is initializedwith five vehicles from which three are flock-potential, while in the second one, ten vehicles, all willingto participate in the flock formation, are assumed.

a- Longitudinal speed of simulated vehicles

b- Lateral speed of simulated vehicles

Figure 2. Longitudinal and lateral speed evolution of vehicles in different control modes for the first scenario

In Figure 2, the results of a 10 minutes simulation run for the first scenario is shown. The flocking
command is triggered at T1 and is released at T4. Following the flock command, vehicle 3 adjusts its
longitudinal speed to catch up with vehicle 2 and they form a flock at T2. A bit later (at T3), vehicle 4also joins the flock, and all three vehicles drive together, with the flock target speed, until the flockcommand is over. In addition, the effect of the flock attraction is reflected in the lateral speed of vehicles
2 and 3, as shown in Figure 2.b. The flock vehicles go to the cruise mode when the flock command isreleased and take their desired speed as the new target speed. The small ripples in the speeds are theeffect of nudging and repulsive forces applied between the flock vehicles and vehicles 1 and 2.

TRISTAN XI Symposium

Original abstract submittal

M. Rostami-Shahrbabaki, S. Weikl, M. Akbarzadeh and K. Bogenberger

a- All vehicles in the cruise modeb- Two formed flocks; each has a follower

4c- All vehicles form a single big flock

Figure 3. Movement of vehicles in three different control modes over the simulation period

The results of the second scenario are depicted in Figure 3. Each vehicle, shown with a triangle, has aunique fixed colour in these figures, while its line colour can be red, yellow or green, indicating thevehicle cruise, catch-up, and flock modes, respectively. Initially, all vehicles are in cruise mode anddrive individually. In the flock phase, as shown in Figure 3.b, two flocks with different sizes are formed,
and each flock has a follower in the catch-up mode. Over time, the vehicles in the catch-up mode alsojoin the flock, and since the two flocks have different target speeds, they also merge and form a single
big flock. Note that the formed flocks are self-organized, and no restrictions are imposed on the flock
size or the flock lateral occupancy. Note to mention that, the vehicles may seem to have a short spacegap between themselves due to the scaling of the road presentation in the plots.

4

DISCUSSION

A two-layer approach for vehicular flocking in the lane-free environment is developed in this work. To
this end, three control modes, i.e., cruise, catch-up and flock modes, are assumed to control vehicle
movements. A framework in MATLAB is developed to test the proposed methodology. The results
demonstrate a promising characteristic of vehicle movement with collision-free behaviour. The defined
flock attraction and repulsion forces lead to self-organized flocks with the requested feature. In future
works, we consider flock management strategies to impose and regulate the flock size, lateral occupancyof the flock, and even consider aerodynamic effects when building efficient flock forms.

5

REFERENCES

Hemelrijk, C. K. and Hildenbrandt, H. (2012) ‘Schools of fish and flocks of birds: Their shape andinternal structure by self-organization’, Interface Focus, 2(6), pp. 726–737.
Kavathekar, P. and Chen, Y. (2011) ‘Vehicle platooning: A brief survey and categorization’, inInternational Design Engineering Technical Conferences and Computers and Information in
Engineering Conference, pp. 829–845.
Olfati-Saber, R. (2006) ‘Flocking for multi-agent dynamic systems: Algorithms and theory’, IEEE
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Papageorgiou, M. et al. (2021) ‘Lane-Free Artificial-Fluid Concept for Vehicular Traffic’, Proceedingsof the IEEE, 109(2), pp. 114–121.
Reynolds, C. W. (1987) ‘Flocks, herds, and schools: A distributed behavioral model’, Proceedings ofthe 14th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1987,
21(4), pp. 25–34.
Virágh, C. et al. (2014) ‘Flocking algorithm for autonomous flying robots’, Bioinspiration andBiomimetics, 9(2).
Wang, F. and Chen, Y. (2021) ‘A Novel Hierarchical Flocking Control Framework for Connected andAutomated Vehicles’, IEEE Transactions on Intelligent Transportation Systems, 22(8), pp. 4801–4812.
Yanumula, V. K. et al. (2021) ‘Optimal Path Planning for Connected and Automated Vehicles in Lanefree Traffic’, IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC, 2021-Septe,
pp. 3545–3552.

6

ACKNOWLEDGEMENTS

This work is based on the project "Simulation and organization of future lane-free traffic" funded byGerman research foundation (DFG), under the project number BO 5959/1-1.

TRISTAN XI Symposium

Original abstract submittal