#
Safe, Smooth, and Fair Rule-Based Cooperative Lane Change Control for Sudden Obstacle Avoidance on a Multi-Lane Road^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- We propose a method to realize safe, smooth, and fair wide-range cooperative lane changing, reacting to a suddenly appearing obstacle on the road. In this strategy, a CV that detects the obstacle immediately notifies the following vehicles of the obstacle by using V2V communication. In turn, the following vehicles can take action to avoid the obstacle smoothly using a wide range behind the obstacle without sacrificing safety and ride comfort. To the authors’ knowledge, existing studies focus on microscopic control around obstacles and do not discuss the control of traffic in a wide range, a few kilometers, as addressed in this study. The microscopic operation for lane-changing trajectory planning is out of this paper’s scope.
- The proposed method works when one lane is obstructed on a three- or more lane road. On three- or more lane roads, vehicles can have multiple choices to change lanes. Thus, we develop a method to select a suitable lane that will not cause unfairness among lanes and deteriorate ride comfort.
- We confirm the effectiveness of the proposed method in realizing fairness among lanes, safety, ride comfort, and traffic throughput through simulations of a two-lane road and a three-lane road with various traffic scenarios, assuming that the vehicles’ microscopic operation depends on the lane change model of SUMO.

- The road length in the simulation environment is increased from $1\mathrm{km}$ to $2\mathrm{km}$ in order to provide sufficient free space before vehicles encounter an obstacle.
- The simulations consider occlusion in a vehicle detection model.
- Two vehicle behavior models (Proposed_NoPrelim and Proposed_NoAdaptive) are introduced to confirm the effectiveness of the proposed scheme.
- A fairness equation is introduced to quantitatively evaluate the fairness level in the simulation evaluation.
- A safety metric is introduced in the simulation evaluation.
- Cumulative distribution function (CDF) graphs are created for each performance metric to analyze the simulation results in more detail.
- Simulations are conducted with various traffic loads to evaluate the performance of the proposed method comprehensively and with various zone sizes of the proposed scheme to investigate the impact of the zone sizes.

## 2. Related Work

## 3. Proposed Scheme

#### 3.1. Assumed Environment

- Vehicles are equipped with sensors such as cameras and LiDAR, which can detect vehicles, road structures, and obstacles.
- Vehicles are equipped with a V2V communication function and are operated by an automatic driving system or a human driver who follows instructions given by a driving assistant system.
- The position, speed, and acceleration of the vehicle are shared among the vehicles within the wireless communication range. Vehicles periodically broadcast messages that include such driving information.
- Each vehicle changes lanes safely when it enters a zone where it is allowed to change. This paper does not specify the detailed trajectory planning technique on lane changing. We assume that the lane changing model used SUMO in the simulations. The actual timing of starting the lane change maneuver of each vehicle depends on the model.

#### 3.2. Basic Strategy

**closed lane**) and the distance to the obstacle, d, satisfies $0<d\le {d}_{\mathrm{avoid}}$ (referred to as the

**avoidance zone**), it attempts to change lanes. If a vehicle is in the lane where the obstacle does not exist (referred to as the

**free lane**) and d satisfies $0<d\le {d}_{\mathrm{avoid}}+{d}_{\mathrm{prelim}}$ (referred to as the

**preliminary avoidance zone**), it attempts to change lanes. If d satisfies ${d}_{\mathrm{avoid}}+{d}_{\mathrm{prelim}}<d\le {d}_{\mathrm{avoid}}+{d}_{\mathrm{prelim}}+{d}_{\mathrm{decel}}$ (referred to as the

**gap adjustment zone**), a vehicle increases the time headway to make space to accommodate vehicles entering from the neighboring lane.

#### 3.3. Obstacle Detection Notification

#### 3.4. Adjusting Time Headway

#### 3.5. Adaptive Lane Change

**Strategy 1: Avoiding congested lanes**: As shown in Figure 4a, the ego vehicle, a vehicle that will change lanes, evaluates the number of vehicles between itself and the obstacle in each destination candidate lane. First, it counts the number of vehicles in front of itself in each lane and in its communication range on the basis of the number of unique vehicle IDs included in the packets sent from the vehicles. Let a and b be indices of the destination candidate lanes and let ${m}_{a}$ and ${m}_{b}$ be the number of vehicles in each of the lanes, respectively. If either the ratio of ${m}_{a}$ or ${m}_{b}$ to the sum of ${m}_{a}$ and ${m}_{b}$ exceeds a predefined threshold L (e.g., 0.6), the vehicle regards the lane as congested and moves to another lane to balance the traffic of the lanes ahead. In other words, lane $i(\in \{a,b\left\}\right)$ that satisfies ${m}_{i}/\left(\right)open="("\; close=")">{m}_{a}+{m}_{b}$ cannot be a candidate destination lane. If neither candidate is selected, the vehicle uses Strategy 2 to determine the destination lane.

**Strategy 2: Adjusting the balance among lanes**: As shown in Figure 4b, a vehicle determines a destination lane in such a way that the number of vehicles in each free lane will have the same amount of traffic. First, the vehicle counts the number of vehicles in each lane behind itself and its communication range on the basis of the number of unique vehicle IDs included in the packets sent from the vehicles. Let us assume that the road has n lanes ($n\ge 1$), then the index of each lane is $i(\in \{0,1,\cdots ,n-1\left\}\right)$, the number of counted vehicles in each lane is ${m}_{i}$, and $M={\sum}_{i=0}^{n-1}{m}_{i}$. If the counted vehicles are evenly distributed among the $n-1$ free lanes, the ideal number of vehicles per free lane is $M/(n-1)$. To adjust the number of vehicles in each lane to be closer to this ideal number, the probability that a vehicle moves from lane i to lane j ${P}_{i\to j}(j\in \{i-1,i,i+1\})$ in either direction from each lane is calculated in three steps as follows, where the index of the closed lane is denoted by c.

## 4. Simulation Model

#### 4.1. Environment Settings

Parameters | Values |
---|---|

Simulation time | $500.0\mathrm{s}$ |

Time step length | $0.05\mathrm{s}$ |

${d}_{\mathrm{avoid}}$ (avoidance zone size) | 10–500 m |

${d}_{\mathrm{prelim}}$ (preliminary avoidance zone size) | 0–300 m |

${d}_{\mathrm{decel}}$ (gap adjustment zone size) | 0–1000 m |

${a}_{\mathrm{comfort}}$ for adjusting time headway | $-2.94\mathrm{m}/{\mathrm{s}}^{2}$ ($-0.3\mathrm{G}$) [25] |

Threshold L for avoiding congested lanes | 0.6 |

Available sensing range | $50\mathrm{m}$ [26] |

V2V communication range | $300\mathrm{m}$ [24] |

Traffic load input value for 2-lane scenario | 720–3600 vehicles/h |

Traffic load input value for 3-lane scenario | 720–5400 vehicles/h |

CV penetration ratio | 0.0–1.0 |

Broadcast interval | $0.2\mathrm{s}$ |

Validity period of the obstacle information | $60.0\mathrm{s}$ |

Vehicle length, vehicle width | $4.47\mathrm{m}$, $1.795\mathrm{m}$ |

Min. inter-vehicular distance | $2.5\mathrm{m}$ |

Regular inter-vehicular gap ($\tau $) | $2.0\mathrm{s}$ |

Gap open ratio | 2.0 |

Lane change duration | $3.0\mathrm{s}$ |

LC2013 lane change mode | 1621 |

Initial speed, road speed limit | $16.7\mathrm{m}/\mathrm{s}$, $33.3\mathrm{m}/\mathrm{s}$ |

Max. acceleration, max. deceleration | $2.9\mathrm{m}/{\mathrm{s}}^{2}$, $-7.5\mathrm{m}/{\mathrm{s}}^{2}$ |

#### 4.2. Lane-Changing Model

**Strategic change**: Changing lanes to reach a destination (e.g., moving to the left lane to make a left turn).**Cooperative change**: Changing lanes to help another vehicle change lanes (e.g., changing lanes to make space for merging vehicles at a merge point).**Tactical change**: Changing lanes to move faster (e.g., overtaking).**Regulatory change**: Changing lanes to comply with regulations and laws (e.g., changing lanes to avoid driving continuously in an overtaking lane).

#### 4.3. Vehicle Detection Model

#### 4.4. Vehicle Behavior Models

**Proposed_Full**: CVs follow the proposed scheme.**Proposed_NoAdaptive**: Simplified version of Proposed_Full. Vehicles randomly select a destination lane from two destination lane candidates.**Proposed_NoPrelim**: Simplified version of Proposed_Full. ${d}_{\mathrm{prelim}}=0$.**Proposed_NoGapOpen**: Simplified version of Proposed_Full. The function of adjusting time headway is disabled.**Manual**: Human-driven vehicle (i.e., NCV) model. Vehicles change lanes to avoid obstacles only when they directly detect an obstacle. If there are lanes on both sides, vehicles in the closed lane randomly select a destination lane.

#### 4.5. Performance Metrics

#### 4.5.1. Traffic

#### 4.5.2. Fairness

#### 4.5.3. Safety

#### 4.5.4. Comfort

## 5. Simulation Results and Discussion

**20**,

**30**, and

**31**. In Scenario 20, there is a 2-lane road, and lane 0 (right edge lane) is closed. In Scenario 30, there is a 3-lane road, and lane 0 (right edge lane) is closed. In Scenario 31, there is a 3-lane road, and lane 1 (center lane) is closed. For all scenarios, we conducted 100 simulations with different random seeds. All of the plotted points on the graphs are average values. Figure 7 shows the some snapshots of simulations.

#### 5.1. Effect of Cooperative Lane Change

**Manual**: In Scenarios 20 and 31, Manual has lower traffic throughput and lower comfort level than the other models. This is because all vehicles in the free lanes are heavily affected by the traffic that moves from the closed lane, resulting in traffic jams in all lanes. On the other hand, in Scenario 30, Manual has similar traffic throughput to the other models and achieves the highest comfort level. However, it has the worst fairness of traffic throughput among lanes. This is because chronic traffic jams occur in lanes 0 and 1 in Scenario 30. Here, lane 2 is the farthest from the closed lane (lane 0), and vehicles in lane 2 are mostly unaffected by lane changes from the closed lane and hence, they keep moving quickly. On the other hand, vehicles in lane 1 need to decelerate to accommodate vehicles changing lanes from the closed lane. The difference in speed between vehicles in lanes 2 and 1 increases; thus, vehicles in lane 1 find it hard to move to lane 2. Therefore, the number of acceleration changes is reduced by the chronic traffic jams in lanes 0 and 1. That is, vehicles in lane 2 keep moving quickly, and vehicles in lanes 0 and 2 move slowly; thus, the discomfort level is very low. Additionally, in Scenario 30, lane 2 has much higher traffic throughput than lanes 0 and 1; thus, the total traffic throughput improves but fairness deteriorates compared with the other scenarios. This can be seen in Figure 8, where there are large differences in the minimum speed and in the travel times.

**Proposed_NoGapOpen**: In Scenarios 30 and 31, Proposed_NoGapOpen has the highest traffic throughput. This is because vehicles do not decelerate to adjust their time headway in this model, so they tend to keep moving at high speed even when changing lanes, thus increasing traffic throughput. On the other hand, the safety and comfort levels of this model are low. This is because the vehicles do not adjust their time headway, so they need to decelerate rapidly in a short time.

**Proposed_NoPrelim**: In Scenario 30, Proposed_NoPrelim shows little difference in fairness, safety, and comfort level compared with Proposed_Full, but has lower traffic throughput. This is because in Proposed_Full, vehicles in the free lane change lanes first in the preliminary avoidance zone to make space for vehicles in the closed lane to change lanes in the avoidance zone, and this reduces the number of times they need to slow down, compared with the case of Proposed_NoPrelim.

**Proposed_NoAdaptive**: Proposed_NoAdaptive shows little difference compared with Proposed_Full in all metrics. The reason is as follows. When the CV penetration ratio is 100%, temporary congestion around the obstacle rarely occurs because vehicles in the closed lanes change lanes with plenty of time to spare when Proposed_NoAdaptive and Proposed_Full are used. Therefore, strategy 1 (avoiding congested lane) has little chance to work. Additionally, the amount of traffic load input is the same in all lanes. Thus, the probabilities of changing lanes from the center lane to the left lane and from the center lane to the right calculated in Proposed_Full are the same (50%) in Scenario 31. The results are the same for Proposed_NoAdaptive when the lane is randomly selected. Note that the effect of the adaptive lane change can be seen when the CV penetration ratio is less than 100%. For scenarios with four or more lanes, Strategy 2 is expected to be more effective and provide an advantage over the random decision case.

**Proposed_Full**: Proposed_Full achieves sufficiently high total traffic throughput in all scenarios. In addition, it achieves very high fairness, safety, and comfort level in all scenarios. However, it has lower traffic throughput than Proposed_NoGapOpen in Scenarios 30 and 31, but higher traffic throughput in Scenario 20. This is because the control of doubling the time headway of vehicles in all three lanes is excessive, resulting in lower traffic throughput. Thus, it is expected that as the ratio of closed lanes to the total roadway lanes becomes smaller, the control of doubling the time headway of all vehicles will become excessive, and a lower traffic throughput will result. There is thus room for improving our method in the future.

- Sharing information about the obstacle through V2V communication allows vehicles to adjust their speed and change lanes in advance, preventing rapid deceleration.
- Adjusting the time headway of vehicles in advance is effective at significantly improving safety and comfort level in obstacle avoidance.
- Shifting the lane change timing between vehicles in the closed lane and vehicles in the free lane by introducing a preliminary avoidance zone is effective in facilitating obstacle avoidance.
- The proposed scheme achieves sufficiently high traffic throughput without degrading fairness, safety, or comfort level in the most balanced way. Note that we assume that vehicles’ microscopic operation depends on the lane change model of SUMO. Therefore, the performance of the proposed scheme may vary depending on trajectory planning.

#### 5.2. Impact of the CV Penetration Ratio

#### 5.3. Impact of the Zone Sizes

**Avoidance zone**: If the avoidance zone is too small, vehicles in the closed lane cannot change lanes. Therefore, the size of the avoidance zone (${d}_{\mathrm{avoid}}$) should be sufficient for vehicles in the closed lane to accomplish a lane change. Simulation results show that traffic throughput, fairness, and comfort level deteriorate when ${d}_{\mathrm{avoid}}<250\mathrm{m}$. On the other hand, all metrics are stable when ${d}_{\mathrm{avoid}}\ge 250\mathrm{m}$. Consequently, we can conclude that a suitable size of the avoidance zone is $250\mathrm{m}$ or more.

**Preliminary avoidance zone**: If a vehicle in the closed lane and a vehicle in a free lane begin attempting to change lanes at the same point in time, the vehicle in the closed lane may be able to change lanes faster than the vehicle in the free lane. In this case, the vehicle density in the free lane temporarily increases, and vehicles in the free lane will be forced to decelerate. Therefore, the size of the preliminary avoidance zone (${d}_{\mathrm{prelim}}$) should be sufficient to shift the lane-change timings for vehicles in the closed lane and the lane change timing for vehicles in the free lane. Simulation results show that traffic throughput improves when ${d}_{\mathrm{prelim}}\ge 30\mathrm{m}$. However, the fairness and comfort level deteriorate when ${d}_{\mathrm{prelim}}>100\mathrm{m}$. This result can be explained as follows. If the size of the preliminary avoidance zone is too large, there is too much of a time lag between the lane change of the vehicle in the free lane and the lane change of the vehicle in the closed lane, and the following vehicle accelerates to shorten the long inter-vehicular gap made by the lane changes of the vehicles in the free lane. As a result, when the vehicle in the closed lane starts to change lanes, there will be insufficient space for it to change lanes smoothly, and the vehicles need to decelerate. Thus, the fairness of the traffic throughput and comfort level deteriorate with frequent deceleration in the lane next to the closed one. Consequently, we can conclude that a suitable size of the preliminary avoidance zone is 30–100 m.

**Gap adjustment zone**: In the gap adjustment zone, vehicles do not decelerate rapidly to double the time headway within a short time because of the minimum acceleration ${a}_{\mathrm{comfort}}$. If the gap adjustment zone is too short, vehicles cannot double the time headway. Therefore, the size of the gap adjustment zone (${d}_{\mathrm{decel}}$) should be sufficient to double the time headway without reducing ride comfort. Simulation results show that traffic throughput and fairness deteriorate when ${d}_{\mathrm{decel}}<200\mathrm{m}$. In addition, traffic throughput deteriorate when ${d}_{\mathrm{decel}}>600\mathrm{m}$. This is because as the gap adjustment zone becomes larger, the travel time of vehicles at low speed becomes longer. Consequently, we can conclude that a suitable size of the gap adjustment zone is 200–600 m.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- National Highway Traffic Safety Administration, Vehicle-to-Vehicle Communication. Available online: https://www.nhtsa.gov/technology-innovation/vehicle-vehicle-communication (accessed on 16 August 2022).
- Persaud, B.; Yagar, S.; Brownlee, R. Exploration of the Breakdown Phenomenon in Freeway Traffic. J. Transp. Res. Rec.
**1998**, 1634, 64–69. [Google Scholar] [CrossRef] - Sugiyama, Y.; Fukui, M.; Kikuchi, M.; Hasebe, K.; Nakayama, A.; Nishinari, K.; Tadaki, S.; Yukawa, S. Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam. New J. Phys.
**2008**, 10, 033001. [Google Scholar] [CrossRef] - Google Maps. Available online: https://www.google.com/maps/ (accessed on 16 August 2022).
- Waze: Driving Directions, Live Traffic & Road Conditions Updates. Available online: https://www.waze.com/ja/live-map/ (accessed on 16 August 2022).
- Vehicle Information and Communication System. Available online: https://www.vics.or.jp/en/ (accessed on 16 August 2022).
- Ishihara, S. Cooperative Lane Change Control for Sudden Obstacle Avoidance on a Multilane Road. In Proceedings of the ITS Symposium, Ishikawa, Japan, 12–13 December 2019. [Google Scholar]
- Simulation of Urban Mobility (SUMO). Available online: http://sumo.dlr.de/wiki/ (accessed on 16 August 2022).
- Asano, S.; Ishihara, S. Rule-Based Cooperative Lane Change Control to Avoid a Sudden Obstacle in a Multi-Lane Road. In Proceedings of the 2022 IEEE 95th Vehicular Technology Conference, Helsinki, Finland, 19–22 June 2022. [Google Scholar]
- Desiraju, D.; Chantem, T.; Heaslip, K. Minimizing the Disruption of Traffic Flow of Automated Vehicles During Lane Changes. IEEE Trans. Intell. Transp. Syst.
**2016**, 16, 1249–1258. [Google Scholar] [CrossRef] - Wang, D.; Hu, M.; Wang, Y.; Wang, J.; Qin, H.; Bian, Y. Model predictive control-based cooperative lane change strategy for improving traffic flow. Adv. Mech. Eng.
**2016**, 8, 1–17. [Google Scholar] [CrossRef] - Luo, Y.; Yang, G.; Xu, M.; Qin, Z.; Li, K. Cooperative Lane-Change Maneuver for Multiple Automated Vehicles on a Highway. Automot. Innov.
**2019**, 2, 157–168. [Google Scholar] [CrossRef] - Li, T.; Wu, J.; Chan, C.Y.; Liu, M.; Zhu, C.; Lu, W.; Hu, K. A Cooperative Lane Change Model for Connected and Automated Vehicles. IEEE Access
**2020**, 8, 54940–54951. [Google Scholar] [CrossRef] - CAR 2 CAR Communication Consortium (C2C-CC), Guidance for Day 2 and Beyond Roadmap. Available online: https://www.car-2-car.org/fileadmin/documents/General_Documents/C2CCC_WP_2072_RoadmapDay2AndBeyond.pdf (accessed on 16 August 2022).
- Gunther, H.; Trauer, O.; Wolf, L. The Potential of Collective Perception in Vehicular Ad-Hoc Networks. In Proceedings of the 2015 14th International Conference on ITS Telecommunications, Copenhagen, Denmark, 2–4 December 2015. [Google Scholar]
- Federal Highway Administration (FHWA), CARMA Program Overview. Available online: https://highways.dot.gov/research/operations/CARMA (accessed on 16 August 2022).
- Tiernan, T.; Bujanovic, P.; Azeredo, P.; Najm, W.G.; Lochrane, T. CARMA Testing and Evaluation of Research Mobility Applications; U.S. Department of Transportation, Federal Highway Administration: San Francisco, CA, USA, 2019.
- Ding, J.; Li, L.; Peng, H.; Zhang, Y. A Rule-Based Cooperative Merging Strategy for Connected and Automated Vehicles. IEEE Trans. Intell. Transp. Syst.
**2020**, 21, 3436–3446. [Google Scholar] [CrossRef] - Jing, S.; Hui, F.; Zhao, X.; Rios-Torres, J.; Khattak, A.J. Cooperative Game Approach to Optimal Merging Sequence and on-Ramp Merging Control of Connected and Automated Vehicles. IEEE Trans. Intell. Transp. Syst.
**2019**, 20, 4234–4244. [Google Scholar] [CrossRef] - Multi-Car Collision Avoidance (MuCCA). Available online: https://mucca-project.co.uk (accessed on 16 August 2022).
- Wartnaby, C.; Bellan, D. Decentralised Cooperative Collision Avoidance with Reference-Free Model Predictive Control and Desired Versus Planned Trajectories. arXiv
**2019**, arXiv:1904.07053. [Google Scholar] - Bae, S.Y.; Saxena, D.M.; Nakhaei, A.; Choi, C.; Fujimura, K.; Moura, S.J. Cooperation-Aware Lane Change Maneuver in Dense Traffic based on Model Predictive Control with Recurrent Neural Network. In Proceedings of the 2020 American Control Conference (ACC), Denver, CO, USA, 1–3 July 2020. [Google Scholar]
- Wegener, A.; Piorkowski, M.; Raya, M.; Hellbruck, H.; Fischer, S.; Hubaux, J. TraCI: An Interface for Coupling Road Traffic and Network Simulators. In Proceedings of the 11th Communications and Networking Simulation Symposium (CNS), Ottawa, ON, Canada, 14–17 April 2008. [Google Scholar]
- Xu, Q.; Mak, T.; Ko, J.; Sengupta, R. Vehicle-to-vehicle safety messaging in DSRC. In Proceedings of the 1st ACM International Workshop on Vehicular Ad Hoc Networks, Philadelphia, PA, USA, 1 October 2004. [Google Scholar]
- Deligianni, S.; Quddus, M.; Morris, A.; Anvuur, A.; Reed, S. Analyzing and Modeling Drivers’ Deceleration Behavior from Normal Driving. Transp. Res. Rec. J. Transp. Res. Board
**2017**, 2663, 134–141. [Google Scholar] [CrossRef] - Texas Instruments. An Introduction to Automotive LIDAR. Available online: https://www.ti.com/lit/wp/slyy150a/slyy150a.pdf (accessed on 16 August 2022).
- Krauss, S.; Wagner, P.; Gawron, C. Metastable States in a Microscopic Model of Traffic Flow. Phys. Rev. E
**1997**, 55, 5597–5602. [Google Scholar] [CrossRef] - Erdmann, J. SUMO’s Lane-Changing Model. In Modeling Mobility with Open Data; Lecture Notes in Mobility; Springer: Berlin/Heidelberg, Germany, 2015; pp. 105–123. [Google Scholar]
- Minderhoud, M.M.; Bovy, P.H.L. Extended Time-To-Collision Measures for Road Traffic Safety Assessment. Accid. Anal. Prev.
**2001**, 33, 89–97. [Google Scholar] [CrossRef] - Vogel, K. A Comparison of Headway and Time to Collision as Safety Indicators. Accid. Anal. Prev.
**2003**, 35, 427–433. [Google Scholar] [CrossRef] - Wang, F.; Segawa, K.; Inooka, H. A Study of the Relationship between the Longitudinal Acceleration/Deceleration of Automobiles and Ride Comfort. Jpn. J. Ergon.
**2000**, 36, 191–200. [Google Scholar] - Savitzky, A.; Golay, M.J.E. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Anal. Chem.
**1964**, 36, 1627–1638. [Google Scholar] [CrossRef]

**Figure 1.**Obstacle avoidance using V2V communication. (

**a**) Avoidance strategy when the obstacle’s existence cannot be shared via V2V communication. (

**b**) Avoidance strategy when vehicles share the obstacle’s existence and location using V2V communication.

**Figure 2.**Control rules based on distance between an obstacle and approaching vehicles on a two-lane road.

**Figure 3.**Control rules based on distance between an obstacle and approaching vehicles on a road with three or more lanes.

**Figure 4.**Adaptive lane change. (

**a**) Strategy 1: Avoiding congested lanes. (

**b**) Strategy 2: Adjusting the balance among lanes.

**Figure 7.**Snapshots of simulations. The green box indicates an obstacle. Red boxes are cars that have detected the obstacle directly. (

**a**) Simulations of obstacle avoidance in Scenario 20. (

**b**) Simulations of obstacle avoidance in Scenario 30.

**Figure 8.**Simulation results for each vehicle behavior model under fixed traffic loads, ${d}_{\mathrm{avoid}}=300\mathrm{m}$, ${d}_{\mathrm{prelim}}=100\mathrm{m}$, ${d}_{\mathrm{decel}}=500\mathrm{m}$, CV penetration ratio = 1.0.

**Figure 9.**Simulation results for each vehicle behavior model under different traffic loads, ${d}_{\mathrm{avoid}}=300\mathrm{m}$, ${d}_{\mathrm{prelim}}=100\mathrm{m}$, ${d}_{\mathrm{decel}}=500\mathrm{m}$, CV penetration ratio = 1.0.

**Figure 10.**Simulation results showing impact of CV penetration ratio under different traffic loads, ${d}_{\mathrm{avoid}}=300\mathrm{m}$, ${d}_{\mathrm{prelim}}=100\mathrm{m}$, ${d}_{\mathrm{decel}}=500\mathrm{m}$.

**Figure 11.**Simulation results showing impact of zone sizes under fixed traffic loads, CV penetration ratio = 1.0.

Lane Type | Index | No. of Vehicles | Ideal No. of Vehicles | Move to the Next Lane to the Right | Move to the Next Lane to the Left | Continue Straight Ahead |
---|---|---|---|---|---|---|

Free (left edge) | $n-1$ | ${m}_{n-1}$ | $M/(n-1)$ | ${P}_{n-1\to n-2}=0$ | ${P}_{n-1\to n}=0$ | ${P}_{n-1\to n-1}=1.0-({P}_{n-1\to n-2}+{P}_{n-1\to n})$ |

Free | $n-2$ | ${m}_{n-2}$ | $M/(n-1)$ | ${P}_{n-2\to n-3}=0$ | ${P}_{n-2\to n-1}=$$\frac{M/(n-1)-(1.0-{P}_{n-1\to n}){m}_{n-1}}{{m}_{n-2}}$ | ${P}_{n-2\to n-2}=1.0-({P}_{n-2\to n-3}+{P}_{n-2\to n-1})$ |

Free | $n-3$ | ${m}_{n-3}$ | $M/(n-1)$ | ${P}_{n-3\to n-4}=0$ | ${P}_{n-3\to n-2}=$$\frac{M/(n-1)-(1.0-{P}_{n-2\to n-1}){m}_{n-2}}{{m}_{n-3}}$ | ${P}_{n-3\to n-3}=1.0-({P}_{n-3\to n-4}+{P}_{n-3\to n-2})$ |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

Free | $c+1$ | ${m}_{c+1}$ | $M/(n-1)$ | ${P}_{c+1\to c}=0$ | ${P}_{c+1\to c+2}=\frac{M/(n-1)-(1.0-{P}_{c+2\to c+3}){m}_{c+2}}{{m}_{c+1}}$ | ${P}_{c+1\to c+1}=1.0-({P}_{c+1\to c}+{P}_{c+1\to c+2})$ |

Closed | c | ${m}_{c}$ | 0 | ${P}_{c\to c-1}=\frac{M/(n-1)-(1.0-{P}_{c-1\to c-2}){m}_{c-1}}{{m}_{c}}$ | ${P}_{c\to c+1}=\frac{M/(n-1)-(1.0-{P}_{c+1\to c+2}){m}_{c+1}}{{m}_{c}}$ | ${P}_{c\to c}=0$ |

Free | $c-1$ | ${m}_{c-1}$ | $M/(n-1)$ | ${P}_{c-1\to c-2}=\frac{M/(n-1)-(1.0-{P}_{c-2\to c-3}){m}_{c-2}}{{m}_{c-1}}$ | ${P}_{c-1\to c}=0$ | ${P}_{c-1\to c-1}=1.0-({P}_{c-1\to c-2}+{P}_{c-1\to c})$ |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

Free | 2 | ${m}_{2}$ | $M/(n-1)$ | ${P}_{2\to 1}=\frac{M/(n-1)-(1.0-{P}_{1\to 0}){m}_{1}}{{m}_{2}}$ | ${P}_{2\to 3}=0$ | ${P}_{2\to 2}=1.0-({P}_{2\to 1}+{P}_{2\to 3})$ |

Free | 1 | ${m}_{1}$ | $M/(n-1)$ | ${P}_{1\to 0}=\frac{M/(n-1)-(1.0-{P}_{0\to -1}){m}_{0}}{{m}_{1}}$ | ${P}_{1\to 2}=0$ | ${P}_{1\to 1}=1.0-({P}_{1\to 0}+{P}_{1\to 2})$ |

Free (right edge) | 0 | ${m}_{0}$ | $M/(n-1)$ | ${P}_{0\to -1}=0$ | ${P}_{0\to 1}=0$ | ${P}_{0\to 0}=1.0-({P}_{0\to -1}+{P}_{0\to 1})$ |

Lane Type | Index | No. of Vehicles | Ideal No. of Vehicles | Move to the Next Lane to the Right | Move to the Next Lane to the Left | Continue Straight Ahead |
---|---|---|---|---|---|---|

Free (left edge) | 2 | ${m}_{2}$ | $M/2$ | ${P}_{2\to 1}=0$ | ${P}_{2\to 3}=0$ | ${P}_{2\to 2}=1.0-({P}_{2\to 1}+{P}_{2\to 3})=1.0$ |

Free | 1 | ${m}_{1}$ | $M/2$ | ${P}_{1\to 0}=0$ | ${P}_{1\to 2}=\frac{M/2-(1.0-{P}_{2\to 3}){m}_{2}}{{m}_{1}}=\frac{M/2-{m}_{2}}{{m}_{1}}$ | ${P}_{1\to 1}=1.0-({P}_{1\to 0}+{P}_{1\to 2})=\frac{M/2-{m}_{0}}{{m}_{1}}$ |

Closed(right edge) | 0 | ${m}_{0}$ | 0 | ${P}_{0\to -1}=0$ | ${P}_{0\to 1}=\frac{M/2-(1.0-{P}_{1\to 2}){m}_{1}}{{m}_{0}}=1.0$ | ${P}_{0\to 0}=0$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Asano, S.; Ishihara, S.
Safe, Smooth, and Fair Rule-Based Cooperative Lane Change Control for Sudden Obstacle Avoidance on a Multi-Lane Road. *Appl. Sci.* **2022**, *12*, 8528.
https://doi.org/10.3390/app12178528

**AMA Style**

Asano S, Ishihara S.
Safe, Smooth, and Fair Rule-Based Cooperative Lane Change Control for Sudden Obstacle Avoidance on a Multi-Lane Road. *Applied Sciences*. 2022; 12(17):8528.
https://doi.org/10.3390/app12178528

**Chicago/Turabian Style**

Asano, Shinka, and Susumu Ishihara.
2022. "Safe, Smooth, and Fair Rule-Based Cooperative Lane Change Control for Sudden Obstacle Avoidance on a Multi-Lane Road" *Applied Sciences* 12, no. 17: 8528.
https://doi.org/10.3390/app12178528