Dynamic Collision Avoidance Research Articles

Unmanned Ship Collision Avoidance Action Plan Deduction Method under Man–Machine Interactive Negotiation in Collision Avoidance Scenarios

With the development of artificial intelligence technology, the future water traffic environment will present a new pattern of coexistence of manned ships and unmanned ships, because unmanned ships are different from manned ships in situation understanding, collision avoidance decision-making, and so on. Therefore, the obstacle avoidance planning between unmanned ships and manned ships becomes extremely complex, and collision avoidance behavior scheme deduction becomes a key step in solving the problems related to situation understanding and collision avoidance decision-making in collision avoidance scenarios. In this paper, the situation understanding of the pilot for different collision avoidance situations is integrated into the dynamic obstacle avoidance model, and an intelligent navigation collision avoidance system is proposed to assist in deducing the collision avoidance action plan of the unmanned ship in the man–machine coexistence scenario. The intelligent navigation collision avoidance system is divided into two parts, namely a ship situation understanding part and a ship obstacle avoidance part, wherein ship situation understanding is used for realizing the transition of the collision state of the unmanned ship in the deduction process by constructing a collision-state set and a behavior decision set by using a finite state machine (FSM). Regarding ship obstacle avoidance, ship velocity obstacle is calculated based on the reciprocal velocity obstacle method (RVO), and the collision avoidance action is selected by using the behavior decision generated by the FSM to realize the dynamic collision avoidance deduction of the unmanned ship. In this study, the validity and effectiveness of the intelligent navigation collision avoidance system proposed in this paper are verified by case studies in a variety of collision avoidance scenarios. The system successfully solves the problem of intelligent collision avoidance planning, provides reliable support for the intelligent collision avoidance of unmanned ships, provides a feasible solution for safety and efficiency in sea navigation, and provides a valuable reference for the design and development of future intelligent navigation collision avoidance systems for ships.

Research on Autonomous Collision Avoidance of USV Based on Improved APF Algorithm

Abstract Aiming at the problem of Unmanned Surface Vessel (USV) avoiding dynamic vessels on the sea surface, an Artificial Potential Field method based on Velocity Obstacle Method (VO-APF) was studied. Under the premise of complying with the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs), the overlapping of ship domains is minimized. The Quaternion ship domain was introduced into VO to make it more suitable for collision avoidance judgment in the ship domain, and the collision avoidance time of the ship was predicted, and the reasonable obstacle avoidance point was finally obtained. The attraction function of the obstacle avoidance target point and the repulsion function of the ship domain based on the APF are set, and the USV is subjected to the repulsion force and attraction in the APF, and finally completes the whole dynamic ship collision avoidance task. In the simulation environment, VO, APF and VO-APF were compared in three different encounter situations. The results show that VO-APF can help USV to complete the collision avoidance task under the premise of complying with COLREGs, and the overlap time between USV’s own ship domain and the other ship domain is the shortest, and the safety degree is the highest.

A Review of Autonomous Berthing Technology for Ships

Autonomous berthing technology is a crucial engineering control problem within the ship intelligence system, encompassing a series of complex operations and technologies. Firstly, this paper analyses the research on autonomous berthing technology from a bibliometric point of view in order to obtain an overview of its past and present development and to outline the importance of this technology. Secondly, a literature review is conducted on each of the four aspects of autonomous berthing technology, namely sensing technology, berthing type, control method, and evaluation method, which can help to quickly understand the main aspects of this technology. Thirdly, the ship-assisting technologies needed to achieve autonomous berthing are discussed and analysed from six aspects: dynamic collision avoidance, path planning, path tracking, heading control, tug assistance, and shore-based systems. Finally, the challenges faced by the ship autonomous berthing technology on the way of development are summarised, and future development is projected. This paper aims to provide a more comprehensive perspective for analysing and researching ship autonomous berthing technology.

Dynamic navigation: Integrating GL-STGCNN and MPC for collision avoidance with future Awareness

Existing ship dynamic collision avoidance methods mostly rely on the instantaneous motion information of surrounding ships to make decisions. This makes it difficult to adapt to changes in the motion states of surrounding ships, which may lead to collisions between ships. To improve the safety of dynamic collision avoidance methods, this paper combines the multi-ship trajectory prediction model GL-STGCNN with model predictive control for ship dynamic collision avoidance tasks. Firstly, the interaction between ships is extracted through GL-STGCNN to predict the future trajectories of surrounding ships. Then, the objective function based on the artificial potential field method and the velocity obstacle method is optimized to control the ship to complete the dynamic collision avoidance task. The performance of the dynamic collision avoidance method is verified and analyzed in the ship navigation scenario simulated by AIS data. The experiments show that the new ship dynamic collision avoidance method not only complies with the COLREGs, but also can flexibly select the collision avoidance method according to different scenarios. In addition, the theoretical collision avoidance threshold distance based on the MPC objective function shows a high degree of fit with the actual collision avoidance trigger distance observed in the simulation verification.

Trajectory Planning for Cooperative Double Unmanned Surface Vehicles Connected with a Floating Rope for Floating Garbage Cleaning

Double unmanned surface vehicles (DUSVs) towing a floating rope are more effective at removing large floating garbage on the water’s surface than a single USV. This paper proposes a comprehensive trajectory planner for DUSVs connected with a floating rope for cooperative water-surface garbage collection with dynamic collision avoidance, which takes into account the kinematic constraints and dynamic cooperation constraints of the DUSVs, which reflects the current collection capacity of DUSVs. The optimal travel sequence is determined by solving the TSP problem with an ant colony algorithm. The DUSVs approach the garbage targets based on the guidance of target key points selected by taking into account the dynamic cooperation constraints. An artificial potential field (APF) combined with a leader–follower strategy is adopted so that the each USV passes from different sides of the garbage to ensure garbage capturing. For dynamic obstacle avoidance, an improved APF (IAPF) combined with a leader–follower strategy is proposed, for which a velocity repulsion field is introduced to reduce travel distance. A fuzzy logic algorithm is adopted for adaptive adjustment of the desired velocities of the DUSVs to achieve better cooperation between the DUSVs. The simulation results verify the effectiveness of the algorithm of the proposed planner in that the generated trajectories for the DUSVs successfully realize cooperative garbage collection and dynamic obstacle avoidance while complying with the kinematic constraints and dynamic cooperation constraints of the DUSVs.

Affine formation maneuver control of underactuated surface vessels: Guaranteed safety under moving obstacles in narrow channels

This research tackles the challenge of dynamic formation control and collision avoidance in underactuated surface vessels (USVs). Firstly, an affine transformation is employed to implement arbitrary configuration transformations within the multi-USV system. Secondly, by considering both distances and velocities between USVs and obstacles, a novel collision avoidance scheme is proposed based on conventional distance-based artificial potential field methods. This method, building on traditional distance-based artificial potential fields, offers a more precise assessment of collision risks, thereby notably shrinking the potential collision zones. Such refinement leads to reduced energy consumption and minimizes disruption to formation integrity. Thirdly, an anti-perturbation formation maneuver safety control scheme is introduced to achieve a time-varying target formation without collisions, ensuring that local position tracking errors remain bounded. The effectiveness of the proposed approaches is substantiated through comprehensive theoretical analysis and extensive numerical simulations, underscoring their practical applicability.

Air–Ground Collaborative Multi-Target Detection Task Assignment and Path Planning Optimization

Collaborative exploration in environments involving multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) represents a crucial research direction in multi-agent systems. However, there is still a lack of research in the areas of multi-target detection task assignment and swarm path planning, both of which play a vital role in enhancing the efficiency of environment exploration and reducing energy consumption. In this paper, we propose an air–ground collaborative multi-target detection task model based on Mixed Integer Linear Programming (MILP). In order to make the model more suitable for real situations, kinematic constraints of the UAVs and UGVs, dynamic collision avoidance constraints, task allocation constraints, and obstacle avoidance constraints are added to the model. We also establish an objective function that comprehensively considers time consumption, energy consumption, and trajectory smoothness to improve the authenticity of the model and achieve a more realistic purpose. Meanwhile, a Branch-and-Bound method combined with the Improved Genetic Algorithm (IGA-B&B) is proposed to solve the objective function, and the optimal task assignment and optimal path of air–ground collaborative multi-target detection can be obtained. A simulation environment with multi-agents, multi-obstacles, and multi-task points is established. The simulation results show that the proposed IGA-B&B algorithm can reduce the computation time cost by 30% compared to the traditional Branch-and-Bound (B&B) method. In addition, an experiment is carried out in an outdoor environment, which further validates the effectiveness and feasibility of the proposed method.

Obstacle Intention Awareness in Automatic Ship Collision Avoidance: Full-Scale Experiments in Confined Waters

In this article, full-scale experiments with a dynamic obstacle intention-aware Collision Avoidance System (CAS) are presented. The CAS consists of the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC) for trajectory planning, dynamic obstacle avoidance, and antigrounding, with a Dynamic Bayesian Network (DBN) used for inferring obstacle intentions online. The novelty of this article lies in the utilization of intention information in deliberate collision-free planning. By inferring multiple different intention states on how and if nearby obstacles adhere to the COLREGS, the PSB-MPC can plan COLREGS-compliant avoidance maneuvers when possible, taking into account its awareness of the situation. The experiments put emphasis on hazardous situations where this intention information is both useful and necessary in order to avoid high collision risk. To the authors’ knowledge, the work is the first field experimental validation of such a probabilistic intention-aware CAS with consideration of multiple intention states. The experimental results demonstrate the validity of the proposed CAS scheme, with adherence to the traffic rules (COLREGS) 7, 8 and 13–17 in a diverse set of situations. The strengths and weaknesses of the proposed CAS are also discussed, giving insights that can be useful for researchers and practitioners in the field. Here, challenges related to detecting obstacle maneuvers and making the intention inference more robust to noise should be addressed as future work to make the scheme better suited for general usage on ships engaged in real traffic.

Automated guided vehicle dispatching and routing integration via digital twin with deep reinforcement learning

The manufacturing industry has witnessed a significant shift towards high flexibility and adaptability, driven by personalized demands. However, automated guided vehicle (AGV) dispatching optimization is still challenging when considering AGV routing with the spatial-temporal and kinematics constraints in intelligent production logistics systems, limiting the evolving industry applications. Against this backdrop, this paper presents a digital twin (DT)-enhanced deep reinforcement learning-based optimization framework to integrate AGV dispatching and routing at both horizontal and vertical levels. First, the proposed framework leverages a digital twin model of the shop floor to provide a simulation environment that closely mimics the actual manufacturing process, enabling the AGV dispatching agent to be trained in a realistic setting, thus reducing the risk of finding unrealistic solutions under specific shop-floor settings and preventing time-consuming trial-and-error processes. Then, the AGV dispatching with the routing problem is modeled as a Markov Decision Process to optimize tardiness and energy consumption. An improved dueling double deep Q network algorithm with count-based exploration is developed to learn a better-dispatching policy by interacting with the high-fidelity DT model that integrates a static path planning agent using A* and a dynamic collision avoidance agent using a deep deterministic policy gradient to prevent the congestion and deadlock. Experimental results show that our method outperforms four state-of-the-art methods with shorter tardiness, lower energy consumption, and better stability. The proposed method provides significant potential to utilize the digital twin and reinforcement learning in the decision-making and optimization of manufacturing processes.

Study on dynamic collision avoidance during UAV inspection based on improved graph theory network algorithm

Abstract With the development of the times, UAVs are gradually promoted and popularized in military and civil fields, and the future airspace will also face more security risks. This paper combines the graph theory network algorithm to plan the initial path of UAV inspection and completes the dynamic collision avoidance path planning in the process of UAV inspection through the established joint model of UAV inspection sensing and avoidance. At the same time, the ant colony algorithm is introduced to improve the graph theory network algorithm to solve the dynamic collision avoidance optimal path in the process of UAV inspection. On this basis, simulation experiments of path planning design for UAV collision avoidance and kinematic simulation with two-fold priority judgment are carried out, and the kinematic parameters corresponding to the collision avoidance path are selected as the analysis anchor points. The extreme values of horizontal speed, climb speed, trajectory inclination angular rate, and heading angular rate are 31.6 m/s, 3 m/s, 5.7°/s, and 18.4°/s, respectively, which are within the given constraints, and verify the reasonableness and effectiveness of the proposed optimization scheme. The average time of the proposed algorithm is 0.0458s, which is much lower than the corresponding 0.7105s of the original scheme algorithm, through data comparison of simulation experiments and experimental validation. Using a graph theory network algorithm, the proposed optimization scheme is more efficient and stable and has a higher success rate for collision avoidance.

Notice of Violation of IEEE Publication Principles: Sequential Convex Programming for Collaboration of Connected and Automated Vehicles

Notice of Violation of IEEE Publication Principles<BR><BR>"Sequential Convex Programming for Collaboration of Connected and Automated Vehicles," <BR>by Xiaoxue Zhang, Jun Ma, Zilong Cheng, Frank L. Lewis, and Tong Heng Lee, <BR>in IEEE Transactions on Intelligent Vehicles, Early Access <BR><BR>After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE’s Publication Principles. <BR><BR>This paper contains significant portions of original text from the paper cited below. The original text was copied without attribution (including appropriate references to the original author(s) and/or paper title) and without permission. <BR><BR>"Networked Model Predictive Control for Vehicle Collision Avoidance" <BR> by Bassam Alrifaee, <BR>in RWTH Aachen University, Dissertation, 04 May 2017 <BR>BR>"Sequential convex programming MPC for dynamic vehicle collision avoidance" <BR>by Bassam Alrifaee, Janis Maczijewski, Dirk Abel, <BR>in the Proceedings of the IEEE Conference on Control Technology and Applications, 2017, pp. 2202-2207 <BR><BR> <br/> This paper investigates the collaboration of multiple connected and automated vehicles (CAVs) in different scenarios. In general, the collaboration of CAVs can be formulated as a nonlinear and nonconvex MPC problem. Most of the existing approaches available for utilization to solve such an optimization problem suffer from the drawback of considerable computational burden, which hinders the practical implementation in real time. This paper proposes the use of SCP, which is a powerful approach to solving the nonlinear and nonconvex MPC problem in real time. To appropriately deploy the methodology, as a first stage, SCP requires linearization and discretization when addressing the nonlinear dynamics of the system model adequately. Based on the linearization and discretization, the original MPC problem can be transformed into a QCQP problem. Besides, SCP also involves convexification to handle the associated nonconvex constraints. Thus, the nonconvex QCQP can be reduced to a quadratic programming (QP) problem that can be solved rather quickly. Therefore, the computational efficiency is suitably improved despite the existence of nonlinear and nonconvex characteristics, whereby the implementation is realized in real time. Furthermore, simulation results in three different scenarios of autonomous driving are presented to validate the effectiveness and efficiency of our proposed approach.

Autonomous ship navigation with an enhanced safety collision avoidance technique

The motion of an autonomous ship is different from that of ground and aerial robots due to its maneuvering and environmental constraints. As a result, many techniques have been introduced for autonomous ship path planning. This paper presents a novel technique for global and local navigation planning of autonomous ships under complex static and dynamic constraints. Our technique, termed safety-enhanced path planning (SPP), has been developed to avoid potential collisions with underwater obstacles near seaside areas. SPP pre-processes the map to preserve the shape of visible obstacles and mark a safety-outline around the shores. Subsequently, an offset safety line (OSL) is drawn about the original shore to protect the ship when passing close to threat-defined offshore areas. The global path is produced with an enhanced A* multi-directional algorithm, considering the kinematic constraint of the ship. To ensure optimal path quality, the global path is further refined with a smoothing filter to improve consistency and smoothness. Additionally, local navigation is introduced to help the autonomous ship avoid collisions with other obstacle ships. Local offset trajectories are produced with 4th and 5th degree polynomials along longitudinal and lateral coordinates in time t. Distance closest point approach (DCPA) is utilized for early obstacle prediction to help the ship maneuver in complex dynamic obstacle avoidance scenarios. The trajectory set is filtered with an efficient cost policy to obtain the best trajectory for dynamic collision avoidance. We conduct simulations in MATLAB and compared with other maritime path planning methods to verify the effectiveness of our approach.

Dynamic adaptive autonomous navigation decision-making method in traffic separation scheme waters: A case study for Chengshanjiao waters

A dynamic adaptive decision-making method in traffic separation scheme (TSS) waters (Chengshanjiao) was explored to achieve fully autonomous navigation. A static traffic environment comprising the digital models of the constituent parts of a TSS was established. A dynamic model was constructed using the target ships. Static and dynamic traffic environments serve as a foundation for decision-making. Based on the mathematical evaluations of the 1972 International Regulations for Preventing Collisions at Sea (COLREGs) and good seamanship, the requirements for motor-vessel collision avoidance in different scenarios and stages were presented. An automatic navigation method was established that could control the ship, automatically track the route, and assess the ship motion state. A collision risk identification model and dynamic collision avoidance mechanism for this type of water were built to identify the most dangerous target ship and a feasible manoeuvring plan to ensure safety in a multi-ship environment. To adapt to the random movement of target ships and correct residual errors, an autonomous navigation decision framework was proposed based on time-series rolling calculations. The ship safely moved through the water by altering its course 5° to starboard at 326 s, 6° to starboard at 887 s, route tracking at 1627 s, altering its course 6° to starboard at 4072 s, and route tracking at 4813 s in an experimental scenario with eight target ships. Six of the eight target ships were randomly manipulated. The results demonstrate that this decision-making technique can be utilised in practice and is precise to 1°.

A partially observable multi-ship collision avoidance decision-making model based on deep reinforcement learning

Unmanned ships have drawn widespread attention for their potential to enhance navigational safety, minimize human errors, and improve shipping efficiency. Nevertheless, the complexity and uncertainty of mixed obstacle environments present significant challenges to developing unmanned ships, particularly in collision avoidance decision-making. This paper proposes a new model using the Partially Observable Markov Decision Process (POMDP) to construct a collision avoidance decision-making model in mixed obstacle environments for autonomous ships, which can address the environment’s complexity and uncertainty and improve decision accuracy. An image-state observation method is proposed as images can provide more accurate, rich, and reliable information. A dense reward function is designed to address the issue of sparse rewards in fitting the algorithm. The Proximal Policy Optimization (PPO) algorithm is utilized for model training. Based on this, a route guidance method called the PPO for POMDP with guidelines under dense reward (G-IPOMDP-PPO) is proposed, which can improve training efficiency. Simulations are conducted in various mixed obstacle environments and compared with conventional algorithms. The results show that the proposed model can safely and efficiently make collision avoidance decisions in complex and uncertain environments. This research provides a new solution and theoretical foundation for developing autonomous ships and can be extended to achieving dynamic interactive collision avoidance in mixed obstacle environments.

Optimized APF-ACO Algorithm for Ship Collision Avoidance and Path Planning

The primary objective of this study is to investigate maritime collision avoidance and trajectory planning in the presence of dynamic and static obstacles during navigation. Adhering to safety regulations is crucial when executing ship collision avoidance tasks. To address this issue, we propose an optimized APF-ACO algorithm for collision avoidance and path planning. First, a ship collision avoidance constraint model is constructed based on COLREGs to enhance the safety and applicability of the algorithm. Then, by introducing factors such as velocity, position, and shape parameters, the traditional APF method is optimized, creating a dynamic APF gradient for collision avoidance decision making in the face of dynamic obstacles. Furthermore, the optimized APF method is integrated with the ant colony optimization algorithm, the latter modified to overcome the inherent local optimality issues in the APF method. Ultimately, validations are conducted in three areas: static avoidance and planning in restricted sea areas, avoidance under conditions of mixed static and dynamic obstacles, and avoidance in situations of multiple ship encounters. These serve to illustrate the feasibility and efficacy of the proposed algorithm in achieving dynamic ship collision avoidance while simultaneously completing path-planning tasks.

Optimized Dynamic Collision Avoidance Algorithm for USV Path Planning.

Ship collision avoidance is a complex process that is influenced by numerous factors. In this study, we propose a novel method called the Optimal Collision Avoidance Point (OCAP) for unmanned surface vehicles (USVs) to determine when to take appropriate actions to avoid collisions. The approach combines a model that accounts for the two degrees of freedom in USV dynamics with a velocity obstacle method for obstacle detection and avoidance. The method calculates the change in the USV's navigation state based on the critical condition of collision avoidance. First, the coordinates of the optimal collision avoidance point in the current ship encounter state are calculated based on the relative velocities and kinematic parameters of the USV and obstacles. Then, the increments of the vessel's linear velocity and heading angle that can reach the optimal collision avoidance point are set as a constraint for dynamic window sampling. Finally, the algorithm evaluates the probabilities of collision hazards for trajectories that satisfy the critical condition and uses the resulting collision avoidance probability value as a criterion for course assessment. The resulting collision avoidance algorithm is optimized for USV maneuverability and is capable of handling multiple moving obstacles in real-time. Experimental results show that the OCAP algorithm has higher and more robust path-finding efficiency than the other two algorithms when the dynamic obstacle density is higher.

A Double-Layer Model Predictive Control Approach for Collision-Free Lane Tracking of On-Road Autonomous Vehicles

This paper proposes a double-layer model predictive control (MPC) algorithm for the integrated path planning and trajectory tracking of autonomous vehicles on roads. The upper module is responsible for generating collision-free lane trajectories, while the lower module is responsible for tracking this trajectory. A simplified vehicle model based on the friction cone is proposed to reduce the computation time for trajectory planning in the upper layer module. To achieve dynamic and accurate collision avoidance, a polygonal distance-based dynamic obstacle avoidance method is proposed. A vertical load calculation method for the tires is introduced to design the anti-rollover constraint in the lower layer module. Numerical simulations, with static and dynamic obstacle scenarios, are conducted on the MATLAB platform and compared with two state-of-the-art MPC algorithms. The results demonstrate that the proposed algorithm outperforms the other two algorithms regarding computation time and collision avoidance efficiency.

Integrated behaviour decision-making and trajectory tracking for dynamic collision avoidance of an ASV using receding horizon optimisation

This paper develops a receding horizon optimisation scheme for integrated behaviour decision-making and trajectory tracking to ensure the dynamic collision avoidance of an autonomous surface vessel (ASV). We apply Q-learning to make behaviour decisions because manoeuvring habit requirements and COLREGS must be satisfied in dynamic collision avoidance scenarios. The heading course and vessel speed are considered to transmit the outcome of behaviour decision-making to a trajectory tracking model predictive control (MPC) controller. Next, a trajectory tracking nonlinear controller for the ASV is developed within the MPC framework, in which a set of nonlinear constraints is designed for collision avoidance. Specifically, depending on the heading course and vessel speed, the collision avoidance constraints can be switched to allow the controller to execute the behaviour decision. Simulation results verify the effectiveness of the proposed receding horizon optimisation scheme.

COLREGS-based collision avoidance algorithm for unmanned surface vehicles using modified artificial potential fields

In this paper, to improve the safety of navigation in dynamic environments, a new collision avoidance method is presented for Unmanned Surface Vehicles (USVs). It is mainly focused on dynamic obstacles and safety requirements. Convention on the International Regulations for Preventing Collisions at Sea (COLREGS) is introduced and the original artificial potential field (APF) algorithm is modified to ensure safe collision avoidance of USVs. The new attractive and repulsive potential field functions are designed and a new process of dynamic collision avoidance is constructed to solve the issue. At last, theoretical simulations and field tests are launched to validate our method. The simulation results show that the proposed method can perform safe navigation well. Through our USV platform, the effectiveness of the improved APF method for collision avoidance is also verified. Meanwhile, it is fast, effective, and deterministic.

The path planning of collision avoidance for an unmanned ship navigating in waterways based on an artificial neural network

Abstract Designing a safe, collision-free navigation route is critical for unmanned ships. This article applies the path planning method to the generation of collision avoidance paths for unmanned ships. Since the path length function is obtained from the distribution points constructed in space, it is necessary to transfer the safe domain of the unmanned ship to the obstacle, treating the unmanned ship as a particle. Then, the constructed artificial neural network (ANN) is applied to compute the collision penalty function for distribution points and obstacles. Furthermore, an evaluation function including the path length function and collision penalty function is designed, and the optimal path is obtained by computing the minimum value of the evaluation function. Meanwhile, the simulated annealing method is introduced to optimize the activation function of the output layer of the ANN to improve its classification performance and suppress the local minima problem. Finally, the application of ANN in ship autonomous dynamic collision avoidance path planning is demonstrated in two types of experiments. Among them, when avoiding static obstacles, the minimum safe passing distance between the two ships reaches 30 m; when avoiding dynamic obstacles (navigating ships), the minimum safe passing distances between the two ships in the head-on situation and the overtaking situation are 378 and 430 m, respectively.