Multi-flying Cars Path Planning Strategy Considering Energy Consumption and Time in Urban Environments

Multi-flying Cars Path Planning Strategy Considering Energy Consumption and Time in Urban Environments

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Tao Deng¹^,²^,³, Jifa Yan⁴, Binhao Xu¹

Automotive Innovation | 2025, 8(1) : 92 - 112

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Automotive Innovation | 2025, 8(1): 92-112

• Papers •

Multi-flying Cars Path Planning Strategy Considering Energy Consumption and Time in Urban Environments

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Tao Deng¹^,²^,³, Jifa Yan⁴, Binhao Xu¹

Affiliations

¹ Chongqing Jiaotong University School of Aeronautics Chongqing 400074 People's Republic of China

² Chongqing Jiaotong University Chongqing Key Laboratory of Green Aviation Energy and Power Chongqing 400074 People's Republic of China

³ Chongqing Jiaotong University The Green Aerotechnics Research Institute Chongqing 400074 People's Republic of China

⁴ Chongqing Jiaotong University School of Mechatronics and Vehicle Engineering Chongqing 400074 People's Republic of China

doi: 10.1007/s42154-024-00312-0

Outline

Abstract

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A new type of transportation vehicle, the flying car, is attracting increasing attention in the automotive and aviation industries to meet people's personalized transportation needs for urban air traffic and future travel. With its vertical takeoff and landing capability, flying cars can expand its feasible routes into 3D space. The above process, however, requires sufficient path planning to obtain optimal 3D path. To solve the above issue, the inspiration was drawn from animals in the natural world to design a type of flying car that can travel in various urban environments such as land and low altitude by using different components like wheels and propellers. Incorporating the motion characteristics of flying cars in the future urban environment, segmenting the energy consumption and time models of various stages of flying cars is conducted. The introduction of temporal A* algorithm into the new field of flying cars for the first time, the priority planning algorithm for multiple flying car groups based on an improved A* algorithm utilizing safety intervals is proposed. The proposed strategy is validated on different sizes of urban environment maps. The results indicate that on a complex map with 452 nodes, the strategy effectively reduces distance by 4.5 m, decreases energy consumption by 85.8% and improves planning speed. Compared with the strategy based on multicommodity network flow integer linear programming, the planning results are roughly the same, but the weighted cost of employing this strategy is decreased by 5.2%, and the path distance is reduced by 0.34 m.

Key words

Multi-flying cars / Path planning / A* algorithm / Priority planning

Cite this Article

Tao Deng, Jifa Yan, Binhao Xu. Multi-flying Cars Path Planning Strategy Considering Energy Consumption and Time in Urban Environments[J]. Automotive Innovation, 2025 , 8 (1) : 92 -112 . DOI: 10.1007/s42154-024-00312-0

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Abbreviations

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ACOPAR	Ant colony optimization with probability-based random-walk strategy and adaptive waypoints-repair
AVs	Autonomous vehicles
GOS	Guidance point strategy
HVs	Human-driven vehicles
LRCA	Lazy-based review consensus algorithm
MCNF	Multi-commodity network flow
RRT	Rapidly-exploring random tree
SIPP	Safety interval path planning
TD-MATD3	Task decomposed multi-agent twin delayed deep deterministic
UAM	Urban air mobility
UAVs	Unmanned aerial vehicles
UGVs	Unmanned ground vehicles

1 Introduction

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Drones have unique advantages in reconnaissance, emergency rescue, island transportation and other unmanned missions [1]. They can perform scheduled tasks or make real-time decisions by sensing the environment through sensors. Unmanned vehicles, which perform outstandingly in various fields such as urban traffic management, logistics and transportation and industrial manufacturing, are capable of flexibly adjusting their actions according to task requirements without the need of human intervention [2]. However, unmanned vehicles, although highly energy-efficient and maneuverable, are mostly limited to flat terrain or structured environments. On the other hand, although drones are agile and have strong obstacle-surpassing ability, they are constrained by battery life. In recent years, with the rise of concept of urban air mobility (UAM), flying cars have attracted wide spread attention due to its excellent sports performance [3]. In comparison with the above two kinds of transport vehicles, flying cars feature the superior performances of both, they have high maneuverability like unmanned vehicles as well as they can also have high obstacle-surmounting capability like aircraft, with the ability of vertical takeoff and landing to shorten the path length when necessary [4]. Therefore, they are expected to become important transport vehicles for the future development of urban air traffic [5].

Imagine the scene traffic congestion in major cities, such as during rush hours and specific holidays, which is shown in Fig. 1. The increased number of vehicles on the road has led to traffic congestion. This increases transportation costs for businesses together with prolonging the commuting time, to some extent, raises the risk of traffic accidents. For example, the resident needs to travel from home A to the city center B to attend an emergency meeting in a short time, but due to the traffic congestion, the traditional ground transportation is unable to meet the time requirement. Furthermore, one day, a certain area of the city experienced a sudden natural disaster, leading to a large number of citizens being trapped and urgently needing to be transported from point $\mathrm{C}$ to hospital D.

However, due to the damage to the city’s ground-level roads, traditional ground transportation vehicles are unable to reach the disaster area for rescue efforts. In this scenario, the flying car can fully utilize its multi-modal mobility capabilities, achieving high maneuverability. For example, when the ground travel is unfeasible, the vehicle utilizes integrated propulsion devices to drive the wheels parallel to the surface, generating lift from the rotating propellers to enable flight. This allows the car to transition into flight. Flying cars overcome the shortcomings of unmanned ground vehicles (UGVs) in terms of pass ability and unmanned aerial vehicles (UAVs) in terms of energy utilization, and it is irreplaceable in terms of transportation convenience, which is the inevitable development of cars in the future [6]. In the three-dimensional urban space, flying cars require perception [7,8], planning [9-11] and control [12,13] to achieve autonomous driving within three dimensions. In the low altitude flying automatic driving system of flying cars, path planning plays a crucial role. Its main goal is to design an aerial path for the flying car in urban environments to ensure that it can safely and efficiently reach any landing point from any take off point. In the above two scenarios, the planning process faces technical challenges in obtaining appropriate take off times and coordinating the routes of multiple flying car fleets, especially in high traffic urban environments. Currently, for individual mobile transportation modes such as unmanned vehicles and drones, mature collaborative path planning research results have been achieved. In a simulated environment, researchers are dedicated to designing a planning strategy to ensure that multiple vehicles can avoid collisions in the simultaneously planned paths, while meeting multiple constraints such as minimal cost, driving efficiency and working time [14]. However, there are currently few studies on collaborative path planning for multi-modal locomotion capable vehicles, so this is a scientific field worth further study.

Some researchers have conducted in-depth studies on the collaborative path planning issue of single-mode transportation vehicles. Cooperative path planning for multiple vehicles is not simply superimposing the motion trajectories of multiple vehicles [15], but it involves considering the cooperative communication between multiple vehicles to effectively plan the travel path, ensuring that they can complete their respective tasks or reach their destinations in a shared environment without colliding [16]. In general, the cooperative path planning of flying cars is one of the core technological means to achieve urban aerial taxi dispatch services in the future. They can quickly respond to passenger demands and plan the shortest and safest routes, thereby improving operational efficiency. Currently, there are four main methods for multi-vehicle cooperative path planning, namely motion coordination [17], priority planning [18], task decomposition [19] and heuristic intelligence [20].In order to address the collaborative planning and online planning issues between autonomous driving vehicles, Su, et al., inspired by ants finding the optimal path through pheromone, proposed a multi-vehicle motion coordination method based on improved ant colony algorithm [21]. Firstly, a multi-objective optimization function was constructed by simplifying the vehicle dynamics model and adding constraints to obtain the best path. Then, the information update mechanism of the ant colony algorithm was improved to obtain the best motion trajectory. At the same time, in order to improve the planning efficiency of the algorithm, an adaptive adjustment evaporation coefficient was designed. Finally, simulations were conducted in two opposing simulation environments, fully demonstrating the efficiency of this method and contributing a good reference method for multi-vehicle coordinated path planning problems. Xu et al. proposed a novel hierarchical planning algorithm at two different levels to solve task allocation and motion planning problems [22]. Inspired by the maximum consensus strategy at a lower level, an inertia-based review consensus algorithm (LRCA) was proposed. At the same time, the introduction of the path generation guiding point strategy (GOS) solves the multi-vehicle task allocation problem as well as addresses vehicle deadlock issues. At a higher level, the Dubins curve was combined with the above method to propose a method named LRGO for solving the task assignment and motion planning of incomplete vehicles. Simulation and actual experiments together proved that the method has optimality and certain practical value. Liu, et al. proposed an ant colony optimization algorithm based on continuous modifications to address the issue of ensuring that multiple unmanned vehicles can complete their respective tasks without colliding with each other [23]. Firstly, a probability-based random walk strategy was combined with the adaptive checkpoint repair method $\left({\mathrm{{ACOPA}}}_{\mathrm{R}}\right)$ to plan the path of each unmanned ground vehicle. Then, at locations where multiple vehicles conflict, collision avoidance was achieved by adjusting the speed of each unmanned vehicle, thereby optimizing their trajectories. The proposed ${\mathrm{{ACOPA}}}_{\mathrm{R}}$ algorithm was compared with other algorithms, showing clear advantages in solving complex high-dimensional issues. Liu, et al. proposed a novel and efficient path planner to coordinate multiple robots to avoid collisions and accomplish specified tasks in a complex environment [24]. They also formulated dynamic priority strategies to collaboratively form goal formations. A multi-robot system was established to validate the proposed path planning strategies. The simulation results indicated that the proposed method successfully addresses the issues of collision avoidance and formation of formations. In order to efficiently find the optimal strategy for multi-vehicle cooperative control problems, researchers have proposed a collaborative framework based on multi-vehicle task decomposition [25]. By decomposing the problem into a lower-level task completion problem and a higher-level task allocation problem, the optimal solution can be quickly identified. The task completion component is responsible for minimizing costs based on environmental constraints and determining control inputs. The task allocation component is responsible for assigning appropriate tasks to each vehicle based on task complexity. Finally, using the RoboFlag competitive game to validate this approach, simulation results indicated that the hierarchical task decomposition method is an effective approach for addressing multi-vehicle cooperative control problems. Sun, et al. proposed a reinforcement learning algorithm based on task decomposition for training optimal strategies for each task of intelligent agents collaborating on multiple tasks [26]. The method simplifies complex issues by decomposing tasks and breaking down the overall reward signal, ensuring efficient learning of optimal strategies by each agent. Finally, through the ablation simulation, the superiority and practicality of this approach have been demonstrated. The issue of autonomous path planning for multiple drones in complex and uncertain obstacle environments is extremely challenging. In order to guide multiple drones to complete tasks without colliding, Zhou, et al. proposed a novel task decomposition multi-agent double delayed deep deterministic policy gradient (TD-MATD3) algorithm [27]. Firstly, the path planning was decomposed into two major modules-navigation and obstacle avoidance, different reward functions were designed for the two modules to guide drones to avoid obstacles while moving quickly to the destination. Furthermore, considering the effectiveness of task decomposition, high-quality feature information was extracted from each navigation module and integrated into the policy evaluation function of the obstacle avoidance module, greatly improving planning efficiency. Simulations showed that the proposed algorithm has fast convergence speed and good environmental adaptability. This method, however, can only be applied to small-scale scenarios of multi-drone cooperative planning and lack universality. Yan, et al. proposed a game-theoretic human-machine mixed traffic trajectory planning framework for the safety issues of coexistence of autonomous vehicles (AVs) and human-driven vehicles (HVs) in complex environments for future human-machine mixed driving [28]. Firstly, a non-cooperative game was constructed between AVs and HVs, as well as a partially cooperative game framework between AVs. Then a HV’s longitudinal game strategy was established considering driver’s longitudinal manipulation characteristics and personalized aggressiveness. The proposed human-machine mixed traffic trajectory planning framework, based on Stackelberg game method, is effective in scenarios involving lane-changing by HVs with different aggressiveness and response delay, as demonstrated by simulation results.

In addition to the mentioned energy consumption, path distance and overall duration, optimizing the route is also an important step after the path planning [29]. In the actual movement of vehicles, the frequent steering consumes a large amount of energy [30]. In a completely known complex environment, by combining the efficient Theta* algorithm with piecewise continuous Bezier curves, mutually non-interfering motion trajectories for drones have been generated, minimizing the flight distance to the maximum extent [31]. Suh, et al. proposed a new method combining graph search and trajectory optimization for planning multimodal motion trajectories [32]. This method allows for efficient operation in higher-dimensional state spaces. By examples of hybrid integrator, amphibious robot and flying drone, it is demonstrated that the proposed planner can efficiently provide probabilistically optimal and dynamically feasible full-state trajectories. Wang and his team designed a robot suitable for on-site application environments, proposing an improved A* algorithm that combined 2D and 3D search to optimize the position of mode switching points [33]. Simulation results have shown that this ultimately provides the robot with an efficient and highly practical global 3D path planning algorithm.

The above study laid a certain foundation for the path planning of vehicles with multi-mode motion capabilities. The difference is that the feasible domain of flying cars is in 3D urban space. Proper mode switching can avoid traffic congestion and shorten commute time. In the past 5 years, some researchers conducted $3\mathrm{D}$ path planning research related to flying cars. Some scholars evaluated the energy consumption and time cost per unit distance based on the vehicle’s kinematic model, designed an objective function that conforms to the flying car characteristics using the improved A* algorithm, to plan for shorter and smoother 3D trajectories of flying cars [34,35]. Some scholars employed RRT-based path planning algorithms to generate paths step-by-step by randomly sampling and rapidly expanding the nodes of the tree [36-38]. Firstly, a comprehensive cost function was established, taking into account of energy consumption and time based on the dynamics model. Then, the cost of reaching the endpoint was calculated using low-altitude flight mode throughout the journey. The cost serves as the baseline for algorithm sampling, continuously narrowing the sampling range based on the designed update mechanism until the target point is reached [39]. In addition, other scholars have also tried to apply improved Q-learning methods to flying cars. Zhao, et al. proposed an improved Q-learning-based smooth path planning strategy that considers mode switching, planning a suitable amphibious route for intelligent and unmanned ground vehicles [40]. They also introduced game theory into the planning process to guide the vehicles in mode switching. However, the above method is only applicable to the path tracking problem in the two-vehicle chase mode. The authors team has already had a certain research foundation in the single flight car path planning. Yan, et al. firstly expanded the sub-nodes based on the behavioral characteristics of the flying car at ground and aerial nodes using different node selection strategies. Secondly, a target function was designed to comprehensively trade off energy consumption, time and mode switching cost, aiming to minimize the motion cost. Finally, based on segment-based Bezier curve optimized paths, unnecessary inflection points were reduced [35]. At the same time, it also laid a solid foundation for the current research on multi-rotor flying cars. Currently, there is no research on how multi-flying car fleets can efficiently and safely select their modes of operation. In the future, further in-depth studies are needed on how to coordinate multiple flying cars to accomplish tasks such as emergency rescue and business travel while avoiding collisions. Special attention should be given to the timing of mode switching.

Based on previous studies, addressing the forward-looking issue of how a group of flying cars in urban environments make decisions, For the first time, the A* algorithm in the time domain will be introduced to the emerging field of flying cars, a multi-flying car group prioritization algorithm based on safety interval path planning (SIPP) improved A* algorithm is proposed to coordinate multiple flying cars to safely and reasonably accomplish tasks. Firstly, a flying car with integrated wheel channels is designed, including the vehicle body and power unit. Next, based on the behavioral characteristics of flying cars in urban environments, different energy costs and time penalties of different motion modes are considered, a new objective function is developed with added safety constraints. Furthermore, to balance cost and planning efficiency, the subsequent function of the SIPP algorithm is improved, considering only the earliest arrival state and the state with the lowest overall cost when obtaining sub-states. Finally, through multiple verifications in a simulated urban road environment, the proposed algorithm successfully coordinates multiple flying cars to travel safely and efficiently from the starting point to the destination.

The main contributions of this research are as follows:

(1) A flying car with integrated wheel-channeling technology has been designed, comprising a fuselage and power system. The power system has been reconfigured to allow seamless transition between ground and aerial modes, apart from reducing commuting time, also enhancing maneuverability.

(2) New objective functions have been developed based on the behavior of flying cars in urban environments. Safety constraints have been incorporated, and the subsequent function of the SIPP algorithm has been enhanced to consider only the earliest arrival state and the state with the lowest overall cost when obtaining sub-states.

(3) A multi-flying car fleet planning algorithm based on SIPP enhanced A* algorithm is proposed. Through simulation on various city environment maps, the proposed algorithm has been thoroughly validated, demonstrating its ability to efficiently coordinate multiple vehicles to reach their destinations safely.

The other chapters of this paper are arranged as follows. Section 2 describes the working principle of the designed flying car. Section 3 introduces the traditional SIPP priority planning algorithm and the specific details of the improvements. Section 4 conducts simulations and comparisons. Section 5 draws conclusions and highlights shortcomings.

2 Descriptions of the Flying Car

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This section first describes the origin of the design of this flying car, and then discusses the functions of the three core components of the designed flying car and how they achieve the working principle of switching between two modes.

2.1 Flying Car Design

Animals with ground and aerial mobility are ubiquitous in the natural world, as shown in Fig. 2. They show great flexibility, using the power plant in different ways and producing two modes of movement. Inspiration was drawn from animals in the natural world to design a type of flying car that can travel in various urban environments such as land and low altitude by using different components like wheels and propellers. Figure 3(a) shows the ground driving state of the designed flying car. Figure 3(b) shows the low-altitude flying state of the designed flying car. Ground driving is the primary driving mode, and appropriate switching of driving modes can help vehicles avoid traffic congestion and reduce commuting time. This flying car consists of the body, power unit and support components.

The power unit includes wheels, propellers, the first drive unit and the second drive unit. As shown in Fig. 3(c). The propeller rotates in coordination with the setting in the perforation. The propeller uses a twin-blade propeller, and the far end of the fixed rod away from the vehicle body is equipped with the second drive device that drives the propeller rotation. The second drive unit uses a propeller motor, and the propeller motor is fixedly connected to the propeller through a coupling. The first drive unit includes a driving gear, a driven gear and a first driving source. The driven gear is coaxially fixed on a fixed rod, and the driven gear meshes with the driving gear. The power unit is hinged on the body of the vehicle. When the power unit is perpendicular to the ground, the driving force on the wheels drives the flying car into ground travel mode. When the power unit is parallel to the ground, the lift generated by the rotor drives the flying car into low-altitude flight mode. Thus, the vehicle can be freely switched between land form and flight state, and the required range of modal conversion is small, stable and reliable.

The vehicle body includes removable support frames mounted on its side walls, with four support frames, each of which is equipped with a power device. The support frame consists of two vertical rods and bolts set at the ends of the vertical rods. The detachably mounted support frame facilitates the disassembly of the power device from the vehicle body by the personnel, making it convenient for the maintenance and replacement of the power unit.

The support component uses a hydraulic rod, and the bottom of the vehicle is provided with a receiving groove for accommodating the hydraulic rod, and the hydraulic rod sliding cooperation is arranged in the accommodating groove. There are 4 hydraulic rods installed. When performing modal conversion of the car, the hydraulic rods are extended from the accommodating groove and supported on the ground, and the body is raised to rotate the power device. After the modal conversion is completed, the hydraulic rods are retracted into the accommodating groove to reduce the resistance during the vehicle movement or flight. The physical model and software architecture of the designed flying car are shown in Fig. 3.

2.2 Working Principle of Motion Mode

Research has shown that the energy consumption for vertical take off flying cars is approximately tens of times higher than that of ground travel [39]. This is due to the need to overcome gravity and resistance during vertical takeoff and low-altitude flight, resulting in low energy efficiency during low-altitude flight. Typically, flying cars operate like regular cars on roads, with flight mode being an auxiliary mode of operation. However, in situations of traffic congestion and difficult obstacles to cross, switching to low-altitude flight mode can significantly reduce travel distance and shorten commuting time.

2.2.1 Ground Driving

When switching to ground travel mode, the flying car functions like a regular vehicle, with the first drive source in the first drive device being a servo motor. The servo motor drives the active gear through a coupling, which in turn drives the wheel hub rotation, thereby driving the wheel rotation. According to the dynamic model established in Ref.[41], the total driving force generated by the wheel motor can be solved through the equations in the model.

When the flying car switches to ground mode, it gains all the superior performance of a regular car, such as high maneuverability on good roads, strong endurance and high driving efficiency. However, when encountering complex environments such as traffic congestion, road interruptions or rivers, the drawbacks of traditional ground vehicles become obvious. The vehicles can only choose to detour or wait, which increases the driving distance and extends the commute time.

2.2.2 Low Altitude Flight

When switching to low altitude flight mode, the power unit is level with the plane where the car body is located, the second driving device adopts the propeller motor, the propeller motor and the propeller are fixedly connected through the coupling, the propeller motor drives the propellers to rotate, and the lift generated by the rotation of the propellers drives the car body to fly, and it uses a 4-wheeled culvert dual-propeller structure with a total of 8 propellers. The working principle of the designed power device refers to the ducted fan-style propeller. When the propeller inside the wheel is subjected to external force applied by the driving motor, it will rotate at high speed and generate lift upwards to drive the vehicle to take off vertically, thus achieving mode switching.

In conclusion, with its amphibious capabilities, a flying car both possesses the superior attributes of a regular car, and has the ability to fly at low altitudes like an electric vertical takeoff and landing aircraft. In terms of route planning, the flying car can bypass congested road traffic by switching to flight mode, expanding its route from 2D ground to $3\mathrm{D}$ low airspace, effectively addressing traffic congestion issues.

3 Safety Interval Based Prioritization Planning Strategy for Multiple Flying Cars with Improved A* Algorithm

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In this section, the objectives of path planning for flying cars are described, and a SIPP is introduced. Aiming at how a group of flying cars in a future urban environment decides which mode of motion to choose, a priority planning algorithm based on safety interval improvement A* algorithm for multiple flight car groups is proposed to adapt to multimode motion. The proposed multi-flying cars path planning strategy principle can be seen in Fig. 4. The Fig. 4 consists of 4 parts, which are 3D environment modeling, path planning with improved A* algorithm based on safety interval, underlying driving factors and the final planning path. The flying car first obtains location information from the operating environment, then determines the type of node the starting point is in. Finally, it is handed over to the path planner for execution. The planning algorithm is based on the constructed $3\mathrm{D}$ environment, which includes ground road environment, no-fly zones and landing pads. The planning algorithm first requests complex map environment information, then plans a set of non-interfering paths for the fleet of flying cars. Finally, the main controller sends corresponding electrical signals to the propellers or support components to achieve mode switching. Due to energy consumption reasons, flying cars mainly operate in ground mode.

Detailed principles of the algorithm’s specific design will be discussed below.

3.1 Description of Planning Objectives

In urban environments, casual switching of flight mode consumes a large amount of energy as well as leads to traffic accidents, causing unnecessary trouble. Therefore, it is necessary to control the position and time of mode switching reasonably. One of the planning goals is to allow flying cars to bypass or detour in appropriate locations.

In addition, traditional search algorithms cannot coordinate a group of flying cars in urban environments to reach specified points without colliding. In actual emergency rescue and air taxi services, multi-vehicle coordinated path planning plays a crucial role. Its rapid response and flexible mobility make flying cars an important transportation vehicle for emergency rescue. Therefore, another goal for path planning is to consider the coordination between multiple vehicles, establish a coordinated planning system to achieve dynamic and personalized path planning, and adapt to the changes in urban traffic and diverse travel needs.

3.2 Depiction of SIPP Algorithm

In discrete environments, the A* algorithm can effectively solve problems of single vehicle path planning through a search process. However, for multi-vehicle routing problems in urban environments, introducing a time dimension is necessary, rendering traditional A* algorithm ineffective. The SIPP algorithm is a path planning algorithm based on safe intervals, designed to ensure vehicles can navigate safely in dynamic environments without colliding with obstacles. It was proposed by Mike Phillips and Maxim Likhachev in 2011. In SIPP algorithm, the definitions of 3 key concepts are as follows:

(1) Safe interval: It refers to a continuous time period during the path planning process, where the agent and dynamic obstacles do not collide, with a conflict occurring one time step before and after this interval.

(2) Conflict interval: In contrast to the safe interval, the conflict interval is when the agent and dynamic obstacles collide during a continuous time period in the path planning process, with the time steps before and after this interval being safe.

(3) Timeline: For each position or configuration in the path, there is a corresponding timeline. The timeline is an ordered list of safe intervals and conflict intervals appearing alternately. In the timeline, adjacent safe intervals and conflict intervals cannot coexist.

The relationship among these 3 key concepts is shown in the lower part of Fig. 5.

The core idea of the SIPP algorithm is to consider safety margins in time during path planning, relying on compressing sequences of waiting and moving operations to improve planning efficiency [42].The environment is first divided into grids, with a time axis assigned to each grid. The time axis is usually represented in discrete time steps. Obstacles are then modeled as moving entities on the time axis and their future motion trajectories are predicted. For each grid, the minimum safe distance between the autonomous vehicle and obstacles is calculated. Finally, dynamic programming is executed to search for a path from the start state to the end state. Safety margin constraints are considered during the search process to ensure that the autonomous vehicle does not collide with obstacles along the planned path.

The search space of the SIPP algorithm is different from traditional A* algorithm. It iterates over states, where each state $S =\left\lbrack {{cfg}\text{, interval}}\right\rbrack$ consists of configuration and safety margin. Configuration includes the position, speed and heading of the intelligent vehicle. The safety margin is a continuous time interval represented by intervals, ensuring safe passage of the vehicle within the specified time frame. In addition, $\left\lbrack {g\left(s\right), h\left(s\right),\text{parent}\left(s\right),{time}\left(s\right)}\right\rbrack$ are also closely related to state S. Like the traditional A* algorithm, $g\left(s\right)$ and $h\left(s\right)$ represent the actual cost and estimated cost, respectively. The sum of both, $f\left(s\right)= g\left(s\right)+ h\left(s\right)$, serves as the evaluation function for searching sub states. Time(s) represents the earliest time point at which the intelligent vehicle can reach state S within the safe interval. For each iterative state, SIPP stores time(s), which is crucial in determining $g\left(s\right)$. Every time the shortest time to reach a child state is found, $\operatorname{time}\left(s\right)$ gets updated. By storing the earliest arrival time of each iteration, it ensures time optimality, significantly reducing the state space and improving the search efficiency of the algorithm.

Combining the environmental analysis in Figs. 5 and 6, the SIPP algorithm is extended with an example, i.e. an intelligent vehicle moves from state S to state $G$, while three dynamic obstacles move one time step in the direction of the arrows. It is evident that the key issue is how to quickly reach state C while avoiding collisions with obstacles. Four states of initial states $S, A, B$, and C will be analyzed, where there are at least three potential sub-states $A, B$ and C. State $A$ has 2 safety gaps ${S}_{A0}= \left\lbrack {0,3}\right\rbrack$ and ${S}_{A1}= \left\lbrack {4,+ \infty }\right\rbrack$, because after 3 time steps, it will be occupied by the obstacle moving from the leftmost side. State $B$ also has 2 safety gaps ${S}_{B0}= \left\lbrack {0,4}\right\rbrack$ and ${S}_{B1}= \left\lbrack {5,+ \infty }\right\rbrack$, as after 4 time steps, it will be occupied by the obstacle moving from the leftmost side. State C is more special, with 3 safety gaps ${S}_{C0}= \left\lbrack {0,2}\right\rbrack,{S}_{C1}= \left\lbrack {3,5}\right\rbrack$ and ${S}_{C2}= \left\lbrack {6,+ \infty }\right\rbrack$, due to two dynamic obstacles that will occupy C after 3 and 6 time steps. By analyzing 3 sub-states, 7 safety gaps are obtained, as shown in Fig. 6. However, it is clear that the safety gaps ${S}_{A1}= \left\lbrack {4,+ \infty }\right\rbrack$ and ${S}_{B1}= \left\lbrack {5,+ \infty }\right\rbrack$ cannot be used as alternatives. This is because no matter how smart vehicles utilize waiting and movement operations, they would be hit by obstacles upon entering these two safety zones. For example, smart vehicles first move right 2 steps to ${S}_{B0}$, then waiting 2 steps in ${S}_{B0}$ is still safe. At this point, the obstacle moves to $A$, even if continuing to move to the ${S}_{A1}$ state is safe, it requires the smart vehicle and obstacle to swap positions, which would result in a spatial collision, also not allowed by the SIPP algorithm. The analysis for ${S}_{B1}$ is the same. As for the initial state, since it takes two time steps to reach state C, it just misses ${S}_{C0}$. Therefore, it can be seen that the initial state S has 4 potential alternative states $\left({{S}_{A0},{S}_{B0},{S}_{C1},{S}_{C2}}\right)$.

In conclusion, the SIPP algorithm analyzes the movement trajectories of mobile obstacles, divides the time intervals where no collisions occur in each state, into corresponding safe margins, iterates to obtain the earliest arrival time of child states, thereby accelerating the search process, and efficiently plans safe paths for multiple intelligent vehicles.

3.3 Improved Priority Planning with SIPP Algorithm

Building upon the above-mentioned SIPP algorithm, considering the motion characteristics of flying cars in future urban environments, a city environment model was constructed, in which city roads, urban infrastructures, helipads, no-fly zones and dead ends were included. The energy consumption and time models for various stages of the flying car journey were developed in segments. A new objective function was devised, introducing the concept of temporal dimension in each search and allowing searches to occur over continuous time. Finally, by incorporating the new objective function into the functions for obtaining child nodes, a multi-flying car prioritized planning algorithm based on safety interval for the improved A* algorithm was proposed.

3.3.1 3D Urban Environment Modeling

The design of the directed graph $G$ of the environment refers to the reference [43]. To ensure that each flying car completes its assigned task without colliding, it is essential to classify the nodes in the urban environment. Specifically, a directed graph consists of 4 different types of nodes, i.e. ground nodes, parking nodes, interface nodes and air nodes. As shown in Fig. 7, parking nodes are typically located at the end or on both sides of a roadway, and they are critical for coordinating multi-vehicle path planning without collisions. The interface nodes above the ground (blue nodes in the Fig. 7) are used to connect ground and aerial nodes, which means that the ground nodes located above must be present in order to switch to flight mode. This design restricts the ability to take off randomly, which is crucial for ensuring the safety of urban residents. The ground nodes are distributed on both sides of the road in the simulated environment, and the nodes form edges between them. To facilitate the calculation of energy consumption and time between two points, the length of each edge is set to $1\mathrm{\;m}$. There are several different traffic exits between edges, for example, a “dead end” with only one exit, a “non branching intersection” with only two exits, an “intersection” with more than two exits, and a special type of “turn off”. These different types of traffic exits fully simulate the urban road environments and are of great significance for finding feasible solutions.

3.3.2 Energy Consumption and Time Models

According to the simplified vertical take off and landing flight profile in Fig. 8, the transition of flying car from ground movement to low altitude flight can be roughly divided into 4 motion costs and one loss cost, including vertical take off and landing costs, ground movement costs, low altitude flight costs and costs of mode switching loss. Due to the different power and speed involved in the 4 motion costs of the flying car, in order to facilitate the calculation of the energy consumption and time cost of each action, assumption is made that the power and speed required for each action remain constant. Based on the team’s previous research and analysis, the energy consumption $E$ and time t consumed by the flying car per unit time can be obtained as follows:

(1)

${E}_{g}= {\mu mgd}+ \rho {A}_{\alpha }{C}_{D}{\left({v}_{g}\right)}^{2}d/2 $

(2)

${T}_{g}= d/{v}_{g}$

(3)

${E}_{h}= \sqrt{\frac{1}{2\pi \rho }}{\left(\frac{mg}{x}\right)}^{\frac{3}{2}}\frac{x}{r}\frac{d}{\eta v}$

(4)

${E}_{t}= {E}_{h}+ {mgd}+ \rho {A}_{u}{C}_{D}{\left({v}_{t}\right)}^{2}d/2 $

(5)

${T}_{t}= d/{v}_{t}$

(6)

${E}_{f}= {E}_{h}+ \rho {A}_{\alpha }{C}_{D}{\left({v}_{f}\right)}^{2}d/2 $

(7)

${T}_{f}= d/{v}_{f}$

(8)

${E}_{l}= {E}_{h}-\rho {A}_{u}{C}_{D}{\left({v}_{l}\right)}^{2}d/2 $

(9)

${T}_{l}= d/{v}_{l}$

where ${v}_{g},{v}_{t},{v}_{f}$ and ${v}_{l}$ are the speeds of ground movements, vertical take off, low level flight, and vertical landing, respectively. ${T}_{g},{T}_{t},{T}_{f}$, and ${T}_{l}$ are the times spent on ground movements, vertical takeoff, low-level flight, and vertical landing. $d$ is the Euclidean distance between two nodes. ${E}_{g}$,${E}_{t},{E}_{f}$ and ${E}_{l}$ are consumptions during ground movements, vertical take off, low level flight and vertical landing. ${E}_{h}$ is the energy spent by the flying car when hovering. The meanings of other letters are shown in Table 1.

However, one cannot focus solely on energy consumption and time. When a flying car transitions from ground driving to low altitude flight, the energy consumed to extend and support the hydraulic rod from the housing slot on the ground must be also considered. Additionally the electrical energy required for the parallel rotation of the drive power unit with the ground should not be overlooked. Therefore, planning algorithms must also take into account the cost of mode switching losses when evaluating path costs. The switching losses should also be estimated based on the energy consumed by the hydraulic rod extending from the receiving slot to the ground and the energy consumed by the power unit rotation. Then,${P}_{\text{change }}$ is integrated with respect to the switching time t to obtain:

(10)

${C}_{c}= {\int }_{0}^{{t}_{\text{change }}}{P}_{\text{change }}\mathrm{d}t $

where ${P}_{\text{change }}$ represents the switching loss, and ${t}_{\text{change }}$ represents the switching time.

3.3.3 Objective Function and Safety Conditions

The energy consumption and temporal cost of movement based on the distance traveled can be calculated, according to the models of environment, energy and time, established based on section 3.3.1 and 3.3.2. This is crucial for obtaining the subsequent function in the SIPP algorithm. Due to the inconsistent dimensions of energy and time, for the sake of calculation convenience, the energy and time of the 4 actions involved in the vertical take off and landing process of the flying car are uniformly dimensioned. The energy cost of each process is compared to the energy cost of ground movement as the actual energy cost. Similarly, the time cost of each process is compared to the time of low altitude flight as the actual time cost, as shown in the formula below:

(11)

$\left\{{\begin{array}{l}{e}_{g}= {E}_{g}/{E}_{g}\\{e}_{t}= {E}_{t}/{E}_{g}\\{e}_{f}= {E}_{f}/{E}_{g}\\{e}_{l}= {E}_{l}/{E}_{g}\\{e}_{c}= {E}_{c}/{E}_{c}\end{array}\;\left\{\begin{array}{l}{t}_{g}= {T}_{g}/{T}_{t}\\{t}_{t}= {T}_{t}/{T}_{t}\\{t}_{f}= {E}_{f}/{T}_{t}\\{t}_{l}= {E}_{l}/{T}_{t}\end{array}\right.}\right.$

where ${e}_{g},{e}_{t},{e}_{f},{e}_{l}$ and ${e}_{c}$ represent the unified dimension ground movement cost, take-off cost, low-altitude flight cost, landing cost, and switching cost, respectively. ${t}_{g},{t}_{t},{t}_{f}$, and ${t}_{l}$ represent the ground movement time, take-off time, low-altitude flight time, and landing time after unified dimensions.

Therefore, the following objective function can be established to calculate the cost between two nodes in the constructed directed graph

(12)

$ c\left(s\right)= {\xi e}+ \left({1 -\xi }\right) t $

where $0 \leq \xi \leq 1$, by setting different values of $\xi$, different weights of energy consumption and time can be achieved. For example, one day, a natural disaster occurs in a certain area of the city, causing a large number of citizens to be stranded and in urgent need of emergency help. Upon receiving the emergency call for help, the air cab dispatch system is quickly activated, and the rescue command center makes the planner place more emphasis on time than on energy consumption by lowering value of $\xi$.

The safety of low altitude flight is at the core of flying car performance. The battery discharge multiplier of the flying car during cruise flight then reaches ${1.2}\mathrm{C}$, and the instantaneous discharge multiplier of the power battery during take off and landing can be as high as ${4.8}\mathrm{C}$, which is much higher than the battery discharge multiplier requirement for electric vehicles [44]. Due to the fact that urban air taxis operate close to the ground, buildings and people during take off and landing, despite potential airspace restrictions and the need to be aware of other air taxis or low flying aircrafts, the battery capacity as one of the power sources is an essential safety consideration. In addition to the objectives mentioned above, safety constraints have been also introduced. For each flying car with a given battery capacity, if the remaining battery capacity C is less than the specified threshold ${C}_{\text{low }}$, the planner will stop planning, which will lead to termination of the mission. The safety constraints are as follows:

(13)

$\left\{\begin{array}{l}\text{ continue planning }C \geq {C}_{\text{low }}\\\text{ stop planning }C ＜{C}_{\text{low }}\end{array}\right.$

3.3.4 Improvement of the Successor Function

The improved SIPP priority path planning algorithm presented in this paper expands upon the algorithms from references [43,45,46]. The traditional SIPP algorithm possesses completeness and optimality. The successor function takes a state and the time at which the UAV reaches that state as input and generates possible successor states after reaching that state. The successor function of the traditional SIPP algorithm always picks the state that can be reached earliest each time to ensure that the maximum number of possible successors is obtained. This is because an UAV that arrives earlier has more options and can wait until a later time within the safety margin, resulting in more successor states being generated. As shown in Fig. 9 (a), let ${t}_{0}$ and ${t}_{1}$ be two instants within a certain safety interval $\left({{t}_{0}＜ {t}_{1}}\right)$, if the flying car extends state from instant ${t}_{0}$, let ${A}_{0}$ be the set of its successors generated. Similarly, let ${A}_{1}$ be the set generated from instant ${t}_{1}$. It is evident from the figure that ${A}_{0}$ contains all the successors in ${A}_{1}$ and may also contain more successors. That is,${A}_{0}$ is a super set of ${A}_{1}$. Extending state S from ${t}_{0}$ will result in more successors as it considers flying cars reaching state S earlier that can also wait within the safety interval to observe and obtain better successors. Conversely, extending state S from ${t}_{1}$ will result in fewer successors as it only considers flying cars reaching state S at ${t}_{1}$ or later, potentially missing out on better path selections offered by flying cars reaching state S earlier.

Due to the high energy consumption of flying cars flying at low altitudes compared to ground transportation [40], in order to save energy, it is hoped that ground transportation will be prioritized more for flying cars. Therefore, in the successor function, it is not appropriate to consider only the flying car that reaches a certain state the earliest. It is essential to comprehensively balance energy consumption and time in the successor function and consider the flying car that reaches a certain state with the lowest cost. As shown in Fig. 9(b), in the successor function of the traditional SIPP algorithm, an objective function that balances energy consumption and time is introduced. When selecting the successor function in each iteration, the flying car that reaches a certain state with the lowest cost should also be considered. In this case, only the flying cars starting from the earliest and with the lowest cost to reach state Sare considered for expansion, without considering other ways of reaching. This simplifies path planning calculations and improves computational efficiency. Although the improved priority planning algorithm loses optimality, it greatly enhances planning efficiency. In future urban environments, autonomous cooperative control of multi-vehicle motion planning also has practical significance. The pseudocode of the improved successor function is shown in Algorithm 1.

Algorithm 1 getSuccessors Function

1.	Function getSuccessors $\left({s, t, v,{curren}{t}_{\text{interval }}}\right)$
2.	Input: $\parallel \leftarrow$ successors, Output:successors
3.	(x, y, z)and category $\leftarrow$ getInformation(s)
4.	for each ${s}^{\prime }$ in Neighbors(s)do
5.	$\left({{x}^{\prime },{y}^{\prime },{z}^{\prime }}\right)$ and category’ $\leftarrow$ getInformation $\left({s}^{\prime }\right)$
6.	intervals $\leftarrow$ getSafeInterval $\left({s}^{\prime }\right),\bigtriangleup t \leftarrow \operatorname{getTime}\left({s,{s}^{\prime }}\right)$
7.	for each safe interval i in intervals do
8.	if $\left({t + \bigtriangleup t}\right) \in$ allowed safe interval $i$ then
9.	$\mathrm{e} \leftarrow$ getEnery $\left({s,{s}^{\prime }}\right)$, cost $\leftarrow$ getCost $\left({e,\bigtriangleup t}\right)$
10.	if ${s}^{\prime } \neq {s}_{g}$ or ${s}^{\prime } \neq$ park point then
11.	add ${s}^{\prime }$ to successors
12.	end if
13.	else if ${\text{current}}_{\text{interval }}$ overlaps with the allowed safe interval i then
14.	${t}_{\text{arrive }} \leftarrow \max \left({t + \bigtriangleup t\text{, safe interval [0] }}\right)$
15.	$\operatorname{cost} \leftarrow \operatorname{getCost}\left({e,{t}_{\text{arrive }} -t}\right)$
16.	if ${s}^{\prime } \neq {s}_{g}$ or ${s}^{\prime } \neq$ park point then
17.	add ${s}^{\prime }$ to successors
18.	end if
19.	end if
20.	end for
21.	end for

The successor function accepts a state S, the time t at which the state is reached, the remaining battery charge $v$, and the current safety interval as inputs, and generates all possible successor states after reaching that state. It then explores all states adjacent to the current state, obtaining safety time intervals and time ${\Delta t}$ required to reach the adjacent states. Next, it traverses the obtained safety intervals of the adjacent states. If the estimated time of arrival falls within the safety interval, the corresponding cost is computed based on the designed energy consumption and cost function (see line 7-9 of the pseudocode in Algorithm 1). If the current safety interval conflicts with the safety interval of the adjacent state, the maximum value between the estimated time of arrival and the left endpoint of the safety interval of the adjacent state is chosen as the time of arrival to calculate the corresponding cost (see line 13-15 of the pseudocode in Algorithm 1). Finally, it checks if the remaining battery charge meets the safety conditions, and if the adjacent node is not a charging station, then the state is added to the successor states. The pseudocode for calculating the objective function is shown in Algorithm 2.

Algorithm 2 getCost Function

1:	Function getCost $\left({e,\bigtriangleup t}\right)$
2:	(x, y, z)and category $\leftarrow$ getInformation(s)
3:	$\left({{x}^{\prime },{y}^{\prime },{z}^{\prime }}\right)$ and category’ $\leftarrow$ getInformation $\left({s}^{\prime }\right)$
4:	dis $\leftarrow$ Euclidean distance $\left({s,{s}^{\prime }}\right)$
5:	if category or category ${y}^{\prime }\in$ air node then
6:	determine the speef of $v$ based on the magnitude of $z$ and ${z}^{\prime }$
7:	${\Delta t} = {dis}/v$
8:	if estimated arrival time $＜\bigtriangleup t$ then
9:	end if
10:	$\mathrm{e} \leftarrow$ waiting cost + moving cost
11:	else if then
12:	e $\leftarrow$ moving cost
13:	end if
14:	$\operatorname{cost}\leftarrow {\xi e}+ \left({1 -\xi }\right)\bigtriangleup t$
15:	Return cost

The objective function of this strategy considers two factors, energy consumption and time, making the selection of subsequent states more complex. Every time, select the corresponding speed based on the types of adjacent nodes, then calculate the time t required to move to the sub-state. If the estimated time to arrive is less than t, it means waiting is necessary. Due to potential conflicts with other vehicles arriving earlier, one needs to wait for a period before being able to move and vice versa (see line 9-12 of the pseudocode in Algorithm 2). Each calculation cost weighs energy consumption and time, because the earliest arriving state does not have the lowest cost, the state with the lowest cost does not arrive earlier. To balance between the two, select the state that arrives earliest and has the lowest cost, to generate the corresponding set of successor states. Once a path is found, the global variable safe interval will be updated. The next flying car will use the updated safe interval set to plan its flying route.

4 Results and Discussion

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This section conducts simulations in an urban environment map with different nodes. Their total number of nodes is 168, 452 and 576. In each map, urban environments with different heights and shapes are randomly generated.

As mentioned earlier, there are three planning strategies for flying cars, including the improved SIPP algorithm strategy that only considers time and the proposed improved SIPP algorithm strategy, which considers energy consumption and time in a combined trade off. The proposed strategies in this paper are compared with the algorithm based on optimal integer linear programming on different maps. In the following analysis of simulation results, for convenience of description, the above strategies are referred to as the first strategy, the second strategy and the third strategy respectively. The simulation data of each strategy are recorded, the path distance, weighted cost and planning speed are compared in detail.

4.1 Comparison of Planning Strategies

Firstly, the planning results of the first two strategies mentioned above are compared on an urban environment map with a total number of nodes of 168, as shown in Fig. 10. The Fig. 10(a)-(c) are the Rviz visualization, trajectory comparison and performance index statistics of the first strategy respectively. Figure 10(d)-(f) are the Rviz visualization, trajectory comparison and performance index statistics of the second strategy respectively.

From Fig. 10,two flying cars with switched modes can be seen during the path planning process in the first strategy. The flying car 2 and 3 both prioritize the low altitude flying mode, successfully flying over the lakes in the environment, and switch to landing mode over the endpoint to land at the parking node. The entire process fully demonstrates the strong obstacle surmounting capability of the flying cars. However, if the low altitude flying mode is selected for a long time, it will inevitably consume a large amount of energy, greatly reducing the endurance capability. In the second strategy, due to the improved SIPP algorithm balancing energy consumption and time, all flying cars do not switch modes. They adopt a working mode driving mainly on the ground and supplemented by low altitude flight, and choose to avoid all obstacles in the map. The second strategy therefore plans a more ideal path. Compared with the first strategy, the planned path is shorter and consumes less energy.

Figure 11 intuitively shows the comparison of specific indicators of the two planning strategies.

In Fig. 11,the path length and weighted cost of the two planning strategies are compared in detail in the form of a histogram. As previously analyzed, the planning strategy, considering only time, results in longer path lengths along with higher weighted costs. While proposed comprehensive strategy in this paper takes both energy consumption and time into account, resulting in a shorter and more energy efficient path, achieving the desired outcome.

The detailed metrics of the two planning algorithms are shown in Table 2.

The path length planned by the first strategy is ${13.2}\mathrm{\;m}$, the weighted cost is ${988.1}\mathrm{\;J}$, and the planning speed is 2.3. While the path length planned by the second strategy is only ${8.9}\mathrm{\;m}$, which is shortened by ${4.3}\mathrm{\;m}$, and the weighted cost is ${101.9}\mathrm{\;J}$, which is reduced by ${89.7}\%$. Both strategies have the same effect on planning speed.

In summary, the second strategy successfully achieves two goals: fully weighing energy consumption and time, collaboratively planning paths to reduce path length, and rational mode switching to reduce battery energy consumption.

The authors increased the complexity of the environment and conducted simulation verification in a map with 452 nodes, as shown in Fig. 12.

Figure 12(a)-(c) show the Rviz visualization, trajectory comparison and statistics of each metric for the first strategy respectively. Figure 12(d)-(f) show the Rviz visualization, trajectory comparison and statistics of each metric for the second strategy respectively.

As shown in Fig. 12,for the first strategy, two flying cars undergo mode switching during the path planning process. Flying car 1 and flying car 3 first select mode switching, then fly over buildings and lakes in the urban environment, and land vertically above the target point. The whole process prioritizes time greatly and shortens the path time. However, due to the fact that the energy consumption of vertical take off and low altitude flight for flying cars is 92 times and 56 times that of ground travel respectively, a significant amount of energy is consumed during low altitude flight. Unlike the first strategy, the second strategy primarily selects ground travel mode to avoid obstacles and does not switch modes arbitrarily. While effectively shortening travel distance, it also greatly reduces energy consumption. The planned route is more energy efficient and environmentally friendly, in line with the current guidelines for intelligent connected vehicle route planning.

Figure 13 intuitively shows the comparison of specific indicators of the two planning strategies.

The simulation results in an environment with a total of 168 nodes are generally similar to those in the first strategy, which primarily involves low altitude flying with longer planned paths and higher costs. The second algorithm adopts a completely opposite planning strategy. By appropriately controlling the mode switching, successful coordination is achieved for the safe operation of three flying vehicles.

The detailed metrics of the two planning algorithms are shown in Table 3.

The path length planned by the first strategy is ${19.2}\mathrm{\;m}$, the weighted cost is ${1850.4}\mathrm{\;J}$, and the planning speed is 12.2. The path length planned by the second strategy is only ${14.7}\mathrm{\;m}$, which is shortened by ${4.5}\mathrm{\;m}$, and the weighted cost is 263.1 J, which is reduced by 85.8%. In addition, the planning speed of the second strategy is also ${6.5}\%$ higher than the first strategy.

The total number of nodes is again increased to 576 and another more complex map is used for strategy validation. The planning results are shown in Fig. 14. Figure 14(a)-(c) show the Rviz visualization, trajectory comparison and statistics of each metric for the first strategy respectively. Figure 14(d)-(f) show the Rviz visualization, trajectory comparison and statistics of each metric for the second strategy respectively.

As shown in Fig. 14,both the first and second strategies involves mode switching for the flying cars. The starting point for flying car 3 is located at a parking node on either side of the road and the endpoint is at the apron. In the first strategy, in the path planning process, there are 2 flying cars that undergo mode switching. Flying car 3 first chooses vertical takeoff and then continuously uses low level flight mode until it is above the landing pad. Similarly, flying car 2 first chooses vertical take off and then continuously uses low level flight mode. They would pass through the same node in the air as flying car 3, but due to the different priorities of each flying car, their time passing through that node is different, so there would be no collisions. On the contrary, due to the fact that the starting points of flying car 1 is all at parking nodes and relatively close to each other, flying car 1 ends up using ground mode to travel to the destination, resembling the movement of a regular car throughout the entire process.

In the second strategy, the flying car 3 adopts ground driving mode to avoid obstacles in the early stage. As the target point is located on the helipad of a high-rise building, it only switches to low altitude flight mode and vertically lands at the target point when moving near the building. Compared with first strategy, second strategy correctly chooses the position for mode switching, resulting in higher energy utilization efficiency. The planned route better meets the requirements of safety and energy conservation. Switching modes casually incur a significant cost increase. The driving route for flying car 1 follows the same planning strategy as the first one, while the driving route for flying car 2 is opposite to the first planning strategy. It consistently adopts ground mode for obstacle avoidance, actively choosing to bypass all obstacles, which to some extent increases the path length but also saves a considerable amount of energy consumption.

Figure 15 intuitively shows the comparison of specific indicators of the two planning strategies. The first strategy and the second strategy planning have their own advantages. This is because the driving routes of flying cars 1 and 2 planned by the two strategies are the same. Only the planned route of speed 3 has a big difference. Long term, low altitude flight can greatly shorten the path distance, but it will inevitably cause higher energy consumption. The two trade off each other. In addition, in terms of planning speed, first strategy is faster. But this is not enough to show that second strategy is invalid.

The detailed metrics of the two planning algorithms are shown in Table 4.

Compared with the first strategy, the second strategy only reduces the weighted cost by ${28.2}\%$, and the other indicators are rather less effective than the first one, but this is not enough to show that the planning strategy that integrates the trade-off between energy consumption and time is not effective.

Another apron-filled map is used for strategy validation, as shown in Fig. 16. Figure 16(a)-(c) show the Rviz visualization, trajectory comparison and statistics of each metric for the first strategy respectively. Figure 16(d)-(f) show the Rviz visualization, trajectory comparison and statistics of each metric for the second strategy respectively.

The effect of the planning strategy on a map filled with tarmac is significantly different from the above map. This map simulates commercial travel between tarmacs in high rise buildings in an urban environment. It can be seen from Fig. 16,all three flying cars switch modes during the path planning process for the first strategy. After loading passengers at the helipad of a skyscraper, they then switch to low altitude flying mode and shuttle through the city’s airspace until they reach the helipad of another skyscraper. In the second strategy, during the route planning process, all 3 flying cars also undergo mode switching. The planning effect is similar to the first strategy.

Figure 17 intuitively shows the comparison of specific indicators of the two planning strategies. The effects of planning for both strategies are roughly similar. The planned paths are of the same length. The second strategy has lower energy consumption. Although the path lengths of the two strategy plans are the same, in terms of planning speed, The second strategy is faster and better than the first strategy.

The detailed metrics of the two planning algorithms are shown in Table 5. The length of the path planned by both strategies is ${13.3}\mathrm{\;m}$. However, the weighted cost of the second strategy is reduced by ${0.2}\%$ and the planning speed of the second strategy is improved by ${0.7}\%$ compared with the first strategy.

From the above 4 sets of comparative simulations, it can be seen that the second strategy proposed can successfully achieve two planning goals, obtain a shorter and more energy efficient path. At the same time, its path planning speed is faster.

4.2 The Comparison of Different Algorithms

This subchapter compares the first two proposed strategies with the strategy based on multi-commodity network flow (ILP) in different maps.

Multi-commodity network flow (MCNF) is a classic network flow optimization problem, which is described in a directed graph $G =\left({V, E}\right)$, where $V$ is the node set, and $E$ is the edge set. Supposing there are $K$ different types of commodities, each commodity $k$ has a starting point ${s}_{k}$, an end point ${t}_{k}$, and a demand quantity ${d}_{k}$. The problem is to minimize the total transportation cost and meet the demand quantity of each commodity. It is mathematically modeled as follows:

(14)

$\begin{array}{l}\min \sum_{(i, j) \in A} \sum_{k \in K} c_{i j} x_{i j} \\\text { s.t. } \sum_{j} x_{i j}-\sum_{j} x_{j i}=\left\{\begin{array}{ll}d_{k}, i=s_{k}, k \in K \\-d_{k}, i=t_{k}, k \in K \\0, \quad \text { else, } \forall i \in V, k \in K, i \neq s_{k}, j \neq t_{k}\end{array}\right. \\\sum_{k \in K} x_{i j}^{k} \leq u_{i j}, \forall(i, j) \in A\end{array}$

where $K$ denotes the set of commodities; $\left({{s}_{k},{t}_{k},{d}_{k}}\right)$ :denotes the starting point, ending point, and demand for the commodity $k;{u}_{ij}$ denotes the capacity of the arc segment $\left({i, j}\right)\in A$, and ${c}_{ij}^{k}$ denotes the unit cost of moving the commodity over the arc segment $\left({i, j}\right)\in A$.

The planning strategy based on multi-commodity network flow ILP proposed by Ref.[43] is used as a comparison benchmark. The results of the three algorithms on a simulation environment map with a total number of nodes of 298 are shown in Fig. 18. Obviously, all the three strategies successfully realize the path planning. The first strategy still prioritizes time, with one out of the three flying cars adopting a mode switch. The second and third strategies employ similar modification methods, considering distance, energy consumption and time simultaneously. Their mode switching actions all occur in the right positions, reducing path distance without increasing the number of mode switches.

Figure 19 intuitively shows the comparison of specific indicators of the two planning strategies, and the detailed metrics of the two planning algorithms are shown in Table 6.

According to the above discussion, three strategies have similar path distances and planning speeds, but the path-weighted costs differ significantly. Figure 20(a) -(c) show the Rviz visualization, trajectory comparison and statistics of each metric for the first strategy, respectively. Figure 20(d) -(f) show the Rviz visualization graph, trajectory comparison graph and the statistical graph of each index for the second strategy, respectively. Figure 20(h) -(j) are the Rviz visualization graphs, trajectory comparison graphs and statistical graphs of various metrics for the third strategy, respectively. Table 6 shows the comparison results of the three strategies based on different algorithms. Combining Figs. 20 and 21 with Table 6 reveals that, despite the similar path distances and planning speeds between the two strategies, there are notable differences in their path weighted costs. The strategies based on the SIPP algorithm have the highest and lowest path weighted costs, while the strategies based on the multi-commodity network flow ILP have costs between the two. The second strategy’s path weighting cost is reduced by ${77.9}\%$ and ${5.2}\%$ compared to the first and third strategies, respectively. This difference is caused by the mode switching motion of flying car 2 as shown in Fig. 18 b. The ground motion patterns occur in all three paths in all three strategies. However, the flying car 2 in the first strategy based on the SIPP algorithm takes a low altitude flight mode throughout the whole path due to mode switching, which consumes more energy. Finally, its total path energy consumption also increases. The second strategy based on the SIPP algorithm rationally utilizes the multi-modal motion of the flying car so that the mode switching occurs at the correct location. Its path distance is shortened by $1\mathrm{\;m}$ and ${0.34}\mathrm{\;m}$ compared to the first and third strategies respectively. The path based on the third strategy of multi-commodity network flow ILP is very similar to the second strategy, but the number of planned paths for the two is obviously different. Although the planning of the third strategy has increased by ${8.9}\%$ compared to the second strategy, other indicators are not as good as the second strategy.

To explore the planning effects and practicality of the proposed algorithm as the number of flying cars increases, one more flying car is added and simulations are conducted on a city environment map with a total of 298 nodes. The planning results of the three strategies are shown in Fig. 20.

Three strategies equally excelled in completing the mission, with simulation results similar to those before. First strategy prioritized time, with two flying cars choosing low altitude flight for the entire journey to complete the task while the remaining two cars traveled on the ground. They operated independently and smoothly completed the outstanding mission in the urban environment. Due to considering energy consumption and time comprehensively, second strategy and third strategy both opted for ground travel. The four paths intertwined, with some vehicles needing to wait at the same intersection to ensure safety.

Figure 21 intuitively shows the comparison of specific indicators of the two planning strategies, and the detailed metrics of the two planning algorithms are shown in Table 7.

As the number of flying cars increases, Figs. 20 and 21, in conjunction with Table 7,reveal that although first strategy and second strategy have similar path distances and planning speeds, there is a significant difference in path-weighted cost. In comparison, second strategy is the ideal strategy, aligning more with the current principle of flying cars primarily traveling on the ground. Also, considering the current lack of complete safety in low altitude flight, fewer mode switches can ensure the safety of residents in urban environments. While second strategy and third strategy have similar path distances and weighted costs, the planning time for second strategy is several times that of third strategy. This would generally lead to a significant decrease in the efficiency of re-planning for flying cars under typical conditions, hindering the completion of diverse and complex tasks.

Comparing with first strategy, as shown in Table 7,the proposed strategy reduces the path distance by $3\mathrm{\;m}$, decreases the weighted cost by ${84}\%$, and improves the planning speed by around 9.7%. In comparison with third strategy, the proposed strategy shortens the path distance by ${0.3}\mathrm{\;m}$, lowers the weighted cost by ${7.1}\%$, and increases the planning speed by about 10 times.

Through the above simulations, it is found that the effectiveness of path planning depends on the weight setting of the objective function. Because a flying car is different from a traditional car or an unmanned aerial vehicle, the designed objective function must consider energy consumption, time and switching losses. The first four sets of simulations have preliminarily demonstrated that if the weight coefficients of the objective function can be carefully adjusted to better align with the motion characteristics of flying cars, then the improved priority planning algorithm can coordinate multiple vehicles to complete tasks smoothly with lower energy consumption. However, if the weight of each cost in the objective function is set to one third, it will be found that the effect of algorithm planning is poor. When the energy consumption weight is set to 0.6, the time weight is set to 0.3, and the switch loss weight is set to 0.1, the algorithm produces relatively ideal results. In addition, it is also found that the effectiveness of the planning algorithm is influenced by the total number of nodes in the simulation environment. From Tables 5 and 6, it is evident that as the total number of map nodes increases, the planning efficiency of the proposed second strategy does not consistently outperform that of the first strategy. Increasing the weight of energy consumption in the cost function is attempted in this research. However, as its weight increases, there is still no ideal path. Finally, as increasing the number of flying cars, it is found that the proposed strategy still outperforms the first and third strategies. The planning effect of the third strategy is similar to that of the second strategy. The difference, however, lies in the faster planning speed of the second strategy. This is due to the improved successor function, which, by balancing energy consumption and time cost, selects the lowest cost state as the alternative state in each iteration when choosing a sub-state based on the designed objective function. This significantly enhances planning efficiency.

In summary, this paper uses two evaluation indicators to measure the performance of the planning strategy, namely path distance and weighted cost. It is fully demonstrated that the proposed strategy can plan a short and energy efficient path. Additionally, the strategy planning is faster.

5 Conclusions

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In this research, a multi-flying car priority path planning strategy based on the improved SIPP algorithm is proposed in an urban environment. The key findings of this research include:

(1) A flying car with integrated wheel-channeling technology has been designed, comprising a fuselage and power system. The power system has been reconfigured to allow seamless transition between ground and aerial modes, therefore enhancing maneuverability in addition to reducing commuting time.

(2) In light of the aerodynamic characteristics of flying cars in future urban environments, a city environment model has been established to segment the energy consumption and time models of various stages of flying cars. For the first time, the A* algorithm in the time domain has been introduced into the realm of flying cars.

(3) By integrating a newly developed objective function into the function for obtaining child nodes, a prioritized planning algorithm for multiple flying car fleets based on safety intervals using an enhanced A* algorithm has been proposed.

(4) The results indicate that in the map with a total of 452 nodes, the path distance is ${4.5}\mathrm{\;m}$ shorter than the first strategy, and the path weighted cost is reduced by 85.8%. In addition, its planning speed is also improved by ${6.5}\%$ higher than the first strategy. In a test map full of apron, although the path lengths planned by the two strategies are both ${13.3}\mathrm{\;m}$, compared with the first strategy, the proposed strategy’s weighted cost is reduced by ${0.2}\%$, and the planning speed is increased by 0.7%. Compared with the strategy based on multi-commodity network flow ILP, they have similar planning effects. They all regulate the motion mode reasonably to reduce the path distance without increasing the number of mode switches. However, there are differences in the number of local path points planned. The weighted cost of using this strategy can be reduced by ${5.2}\%$, and the path distance can be reduced by ${0.34}\mathrm{\;m}$.

Flying cars have vertical take off and landing capabilities, enabling commercial applications of point-to-point fixed routes in urban environments. In future work, as the test platform gradually improves, the proposed strategy will also be correspondingly verified.

Funding This work is supported by National Natural Science Foundation of China (Grant No. 52275051),the Natural Science Ranking Projects of Chongqing Jiaotong University (Grant No. XJ2023000701),and Team Building Project for Graduate Tutors in Chongqing (Grant No. JDDSTD2022007).

Declarations

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Conflict of interest The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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doi: 10.1007/s42154-024-00312-0

Receive Date：2024-03-09
Online Date：2025-07-21

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Received：2024-03-09
Accepted：2024-06-13

Affiliations

¹ Chongqing Jiaotong University School of Aeronautics Chongqing 400074 People's Republic of China

² Chongqing Jiaotong University Chongqing Key Laboratory of Green Aviation Energy and Power Chongqing 400074 People's Republic of China

³ Chongqing Jiaotong University The Green Aerotechnics Research Institute Chongqing 400074 People's Republic of China

⁴ Chongqing Jiaotong University School of Mechatronics and Vehicle Engineering Chongqing 400074 People's Republic of China

Corresponding:

Tao Deng d82t722@cqjtu.edu.cn

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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Table 1 Meaning of formula letters

Parameter	Meaning
$m$	Vehicle mass (kg)
$\mu$	Rolling resistance coefficient
$g$	Gravity acceleration $\left({\mathrm{m}/{\mathrm{s}}^{2}}\right)$
${C}_{D}$	Air drag coefficient
${A}_{\alpha }$	Frontal area $\left({\mathrm{m}}^{2}\right)$
${A}_{u}$	Top area $\left({\mathrm{m}}^{2}\right)$
$r$	Wheel radius(m)
$\rho$	Air density
$d$	Movement distance (m)
$\eta$	Motor efficiency
$x$	Number of propellers

Table 2 Comparative results of two planning strategies

Strategy	Path length (m)	Weighted cost (J)	Planning speed (s)
First strategy	13.2	988.1	2.3
Second strategy	8.9	101.9	2.3

Table 3 Comparative results of two planning strategies

Strategy	Path length (m)	Weighted cost (J)	Planning speed (s)
First strategy	19.2	1850.4	12.2
Second strategy	14.7	263.1	11.4

Table 4 Comparative results of two planning strategies

Strategy	Path length (m)	Weighted cost (J)	Planning speed (s)
First strategy	15.8	3351.7	16.2
Second strategy	18.5	2405.2	16.7

Table 5 Comparative results of two planning strategies

Strategy	Path length (m)	Weighted cost (J)	Planning speed (s)
First strategy	13.3	3541.5	30.5
Second strategy	13.3	3535.2	30.2

Table 6 Comparative results of three planning strategies

Strategy	Path length (m)	Weighted cost (J)	Planning speed (s)
First strategy	10.5	541.9	5.5
Second strategy	9.5	119.5	5.6
Third strategy	9.84	126.0	5.1

Table 7 Comparative results of three planning strategies

Strategy	Path length(m)	Weighted cost(J)	Planning speed(s)
First strategy	15.4	945.1	8.2
Second strategy	12.4	150.4	7.4
Third strategy	12.7	162.0	79.0

Fig. 1 Imagined emergency rescue scenarios in future urban environments

Fig. 2 Animals that use the same appendage to produce different modes of movement. Scidraw, S.(2020). bird silhouette. Zenodo. https://doi.org/10.5281/zenodo.3926155

Fig. 3 Flying car system overview. a Shows ground mode. b Shows flight mode. c Shows the power plant. d Demonstrates the electronic architecture of the flying car, including communication, controllers, and power electronics components

Fig. 4 SIPP-based path plan-ning strategy for multi-flying car groups considering energy consumption and time

Fig. 5 SIPP algorithm case study illustration path planning

Fig. 6 SIPP algorithm extension case study graph

Fig. 7 Constructed 3D urban environment model

Fig. 8 Flying car vertical take off and landing flight profile

Fig. 9 Analysis diagram of successor state selection

Fig. 10 Result diagrams of two planning strategies

Fig. 11 Comparison of path lengths and weighted costs of the two strategies

Fig. 12 Result diagrams of two planning strategies

Fig. 13 Comparison of path lengths and weighted costs of the two strategies

Fig. 14 Result diagrams of two planning strategies

Fig. 15 Comparison of path length and weighted cost of the two strategies

Fig. 16 Result diagrams of two planning strategies

Fig. 17 Comparison of path length and weighted cost of the two strategies

Fig. 18 Result diagrams of three planning strategies

Fig. 19 Comparison of path length and weighted cost of the three strategies

Fig. 20 Result diagrams of three planning strategies

Fig. 21 Comparison of path length and weighted cost of the three strategies

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