Path planning for EVs based on RA-RRT* model

Abstract

The optimal path planning for EVs (electric vehicles) has gained great attention during the last decade due to the zero pollution emission characteristics and limited power capacity of EV batteries. In this paper, an optimal route search is proposed considering multiple charging stations in a dynamic urban environment, while it is still applicable when the initial available amount of the battery fails to cover a certain travel range. The TRDP (transit route design problem) and TNDP (transit node design problem) are used to search for the most feasible routes based on time and driving range via the improved route-assisted rapid random tree (RA-RRT*) algorithm. Considering the status of charge of an EV’s battery during optimal routes search, three states are investigated between the destination and the aggregators: (1) bypassing the aggregators, (2) stopping over a single aggregator, and (3) stopping over multiple aggregators. During the states (2) and (3), it is required that the EVs be charged at the charging stations obtained by the RA-RRT* algorithm while approaching the destination. The proposed algorithm is tested on a random dataset under certain conditions, that is, traffic flow with congestion and assigned target locations from a given map data, with comparison experiments for efficacy verification.

1 Introduction

Electric vehicles (EVs) have paved the way for green and intelligent transportation systems over the last few decades. EVs are gradually taking the place of fuel-powered vehicles due to their minimum mileage cost and environment-friendly characteristics of no carbon emissions. The main obstacle to EV’s promotion is the limited battery capacity through which EVs cannot cover long distances (Zhou et al., 2020).

In recent years, EV-related energy-harvesting schemes have received a lot of attention to increase the driving range with smart route search algorithms. The related factors, that is, battery capacity, charging duration, and charging station placement, should be explicitly considered during the route planning of the EVs (El-Taweel and Farag, 2019). A reinforcement learning (RL) model is developed for EV energy management by optimal route planning (Zhang et al., 2020a), where the RL model is used to evaluate each route and approximate the energy consumption. A transit route network-based path planning model, TRDP (transit route design problem), has been introduced to reduce the time consumption with the shortest optimal route (Yang and Jiang, 2020).

To reduce the complexity of the TRDP model, an optimization model, TNDP (transit node design problem), has been developed considering time and the xy-dimension to obtain the optimal path location (Sun et al., 2020). A significant gap is discussed between the theory and practice of the TNDP model by addressing multiple routes, nodes, and the selection of the route and node (Durán-Micco and Vansteenwegen, 2021). A multi-level network system based on different modes of transportation, that is, subway, trolleybus, and common bus, and the user constraints such as bus routes and city size has been proposed to design the transit route network in urban areas (Chavhan et al., 2021), which is applied to the Mandle dataset to reduce the travel time cost. In a study by Hellsten et al. (2021), a heuristic route network is discussed based on multi-commodity network scenarios, that is, exponentially increasing route formulation, polynomial-based path indices, and time indices. An ant colony algorithm is introduced to further reduce the complexities involved in the optimal route search task (Ghaffari et al., 2022), while a genetic algorithm (GA) can also be implied for the optimization of large-scale routes via the network data obtained from multiple cities (Bourbonnais et al., 2021). In (Miandoabchi et al., 2012), a synchronous city road network with vehicle routes has been studied via a hybrid GA and clonal selection scheme. A cloud-enabled real-time routing scheme for MoD (mobility on demand) requiring on-route charging has been developed, aiming to improve the comfort of EV users (Ammous et al., 2018). The MoD suggests that with charging delays, the total trip time for all clients will be increased in comparison to the corresponding travel lengths.

A significant amount of research has been carried out to improve the efficacy of the route search algorithms by using the traffic information from ITS (intelligent transportation systems) in terms of minimal distance and travel time cost (Tisa, 2022). The navigation systems of EVs can be updated with new technologies when the charging infrastructure is considered during route planning (Morlock et al., 2019).

An optimal route selection for EVs toward charging stations considering the traffic congestion is obtained by using Yen’s algorithm with the information of transportation and distribution systems (Zhang et al., 2019). The A* algorithm is used to obtain the K-short path in order to get the K-shortest-path-joint-routing-scheduling (KSP-JRS), which can minimize the power consumption by shortest route selection while increasing the revenue via the discharge battery to the grid (Liu et al., 2020). A polynomial-time variant-based algorithm has been derived to obtain the optimal path between two target locations (Baum et al., 2020). In order to plan a simultaneous search for both velocity and path while avoiding obstacles, the A* algorithm has been implemented in multiple dimensions, including position, velocity, and heading angle (Morsali et al., 2020). A modified and efficient random with star tree network (RRT*) model for online informative path planning (Schmid et al., 2020) has been developed to use the single search tree expansion with a continuous pattern to obtain a refined path. In a study by Qi et al. (2020), a multi-objective dynamic rapidly exploring random tree (MOD-RRT*) algorithm has been developed that can navigate the path in an unknown dynamic environment to choose an optimal node while considering the length and smoothness of the path over a short period of time. By merging the urban electrified transportation network with the power grid, an intelligent path planning method has been developed for each EV to participate in the traffic network. It can ensure the timeliness of path planning by updating the connection weights in real-time while using the Floyd algorithm to search for the shortest path in a directed weight graph (Zhou et al., 2022). An optimal route can be achieved for public buses via the Greedy and Dijkstra algorithms by labeling the available passenger pick-up and drop-off station data with unique identities (Wei et al., 2020). To achieve an optimal and free route, an extended framework of the RRT has been introduced by utilizing the way-points of a straight line while producing a collision-free path (Hu et al., 2020). Considering the EVs’ charging demand and distribution network penetration, a spatial and temporal distribution prediction model has been developed with reliability assessment (Zhang et al., 2020b).

The remainder of the paper is organized as follows: Section 2 describes the system model and problem formulation. The RA-RRT* algorithm design and implementation in a dynamic environment are discussed in Section 3. Experiments and results are analyzed in Section 4. The conclusion is provided in Section 5.

2 Problem formulation

Here, multiple routes can be selected for large-scale vehicles with different types of aggregators and battery replacement centers, as depicted in Figure 1. The aggregators are divided into two categories: fast charging (FC) and slow charging (SC). The route is named EV assist route (EV-AR), which allows the users to charge or replace the battery before reaching the low limit SOC_min (minimum state of charge) so as to complete the current travel demand.

FIGURE 1

In Figure 1, the road network is directed by graph point (destination) , and represents the charging stations and represents the set of routes. A route R is defined as a path of EVs to and . The involved variables are listed in Table 1. The charging stations, departure points, and destination points are used to formulate the optimal route for path planning. Hence, the demand matrix can be extracted from the given set of the charging stations and the travel time cost matrix is formulated through route search T = {t_ij | (i, j) ∈ R_N}. TRDP requires searching the paths through the objective function of route R_N over graph G. Selection of D is dependent on several factors, that is, availability of the regulators and specific charging hours.

The efficiency of the EV-AR design has to be evaluated, and certain assumptions are made to evaluate the solution of TRDP. In order to minimize the travel distance cost, the aggregators are placed at the maximum traffic flow positions. The availability of more electric piles is considered at each charging station to avoid congestion at one charging station.

3 The RA-RRT* model for path planning

In this paper, an optimal path is designed where the EVs can easily reach the charging station, battery replacement center, and destination with minimal route selection and maximum mileage.

Let a space X be configured, where the traffic congestion is defined as X_obs, the free region is X_free = X/X_obs and the goal G is the destination. A feasible route x(t)ϵX_free can be found via the RRT* in the T interval, starting from r [0, T]ϵR, which begins from X (0) = E_start to X(T) = E_End, consistent with the given constraints of the system. During the search for the feasible routes, RRT* conserves a tree network τ = (E_i, G) of the vertices (starting points) E_i from the space X_free, while G represents the destination. The RRT* algorithm can be performed as follows:

Sampling: It is a random process where a route r_rand = X_free is taken from the traffic congestion-free space.

Distance: It provides the route cost between target points without traffic congestion. The cost can be calculated in the form of Euclidean distance.

Nearest neighbor: Function Nearest (τ, r_rand) is used to obtain the maximum nearby nodes between τ = (E_i, G) to r_rand with respect to the distance cost.

Collision check: The collision check is obtained by Obstacle_free(x) while examining the route x [0, T] if it is lies in range of the free space X_free during the [0, T] interval.

Nearby vertices: Function Near(τ, r_rand, n) provides the adjacent nodes in the space α(logn/n) around r_rand where α is a constant dependent on the route plan, while n is the iteration number.

ExtractNode: In order to obtain a new node, the state function ExtractNode (r_initial, r_new, τ) adds a route r_new to the tree τ = (E_i, G) and connects it to the previously existing node r_initial.

Reroute: The state function Reroute (R_near, r_min, r_new) examines the routes to check whether the r_new is less than the older route cost. If the state r_new > r_previouse, the new route is replaced by the old one due to the minimum distance cost.

The steps involved in the RA-RRT* are defined in Algorithm 1. Steps 1 to 4 and 7 to 13 are the same as those in RRT* algorithm, while the RA-RRT* algorithm is modified by the incursion of Steps 5 to 6 and 14 to 19. In the proposed RA-RRT* algorithm, the initial found route (e.g., in Step 14) returns the iteration number n which is further used for biased sampling so as to insert the time interval b (Step 4), to repeat the tree search growth during that period. The optimized route is obtained via the function (τ, routecost) ← RouteOptimization (τ, r_init, r_goal) by connecting the feasible nodes from the initial route r_init to the destination r_goal and returns the cost in Step 16. A connected topology network is depicted in Figure 2 with random route costs among different nodes. The route topology network in Figure 2A describes the distance in km between different charging stations, while the possible routes are extracted in Figure 2B. In Step 18, is the optimized routes’ selection to the charging stations obtained from the function , where a new route can be chosen over an old route with the cost condition as .

As shown in Figure 1, multiple routes toward G are taken, named EV-AR. The assist routes point the EVs toward G and different charging stations (CS_i), which play a vital role in EV energy management. While approaching G, the first task is to select the potential CS_i with the help of EV-AR along with optimal route selection.

In order to obtain the EV-AR, it is required to search for the most cost-effective routes in terms of less power consumption, less distance, and maximum mileage considering traffic congestion and road infrastructure. The range R_A of the EVs can be calculated using the current battery level (SOC_R) and EVs’ mileage (E_M) as follows,

The full range R_FC can be obtained with the fully charged battery level SOC_max and E_M,

As described earlier, the selection of the charging stations for EVs is based on their locations and types of charging. With FC aggregator, the charging time duration is only 30 min to be fully charged (Duan et al., 2020), but it requires an isolated infrastructure of power supply, which is not economically feasible.

FIGURE 2

Bypassing the aggregators: If the EVs have enough power to reach the destination, the conventional route calculation, that is, Dijkstra (Algorithm 2), is considered to be efficient. Hence, the EVs’ remaining battery level at the arrival point (SOC_RA) is obtained with the SOC_R at departure E_i, route distance D (Start, End), and E_M,

During the bypassing, the status SOC_RA > 0 is always satisfied.

Stopping over single aggregator: When the EVs cannot reach their destinations with the SOC_R, the users have to charge the battery on their routes. In Figure 1, the EVs’ R_A level is denoted by the two small circles with two departure points E₁ and E₂, while the R_FC is represented by a large circle with the center of the destination G.

The overlapped areas show that the EVs have to be recharged if R_FC > R_A. Therefore, it is necessary to search for the optimal route toward the CS_i while covering the distance D to G. The overlapped area around the EVs is distributed irregularly; hence, Euclidean distance is used to calculate D to the nearest aggregator.

The charging time cost C_T from the initial point to the target while reaching a single aggregator can be calculated as,

By setting E₁ as the charging point CS_h(1, 2, 3, … ), Eq. 4 can be rewritten as,where h is the charging time. Similarly, the total travel time cost from the starting point to the endpoint while stopping by a single aggregator can be obtained as,

EV_T (E_i, G) and EVs battery SOC_RA are used as the EV-AR, and then the EVs’ total routes EV_R can be calculated as follows,where δSC₁ is the charging station, while R is the route between two adjacent nodes presented in Figure 2A. Similarly, EVs’ total travel distance EV_D is calculated as,

It can further be modified with N number of search targets,and SOC_RA of EVs at the destination is calculated as,

Stopping over multiple aggregators: The EVs have to be charged at more than one aggregator when traveling a long distance. The charging time cost with multiple aggregators is calculated as,

Then, the route can be obtained as,

whereas the optimal route equation can be modified as the successive product of routes set from the departure point to the destination,and the overall distance from the starting point to the destination is calculated as,

To sum up, the total time taken by the EVs from the starting point to the destination is expressed as,

Similarly, the remaining battery level at the destination can be obtained from the statistics of SOC_max and overall covered distance,

Assistive route analysis: The developed RA-RRT* model is implied on a given set of data collected from the Public Transport Bureau of Shenzhen, Guandong Province, China, including the longitudinal angles, latitudinal angles, and the public transport terminal locations. The retrieved routes by RA-RRT* can be reduced in length with the dynamic constraints on its trajectory. The entire framework is depicted in Figure 3, which is implemented as follows:

FIGURE 3

A suitable aggregator is selected considering the route and battery status details, that is, R_A, R_FC. In order to obtain the smooth route, an efficient route formulation strategy is jointly used with the obtained route details (Eqs 1-16). The routes are plotted based on the provided details of the route transfer mechanism among different traffic terminals using python gmplot function. Furthermore, the latitudinal and longitudinal angular data are converted into distance by using the Haversine Formula in Algorithm 3 as follows,where d_lat is the error between the two consecutive latitudinal angles lat_i, while d_lon is the error between the two consecutive longitudinal angles lon_i and np is the python numpy library which is a source for multiple functions, that is, N-dimensional array. c and d are constant variables, while r is the radius of the Earth, equal to 6,371 km.

4 Experiment and result analysis

In this section, experiments are performed to verify the efficacy of the proposed RA-RRT* model for EV optimal path planning. The experiments are conducted on a Windows operating system with an Intel Core i7 with a RAM of 16 GHz and 8 GHz processor. Simulation experiments are carried out by using the software tool Python (Jupyter notebook and PyCharm environment). GMPLOT, a Google map plot function built into the Python library, is used to obtain the locations on the map with latitudinal and longitudinal angles retrieved from different target locations. In Figure 4A, the target locations are identified using a heat map function, while the routes between the target locations are plotted in Figure 4B. The route distances between different public transport terminals can be calculated via the heuristic (Dijkstra) algorithm.

FIGURE 4

Two scenarios have been considered to validate the RA-RRT* model. During the 1^st scenario, the RA-RRT* model is used for the optimal route selection between the target locations, that is, start point, endpoint, and charging station CS_i, while the algorithm is implemented for traffic congestion avoidance in the 2^nd scenario.

4.1 Optimal route selection

The developed RA-RRT* algorithm is used on the target locations obtained by the Haversine formula (Mahariba et al., 2022) in Figure 4, from a given set of data. The average mileage per kilowatt-hour (kWh) is taken as 6 km, while the full battery capacity is taken as 24 kWh.

The known initial SoC_ini of the EV is used to calculate R_A and R_FC. The target locations are presented with the start points (highlighted in Figure 5) and final point in an undirected and non-convex environment in Figure 5. Based on the given target locations, the distance, point of aggregators, and route search time are calculated and listed in Table 2.

FIGURE 5

In Figure 5A, the starting point and the end point are taken at axis (10,10) and (90,90), respectively. The charging stations are denoted as circles in the free search area. Figure 5B shows the results of the optimal routes between two points via the proposed RA-RRT* algorithm. While approaching the target location with the shortest route, it has considered passing across the route if it has enough aggregators. The obtained route is highlighted with a yellow color, which is smooth between the start point, charging station allocation, and destination. In order to avoid the charging shortage, an early warning model about insufficient battery levels can be developed by using the appropriate energy consumption factor (Wang et al., 2021).

4.2 Bypassing the traffic congestion

The proposed RA-RRT* algorithm is further elucidated in a 2D environment considering the traffic congestion to be formed as blocks X_obs with the indirect connection between the starting point and the destination, shown in Figure 6A.

FIGURE 6

In Figure 6A, the departure point is taken at (10,10) with map location at north-south, while the destination point is taken at (90,90), the east-west positions, respectively. It is a non-smooth path search in the free space X_free = X/X_obs; hence, the RA-RRT* model is further compared with the RRT* by increasing the number of search samplings in the free space to find an initial route immediately. The RA-RRT*-based graph is achieved in Figure 6B, illustrating the improved results in terms of route smoothness and length.

4.3 The comparison among path planning algorithms

The performance of the proposed RA-RRT* is compared with both A* and Dijkstra algorithm in Figure 7. The obtained results in Table 3 can demonstrate that the RA-RRT* is faster compared to both A* and Dijkstra algorithms in the search for the target location. In order to retrieve the optimal route toward the target location, RA-RRT* compiled 16 iterations, while A* and Dijkstra took 55 and 67 compilation iterations, respectively. The algorithms are evaluated in Table 3 based on their iteration time costs. During charging station searching and following the optimal path towards the destination, the wide-spreading search property of the RA-RRT* algorithm makes it more suitable for multiple targets searching simultaneously.

FIGURE 7

Furthermore, a deep reinforcement learning algorithm, the Proximal Policy Optimization algorithm (PPO), is used for path planning comparison with the RA-RRT* model in an obstacle environment. The PPO algorithm (Sadhukhan and Rastko, 2022) performs on an iteration basis to search for the target location with more time consumption for the target location, while RA-RRT* can explore in all directions due to its tree search property with less time consumption. The PPO algorithm is carried out in a Jupyter notebook on a Windows operating system with an Intel Core i7 with a RAM of 16 GHz and 8 GHz processor.

In Table 4, a metric evaluation of the RA-RRT* algorithm with the A*, RRT*, and Dijkstra algorithms regarding speed and accuracy is shown. It is found that the A* algorithm is more efficient in a directional and known environment, whereas the Dijkstra and RRT* algorithms are more feasible in an undirected environment (Erokhin et al., 2018). Based on the experimental results, the proposed RA-RRT* is proven to be more efficient due to the requirement to simultaneously search for the charging stations and the minimum optimal path in an undirected environment because of the tree structure.

5 Conclusion

In this paper, a route search-based problem has been carried out with the proposed RA-RRT* algorithm via an assistive route heuristic model, achieving fast route search capability for multiple targets in a wide range area. Different scenarios are considered with stops at a single aggregator, multiple aggregators, or for battery replacement. A comparative analysis of the proposed model is taken with the A*, Dijkstra, and PPO algorithms, where the proposed RA-RRT* model is more feasible for multi-target fast route search results in an undirected environment. Further research will apply the proposed RA-RRT* algorithm for real-time path planning in autonomous urban driving scenarios.

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