Research on Unmanned Vehicle Path Planning Based on the Fusion of an Improved Rapidly Exploring Random Tree Algorithm and an Improved Dynamic Window Approach Algorithm

Abstract

Aiming at the problem that the traditional rapidly exploring random tree (RRT) algorithm only considers the global path of unmanned vehicles in a static environment, which has the limitation of not being able to avoid unknown dynamic obstacles in real time, and that the traditional dynamic window approach (DWA) algorithm is prone to fall into a local optimum during local path planning, this paper proposes a path planning method for unmanned vehicles that integrates improved RRT and DWA algorithms. The RRT algorithm is improved by introducing strategies such as target-biased random sampling, adaptive step size, and adaptive radius node screening, which enhance the efficiency and safety of path planning. The global path key points generated by the improved RRT algorithm are used as the subtarget points of the DWA algorithm, and the DWA algorithm is optimized through the design of an adaptive evaluation function weighting method based on real-time obstacle distances to achieve more reasonable local path planning. Through simulation experiments, the fusion algorithm shows promising results in a variety of typical static and dynamic mixed driving scenarios, can effectively plan a path that meets the driving requirements of an unmanned vehicle, avoids unknown dynamic obstacles, and shows higher path optimization efficiency and driving stability in complex environments, which provides strong support for an unmanned vehicle’s path planning in complex environments.

1. Introduction

With the rapid development of driverless technology, the path planning of unmanned vehicles has become one of the critical issues in realizing their autonomous driving capability. Path planning, as one of the critical technologies for unmanned vehicles, directly affects the driving safety, efficiency, and adaptability of the vehicles. Based on environmental information, planning can be divided into global planning [1] and local planning [2]. Global planning considers the information of the complete environment and generates a series of trackable target points, whereas local planning requires only the information of the local environment that is in close proximity to the vehicle. Global planning is usually performed on large-scale maps and is able to search for globally optimal paths. Local planning can react quickly to changes in the surrounding environment, e.g., dynamic obstacles, but can easily fall into a local optimum. Therefore, combining the two planning methods has the potential to balance computational complexity and optimality [3].

For global path planning, there are sampling-based algorithms [4], heuristic search algorithms [5], and evolutionary optimization algorithms [6], among which RRT (rapidly exploring random tree) is a typical sampling-based algorithm [7] that has attracted the attention of researchers in recent years. The rapidly exploring random tree [8] (RRT) has been proven to be a very effective global path planning algorithm in static environments due to its fast sampling rate and ability to handle high-dimensional spaces without requiring a priori environmental modeling. However, the RRT algorithm has some limitations, including not being asymptotically optimal [9,10] and being unable to avoid dynamic obstacles, which restricts its applicability in dynamic environments. Therefore, improved variants of the RRT algorithm have been proposed. Since the global paths planned directly using the basic RRT algorithm do not meet vehicle kinematics constraints, its improvement to meet the needs of vehicles in actual driving is an important research direction at present. D. Živojević [11] and others used Dubins curves instead of line segments in the traditional RRT algorithm to generate global paths and controlled the curvature of the Dubins curve to make the algorithm plan the global paths. By controlling the curvature of the Dubins curve, the path planned by the algorithm conforms to the vehicle’s own kinematic constraints. However, the path planned by this algorithm has many poor practicalities, and the length of the path increases significantly. W. Xinggang [12] and others proposed a two-way RRT algorithm with variable probability, which adds the restriction of the turning angle in the process of generating random points and meets the time and accuracy requirements of the path planning by rasterizing the environment space and introducing the coverage rate. However, this method needs to model the space and consumes vast storage space for complex environments. Han Xiaojian [13] and others proposed the RS-RRT algorithm, which combines local bias and Gaussian distribution sampling to improve the efficiency of path planning and utilizes the law of separated axes to detect collisions between the vehicle and surrounding obstacles in the process of random tree expansion. However, this algorithm performs poorly when the environmental space is complex, and the time consumed for pathfinding is long. Taketoshi Suzuki [14] et al. use quadratic B-spline curves to generate collision-free two-lane paths for unmanned mining vehicles that satisfy the minimum turning radius constraints and use the same third-order derivatives at the turning nodes of the paths to ensure that the curvature of the paths varies continuously. The method is computationally intensive in complex environments, and the time consumed by the algorithm is immeasurable as the number of path nodes increases.

While global planning ensures that vehicles are able to follow optimal routes based on known maps and static obstacles, local planning must deal with real-time dynamic changes in the environment, such as sudden pedestrians, bicyclists, small dogs that appear out of nowhere, or vehicles that move irregularly. These dynamic obstacles usually do not strictly follow traffic rules, thus requiring an advanced and flexible path planning method. Since it is difficult to predict the moving paths of obstacles, local path planning in dynamic environments is a hot topic in current research. For local path planning, the DWA [15], artificial potential field [16], and fuzzy path planner [17] methods are widely used. The artificial potential field method plans paths with fast convergence and smooth paths. However, when facing complex dynamic environments, there are situations where the combined force is zero, and the smart car will stop moving in the middle of the movement process. The DWA algorithm, which is one of the most popular algorithms, was proposed by Fox et al. in 1997 [18] and is still frequently used. The dynamic window approach combines the sampled multiple sets of velocities with the motion constraints of velocity and acceleration and then evaluates the simulated multiple sets of trajectories with an evaluation function and selects the optimal velocity corresponding to the trajectory as the vehicle’s drive. Compared with the artificial potential field method, this method is characterized by fast planning speed, safety and reliability, and good real-time performance [19,20,21]. However, the path screened by the DWA algorithm using a function with fixed weights cannot be adapted to a complex dynamic environment. Later, Zhong [22] et al. proposed an adaptive rolling window method based on obstacle edges and target points with reasonable safety and environmental applicability. Chang et al. [23] combined Q-learning with the DWA algorithm and proposed two new evaluation functions. This demonstrated a high navigation efficiency and success rate in complex unknown environments but also brought a high time cost. Wu et al. [24] combined the A* algorithm with the DWA algorithm to produce an algorithm that is closer to the global optimal path but is less smooth. Zhang et al. [25] proposed a fusion method based on RT* and DWA. After generating the global path using RRT*, the DWA algorithm with deviation function is introduced to track the global path so as to obtain the optimal path and realize dynamic obstacle avoidance. However, the planned paths are poorly adapted to the environment. Jian et al. [26] switched the use of RRT* and DWA to adapt to different obstacle environments, realizing the balance between real-time computation and a global optimal solution. However, the path is tortuous, and security is not guaranteed.

In summary, existing vehicle path planning algorithms have their advantages and shortcomings in practical applications, which usually need to be weighed in terms of algorithm performance, vehicle kinematics constraints, and path safety. Researchers want to solve the problems that traditional path planning methods often have high computational complexity, cannot avoid unknown dynamic obstacles, and quickly fall into local optimization. While traffic rules provide the infrastructure for road navigation, real-world scenarios often involve unpredictable factors such as pedestrians, animals, or other vehicles that do not follow these rules. In this paper, we propose a fused path planning algorithm based on improved RRT and DWA. The method achieves safe and efficient navigation by dynamically adapting to unpredictable obstacles, thus extending the application of traditional traffic-rule-based navigation systems to more complex and irregular environments.

This paper is organized as follows. Section 2 describes the RRT algorithm, goes through the constraints of the vehicle, and proposes an improvement strategy for the shortcomings of the RRT algorithm. Section 3 makes corresponding improvements to the limitations of the DWA algorithm in local path planning and solves the defect that the DWA algorithm easily falls into the local optimum. Section 4 verifies the feasibility of the improved fusion algorithm in this paper through simulation. Section 5 summarizes the whole paper and gives an outlook on the future research direction of this paper.

2. Global Path Planning Based on Improved RRT Algorithm

Global path planning allows an unmanned car to smoothly plan a path from the starting point to the destination. In the global planning process, firstly, the car is required to reach the target point accurately without colliding with the obstacles in the environment. Secondly, it is required to choose a path that can reach the destination as soon as possible.

2.1. Traditional RRT Algorithm

LaValle first suggested the rapidly exploited random tree (RRT) algorithm in 1998 as a way to search for pathways. It is based on state space search sampling, which is employed in complex environmental settings to solve the path planning problem and meet certain limitations. The RRT approach can avoid modeling in space, is appropriate for non-completeness requirements, and cannot be geometrically partitioned into the state space. It is also helpful for multi-complex space condition systems. It is currently widely used in the disciplines of intelligent driving, automated driving, and other areas, with positive outcomes following scholarly research and improvement [27].

Principle of RRT Algorithm

The RRT algorithm’s fundamental arithmetic logic is depicted in Figure 1. With $X_{start}$ acting as the root node, the search tree spreads out and investigates an uncharted area that is full of barriers. To create a new node $X_{new}$ in the tree, the sampling function takes a point on the line between $X_{near}$ and $X_{rand}$ with a step of λ. It then finds the closest node $X_{near}$ in the tree by sampling uniformly and randomly throughout the exploration space to produce a sample point $X_{rand}$. This procedure is carried out repeatedly until the new node of the search tree finds a workable connection between $X_{start}$ and $X_{goal}$ or until the new node is close to the target point $X_{goal}$.

The figure above illustrates how the fundamental RRT algorithm uses random sampling in the state space to swiftly find a collision-free path from the beginning point to the target point. Its benefits include high adaptability, which allows it to quickly explore high-dimensional space; environment independence, which eliminates the need to model the environment; high efficiency, which can meet the demands of real-time path planning; and high success rate, which almost always finds a collision-free path as long as the target point exists and the number of iterations is large enough. Because of these characteristics, the RRT algorithm is widely applied in the field of automated driving, among other areas, with positive outcomes.

The RRT algorithm has several apparent drawbacks despite its many benefits for path planning. The generated paths might not follow the vehicle’s kinematic constraints, and there are issues like abrupt curvature changes and discontinuities; blind path selection, which typically selects a path that is not optimal; a large computational volume; ease of traversing the invalid region, which lowers efficiency; highly randomized, weak goals; and non-smooth paths. In a complex environment, a fixed growth step performs poorly and has the potential to oscillate or collide as it approaches the destination. These issues restrict the RRT algorithm’s use in specific situations. To optimize and enhance performance, this study integrates the benefits and drawbacks of the RRT algorithm with the actual driving needs of unmanned vehicles, hence proposing multiple strategies for improvement.

2.2. Constraints

Various constraints are an essential part of the development of path planning algorithms for driverless vehicles, and the designer should fully consider the impact of the constraints on the driverless vehicle in the actual scenario. The main constraints are actual environment constraints, obstacle shape constraints, wheel corner constraints, and path curvature continuity constraints. The following analyses and studies are carried out for each of these four constraints.

The path planned by the RRT algorithm is applied to the movement of the driverless vehicle, which is guaranteed to be in the set scenario, conforms to the road environment constraints, and satisfies that all the coordinate points in the random tree are in $T(i)$:

$$\left\{\begin{array}{l}{X}_{\min }\le T{(i)}_x\le X_{\max }\\ Y_{\min }\le T{(i)}_{\mathrm{y}}\le Y_{\max }\end{array}\right.$$

(1)

During the process of planning a path, there must be obstacles in the scene, so it is required that neither the node nor the path be inside an obstacle. To simplify the problem of performing collision detection due to the mostly irregular shape of obstacles, the obstacle description is regularized.

Figure 2 shows the outer circle in the irregular obstacle envelope, the obstacle circle. Defaulting to not being inside the obstacle circle is sufficient. (1) The random node of the random tree is not inside the obstacle circle. (2) The line connecting the parent node and the child node is not inside the obstacle circle. Random tree node $({\mathrm{X}}_{\mathrm{i}},{\mathrm{Y}}_{\mathrm{i}})\in \mathrm{T}$, parent node $({\mathrm{X}}_{\mathrm{i}\mathrm{p}},{\mathrm{Y}}_{\mathrm{i}\mathrm{p}})\in \mathrm{T}$. Let obstacle circles${ (x-x_0)}^2+{(y-y_0)}^2=r^2$ and $({\mathrm{x}}_0,{\mathrm{y}}_0)$ be the center of the obstacle circle and r be the radius. Adopt the line segment equipartition method, along with obstacle circle detection, by judging whether the equipartition point is within the obstacle circle as a criterion. As long as there is a node in the circle that is not satisfied by the rule for resampling, the obstacle constraints are represented by the following equation:

$$\left\{\begin{array}{l}{({\mathrm{x}}_j-{\mathrm{x}}_0)}^2+{({\mathrm{y}}_j-{\mathrm{y}}_0)}^2>r^2\\ \left[\begin{array}{l}{\mathrm{x}}_j\\ {\mathrm{y}}_j\end{array}\right]=\frac{j}{5}\ast \left[\begin{array}{l}{\mathrm{x}}_i\\ {\mathrm{y}}_i\end{array}\right]+(1-\frac{j}{5})\ast \left[\begin{array}{l}{\mathrm{x}}_{ip}\\ {\mathrm{y}}_{ip}\end{array}\right]\end{array}\right.$$

(2)

where $({\mathrm{x}}_{\mathrm{j}},{\mathrm{y}}_{\mathrm{j}}),\mathrm{j}=\mathrm{0,1},2,...,10$, is the equidistant point of the line between node $({\mathrm{X}}_{\mathrm{i}},{\mathrm{Y}}_{\mathrm{i}})\in \mathrm{T}$ and the parent node.

As the vehicle is restricted by the mechanical structure, the wheels can only rotate within the design range; in the traditional RRT algorithm, to plan the path there is a path clamp angle that is too large beyond the vehicle limitations of the corner, resulting in the vehicle can not track the planned path, does not meet the vehicle kinematics requirements. Therefore, the algorithm in this paper considers the kinematic constraints of the vehicle during path planning, and the vehicle kinematic model is shown in Figure 3.

The center of the rear axle of the vehicle is taken as the reference point of the vehicle, $b$ is the wheelbase of the vehicle, $\phi$ is the turning angle of the front wheels, $\theta$ is the heading angle, $r$ is the turning radius, and $k$ is the path curvature. Assuming that the velocity of the vehicle is $v$, then the kinematic equations of the vehicle can be obtained according to Figure 3 as in Equation (3):

$$\left[\begin{array}{c}\dot{x}\\ \dot{y}\\ \dot{\theta }\end{array}\right]=\left[\begin{array}{c}\cos \theta \\ \sin \theta \\ k\end{array}\right]v$$

(3)

The kinematic constraints imposed on the vehicle need to satisfy the following equation:

$$\left\{\begin{array}{l}\phi \le \left|{\phi }_{\max }\right|\\ k\le k_{\max }=\frac{\tan {\phi }_{\max }}{b}\end{array}\right.$$

(4)

To ensure the stability of driverless vehicles that are tracking the planned path of travel, the steering wheel corner does not produce sudden changes, and the path curvature must remain continuous. The curvature constraints are satisfied. The construction of the random tree is carried out under the non-complete constraint of the front wheel turning angle introduced in the search process of the algorithm. As shown in Figure 4, the node A-B line and the node B-C line have an angle $\mathsf{\alpha }$ and a general model wheel-turning angle between 30° and 40°; according to the above derivation, it can be known that the vehicle is subject to the kinematic constraints that need to meet the following Equation (5):

$$\alpha <{\phi }_{\max }$$

(5)

When the random tree produces a new node $X_{new}$, calculate the angle between the line connecting $X_{new}$ and its parent node $X_{new\_p}$ on the coordinate system as $a_n$ and the angle between the line connecting $X_{new\_p}$ and its parent node $X_{new\_gp}$ on the coordinate system as $a_{n\_p}$; then, determine whether the kinematic constraints are met by determining whether the difference in the angle between $a_n$ and $a_{n\_p}$ is within the allowable turning angle.

Simulation experiments show that, as shown in Figure 5a, in the improved RRT algorithm, without adding wheel corner constraints, the final path has extra folds, which does not satisfy the constraints for vehicle travel. Figure 5b shows that after adding the corner constraints in the set range of wheel corners, the path is smoother, indicating that the path corner constraints have a certain role in path optimization.

To ensure that the path curvature is continuous, based on the above derivation, it can be seen that the kinematic constraints imposed on the vehicle need to satisfy the following Equation (6):

$$k\le k_{\max }=\frac{\tan {\phi }_{\max }}{b}$$

(6)

The maximum path curvature constraint is

$$\arctan (\frac{k_1-k_2}{1-k_1{k}_2})<\frac{\tan {\phi }_{\max }}{b}$$

(7)

where $k_1=\frac{y_B-y_A}{x_B-x_A}$ is the slope of the A-B line and $k_2=\frac{y_C-y_B}{x_C-x_B}$ is the slope of the B-C line.

For the study of path planning algorithms for driverless vehicles, it is necessary to ensure that both the vehicle and the planned path meet the constraints.

2.3. Improved RRT Algorithm

2.3.1. Target Point Bias Sampling Strategy

In the RRT algorithm, to improve the search efficiency and optimize the search direction, C Urmson proposed the target bias [28]. Firstly, the target bias coefficient ${\rho }_0$ is selected, and the algorithm obtains the probability value $\rho$ at random sampling; if $\rho$ > ${\rho }_0$, then $X_{rand}$ is obtained according to the function obstaclefree (); conversely, $X_{rand}$ = $X_{goal}$, and $X_{rand}$ satisfies Equation (8).

$$X_{\mathrm{r}and}=\left\{\begin{array}{l}obstraclefree(),\\ X_{\mathrm{goal}},\end{array}\right.\begin{array}{l}\rho >{\rho }_0\\ \rho \le {\rho }_0\end{array}$$

(8)

The random tree gets closer to the goal point faster as it becomes more prominent because the bias coefficient rises as it gets closer. In this study, we develop a linear bias coefficient method, where the bias coefficient increases as the random tree approaches the target. To make the bias coefficient vary linearly, the distance ratio is calculated and updated.

The target point bias coefficient is A; A takes the value range [0.3, 0.8] by calculating Equation (9) as the updated coefficient.

$${\rho }_{\mathrm{goal}}=0.3+\frac{1-\frac{\mathrm{dis}\tan ce({\mathrm{x}}_{nearst},x_{goal})}{\mathrm{dis}\tan ce({\mathrm{x}}_{star},x_{goal})}}{2}$$

(9)

2.3.2. Collision Detection

The primary concern is how to keep unmanned vehicles safe while they are moving, and collision avoidance should be taken into account by the enhanced RRT algorithm. Collision detection works based on the algorithm’s real-time path planning detection, which creates several randomly generated nodes in the state space and evaluates each node to determine whether or not it is within an obstacle. As illustrated in Figure 6, a node is discarded if it is inside an obstacle, and the path is likewise eliminated if a collision happens while the node is moving.

The elliptical vehicle safety model is developed, the unmanned vehicle uses the center as the mass point, and the driving trajectory of the elliptical vehicle safety model is the vehicle driving trajectory. After positioning the obstacle vehicle ahead of the vehicle, the RRT algorithm uses the DDA (numerical differentiation technique) algorithm to judge the obstacle and determine its color-judgment unit grid points.

Given the coordinates of the two endpoints $P_1({\mathrm{x}}_1,{\mathrm{y}}_1)$ and $P_2({\mathrm{x}}_2,{\mathrm{y}}_2)$ of a line, for this line, any increment $△x$ of $x$ and increment $△\mathrm{y}$ of $y$ on the line is as follows:

$$\frac{d_y}{d_x}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}=k$$

(10)

In the DDA algorithm, the first-order derivative of a straight line is continuous, and the coordinate position of the next point is determined by increasing the current point coordinate by a certain amount along the direction of the line. The principle comes from the incremental algorithm, where the increased $x,y$ value consists of the sum of the previous step value and the value added, as shown in Figure 7.

In the above figure, $\epsilon ·△x$ and $\epsilon ·△\mathrm{y}$ are increments in the $x$ and $y$ directions, respectively, and $\epsilon$ is an infinitesimal value. By letting one of $\epsilon ·△x$ and $\epsilon ·△\mathrm{y}$ be 1 in the devaluation and increasing by one unit point and then by judging the difference between integer values to detect an obstacle, if it is an obstacle, the $x,y$ value is made to be an integer.

$$\left\{\begin{array}{l}{x}_{i+1}=x_i+\epsilon ·△x\\ y_{i+1}=y_i+\epsilon ·△\mathrm{y}\end{array}\right.$$

(11)

2.3.3. Adaptive Step-Size Policy

Standard RRT algorithms’ set step sizes might be too big or too small, which can lead to long routes, sluggish convergence, and a lack of exploration potential in complicated situations. While the current adaptive step-size RRT algorithms help with exploration to some degree, they are less efficient and still require human step-size determination at first. This study offers an adaptive step-size formula to alter the step size in real time based on the gathered data, enabling fast passage across a complicated region. The equation is

$$step=s\times e^{k(\frac{N_1}{N})}$$

(12)

where s is the initial step size, k is the control coefficient, $N_1$ is the effective number of samples, and N is the total number of samples, and to be able to reflect the complexity of the current environment in real time, the forgetful counting scheme is used to recount every three samples.

2.3.4. Adaptive Radius Node Screening Strategy

The node rejection method proposed in the literature [29] discards new nodes that are too close to existing tree nodes by setting a distance threshold, dis. This method can reduce the repeated search to some extent, but as was stated, the distance threshold needs to be set by humans, which may affect the algorithm’s performance if it is not set correctly. In the original RRT algorithm, randomly generated new nodes may create the problem of repeated searches in already explored regions, which can lead to a reduction in the efficiency of the algorithm.

The improved method in this paper is the node-discarding method, further developed based on the node rejection method, as shown in Figure 8. Instead of setting the distance threshold artificially, this method uses the current step size λ as the judgment criterion. After a new node is generated, a circle is drawn with the node as the center and the current step size λ as the radius, and it is checked to find whether there is any other node within the circle. If there is, it means that the new node is located in or close to the explored region, so it is discarded; if not, it means that the new node is in the unexplored region, and it is added to the random tree. This improved RRT algorithm can improve the efficiency of path planning and exploration tasks, especially in complex environments, and can better balance the problems of exploration and repetitive search.

2.3.5. Termination Guidelines Strategy

The convergence condition of the basic RRT algorithm is that when the distance between the new node $X_{new}$ and the target point $X_{goal}$ is less than a set threshold, it is considered that the target point $X_{goal}$ is found, and the planning ends. However, there are three problems with this method: no obstacle detection is performed, which may invalidate the path; in the open area, even if there is an unobstructed node close to the target point, the tree still expands with a fixed step size, which reduces the efficiency; and different growth steps and convergence radii lead to an oscillatory search near the target point, increasing the time cost. So in this paper, the improvement method is to carry out obstacle detection after generating a new node $X_{new}$. If there is an obstacle, the tree continues to expand. If there is no obstacle, add $X_{goal}$ to the tree and complete the planning.

2.3.6. Greedy Strategy

The conventional RRT method creates paths that are complicated and contain a large number of superfluous nodes, which leads to high path costs and low quality. A node rejection method was presented by Y. Cui et al. [30] to enhance the path quality. Starting at node zero, the approach iteratively verifies that every node is free of impediments by comparing it to the starting point. When the starting point, n(0), and the point n(i), which is an integer (0 < i < 9), are free of obstacles, the two points are connected, and n(i) is used as the new starting point. This process is repeated until the endpoint, n(8). The process is shown in Figure 9.

The simplified path needs to be smoothed to decrease the path’s inflection points, prevent the vehicle from jittering while tracking the path, and enhance motion stability and tracking accuracy. The B-spline curve is frequently used for path smoothing because of its locally adjustable characteristic. Smoother pathways can be achieved with higher-order B-spline curves, but the computation is more complicated. Therefore, this work decides to employ the cubic B-spline curve to smooth the processing path in light of the computing difficulties and the smoothing impact.

Taking k = 3, the expression for the basis function of the cubic B-spline curve is

$$\left\{\begin{array}{l}{B}_{0,3}(t)=\frac{1}{6}(-t^3+3t^2+1)\\ B_{1,3}(t)=\frac{1}{6}(3t^3-6t^2+4)\\ B_{2,3}(t)=\frac{1}{6}(-3t^3+3t^2+3t+1)\\ B_{3,3}(t)=\frac{1}{6}{t}^3\end{array}\right.t\in [0,1]$$

(13)

The matrix expression for the cubic B-spline curve is given by

$$S_i(t)=\frac{1}{6}(k^3,k^2,k,1)\left[\begin{array}{cccc}-1& 3& -3& 1\\ 3& -6& 3& 0\\ -3& 0& 3& 0\\ 1& 4& 1& 1\end{array}\right]\left[\begin{array}{c}{p}_0\\ p_1\\ p_2\\ p_3\end{array}\right]t\in [0,1]$$

(14)

where $t$ is inside the interval [0, 1], and $S_i(t)$ is the analytical B-spline curve of the ith arc.

According to Equation (14), the x and y values of the B-spline curve are found, and finally, the final smoothing path can be generated by connecting them sequentially.

The improvement of the RRT algorithm path planning in this paper is the subject of the above content. Specifically, the planning time is too long, the dynamics constraints are not followed, the path feasibility is poor, the growth step is fixed, and the RRT algorithm path is not smooth. To address these issues, the target point bias sampling strategy, collision detection, adaptive step-size strategy, adaptive radius node screening strategy, termination criterion strategy, and greedy strategy are proposed. As a result, the improved RRT algorithm can obtain a safe and smooth traveling path in a shorter amount of time; finally, the improved RRT flowchart is displayed in Figure 10.

2.4. Comparative Evaluation and Simulation Validation of the Enhanced RRT Method

To verify the effectiveness of the improved algorithm to meet the driving of unmanned vehicles in daily life, in this paper, the driving scenario of an intersection is designed, and several simulation experiments are carried out with the traditional RRT algorithm, the RRT* and RRT-connect algorithms, and the improved algorithm proposed in this paper. Figure 11 displays the simulation experiment findings, and

Table 1. Performance comparison of four evaluation functions for intersection scenarios.

Scenario	Algorithm	Path Length	Running Time	Number of Corners	Number of Iterations
Intersection	Conventional RRT	21.94 m	1.35 s	35	1101
	RRT*	19.44 m	17.71 s	3	2000
	RRT-connect	15.86 m	2.72 s	37	109
	The algorithm in this paper	12.63 m	0.06 s	0	97

displays the algorithms’ performance comparison. The light-blue solid line represents RRT*, the purple solid line represents RRT-connect, the red line represents the enhanced RRT algorithm, and the green solid line represents the conventional RRT method. The intersection scenario’s simulation environment measures 25 by 25 m, with a step size of 0.5. The root node’s coordinates are xstart = [13.5, 5], and the destination point’s coordinates are xgoal = [10.5, 5], accordingly.

The optimization method proposed in this paper shows significant advantages over the other three algorithms (RRT algorithm, RRT* algorithm, and RRT-connect algorithm) in terms of evaluation indexes like the number of sampling times, the planning time, the length of paths, and the number of corners in the left turn at the intersection scenario. This can be seen by comparing the planned routes in Figure 11 with the data in Table 1. This is based on the improvement of the above strategies. They reduce time by 95.6%, 99.6%, and 97.8%, respectively, in comparison to the traditional RRT algorithm, RRT* algorithm, and RRT-connect algorithm; they reduce the number of samples by 99.2%, 95.2%, and 11%, respectively; they reduce path length by 42.4%, 35%, and 20.4%, respectively; and the number of corners ideally reaches 0. In every indicator, the enhanced RRT algorithm performs better than the other three.

Several important tactics were introduced and optimized, which is why there has been such a noticeable improvement. While the target point bias technique enhances search efficiency and direction optimization, the global adaptive step-size strategy allows quick navigation through constrained areas of the map. In the meantime, the path cost is significantly decreased by the adaptive radius node technique. Furthermore, during the planning phase, real-time detection of whether a node is inside an obstruction guarantees that every step of the path is viable and safe to prevent collisions. To prevent the creation of illegitimate paths, the termination requirement, in conjunction with obstacle detection, guarantees that the path is legitimate. Convergence speed is increased, and the enhanced termination condition decreases the oscillatory search close to the goal point. Unnecessary nodes and path inflection points are eliminated to provide smoother paths through node rejection and path smoothing processing. This lowers jitter during vehicle tracking and enhances motion stability and tracking accuracy. To sum up, the enhanced RRT algorithm demonstrates notable gains in path planning effectiveness and security, making it appropriate for unmanned vehicle path planning requirements in diverse settings.

3. Localized Path Planning Based on Improved DWA Algorithm

RRT, a global path planning algorithm, can determine the overall route for unmanned vehicles in a static environment. However, in a complex working environment, the emergence of transient obstacles will impede the unmanned vehicle’s progress based on the global path, thereby affecting it. Therefore, this paper improves the traditional DWA algorithm and designs an improved RRT-DWA fusion path planning algorithm to make up for the shortcoming that the global path planning algorithm based on RRT cannot avoid unknown obstacles. The local path planning algorithm using DWA can easily fall into local dilemmas when encountering “C”-shaped obstacles and entering the corners of obstacles. regarding the algorithm for DWA fusion path planning, the algorithm creates an adaptive weighting scheme, enhances the DWA algorithm’s trajectory assessment function, and extracts the global route critical points, which are the subtarget points of the DWA algorithm. In a complicated environment where moving and stationary obstacles coexist, the autonomous vehicle can reach the target point swiftly and safely thanks to the fused path planning algorithm.

3.1. Dynamic Windowing Algorithm

Dieter Fox and Sebastian Thrun proposed the dynamic window approach (DWA) algorithm in 1997. To obtain the optimal predicted trajectory that complies with the vehicle kinematics model and outputs the speed and angular velocity for real-time obstacle avoidance, the DWA algorithm first limits the velocity space by the vehicle kinematics model, then generates the predicted trajectory in the forward simulation time and evaluates the predicted trajectory through the evaluation function. The evaluation function determines the best-predicted trajectories by the vehicle kinematics model by evaluating the generated predicted trajectories for obstacle avoidance capability, speed, heading, angle, and other factors. It then outputs the speed and angular velocity for real-time obstacle avoidance.

Steps in the Dynamic Window Approach

(1) Sample data from the velocity space to determine the vehicle’s current condition. (2) Calculate the car’s trajectory at each measured velocity (v,w) over a specified duration. (3) Utilizing the assessment function’s criteria, assign a score to each route and exclude those that are not possible. (4) Based on the scoring, choose the best path for the car’s actual trajectory.

• Velocity sampling.

The number of velocities (v, ω) is theoretically infinite; therefore, it is necessary to limit the velocity sampling range as follows:

(1) Vehicle speed magnitude. This is the range of speeds of a vehicle at its maximum and minimum speeds.

$${\mathrm{v}}_s=\left\{v\in [{\mathrm{v}}_{\min },{\mathrm{v}}_{\max }],w\in [w_{\min ,}{w}_{\max }]\right\}$$

(15)

where max v denotes the vehicle’s top speed, min v is its lowest, max w its greatest angular velocity, and min w its minimum angular velocity.

(2) Motor performance. There is a maximum acceleration and deceleration limit, as the torque of the motor is limited and the performance of the car is affected by the motor drive module. Therefore, in the simulated car driving cycle, the speed of the car in the dynamic window is the speed that the car can reach the following:

$${\mathrm{v}}_d=\left\{(v,w)|v\in [{\mathrm{v}}_c-{\dot{\mathrm{v}}}_b\Delta t,{\mathrm{v}}_c+{\dot{\mathrm{v}}}_a\Delta t]\wedge w\in [w_c-{\dot{w}}_b\Delta t,w_c+{\dot{w}}_a\Delta t]\right\}$$

(16)

where $\Delta t$ is the time interval, ${\mathrm{v}}_c$ and $w_c$ are the current speed, ${\dot{\mathrm{v}}}_a$ and ${\dot{w}}_a$ correspond to the maximum acceleration, and ${\dot{\mathrm{v}}}_b$ and ${\dot{w}}_b$ correspond to the maximum deceleration.

(3) Safe distance. Also, for the car to stop before it encounters an obstacle, the speed should have a range of maximum deceleration conditions for safety reasons:

$${\mathrm{v}}_a=\left\{(v,w|v\le \sqrt{2\cdot dist(v,w)\cdot v_b}\wedge w\le \sqrt{2\cdot dist(v,w)\cdot w_b}\right\}$$

(17)

where $dist(v,w)$ denotes the minimum distance between the car and the obstacle, and $v_b$ and $w_b$ denote the translational and rotational acceleration of the car, respectively.

Combining the three speed constraints as shown in Figure 12 and the dynamic window in which the vehicle takes into account its own mechanical properties, the map environment is defined:

$${\mathrm{v}}_r={\mathrm{v}}_s\cap {\mathrm{v}}_d\cap {\mathrm{v}}_a.$$

(18)

2.

Trajectory evaluation function.

There are several feasible trajectories in the group of sampled speeds. Therefore, each trajectory needs to be evaluated in the form of an evaluation function to obtain the optimal value of the car at moment k + 1 in the velocity vector space:

$$G(v,w)=\alpha ·\mathrm{heading}(v,w)+\beta ·\mathrm{dist}(v,w)+\gamma ·\mathrm{vel}(v,w)$$

(19)

where $\alpha ,\beta ,\gamma$ denote the weight coefficients of each subfunction. By varying the weight coefficients’ sizes and their relationships, one can alter which trajectory is chosen. The subfunction for azimuth evaluation is the heading $(v,w)$. If the vehicle travels straight toward the goal, it reaches its maximum. The maximum value is when the angle between the vehicle and the target point is 0 degrees:

$$\mathrm{heading}(v,w)=1-\frac{\theta }{\pi }$$

(20)

where $\theta$ denotes the angle between the car and the target point.

Dist $\left(v,w\right)$ is the distance to the nearest obstacle on the trajectory. Moreover, it is the straight-line distance between the current position of the unmanned vehicle and the target point. When the function value is high, it means that the unmanned vehicle is far away from the target point and has a low risk of collision; a low function value indicates that the unmanned vehicle is close to an obstacle and the possibility of collision is increased, so the unmanned vehicle prefers to go around the obstacle:

$$\mathrm{dist}(v,w)=\left\{\begin{array}{l}\frac{1}{L},0\le l\le L\\ 1,L\ll l\end{array}\right.$$

(21)

Vel$(v,w)$ is the forward speed of the car and supports rapid movement:

$$\mathrm{vel}(v,w)=\frac{v}{v_{\max }}$$

(22)

where $v$ is the average speed of the car and $v_{\max }$ is the maximum speed of the car in the velocity space.

3.

Initial angle.

Set the DWA initial position formula as shown in Equation (23):

$$S_{angle}=\arctan \frac{y_1-y_{\mathrm{star}t}}{x_1-x_{\mathrm{star}t}}$$

(23)

where $x_1$ and $y_1$ denote the horizontal and vertical coordinates of the first selected node, while $x_{start}$ and $y_{start}$ denote the coordinates of the starting point. $S_{angle}$ denotes the angle between the starting point and the next node. The setting of the initial position formula enables the unmanned vehicle to pre-turn to the appropriate angle, facilitating its operation, reducing the time required for path planning, and ensuring more accurate navigation.

The initial angle is an important consideration when improving DWA. The initial angle in DWA is usually the current orientation of the unmanned vehicle. In some specific application scenarios, the handling of the initial angle can significantly affect the effectiveness of path planning. Before using the DWA algorithm, the initial angle of the unmanned vehicle is calibrated using Equation (23) to ensure the accuracy of the initial orientation and avoid path planning problems caused by incorrect initial orientation.

3.2. Improved Dynamic Window Approach Algorithm

The traditional DWA algorithm only selects the optimal speed in the current environment. The obtained path is locally optimal but not globally optimal. If it encounters a “C”-shaped obstacle or a corner, the unmanned vehicle may get into trouble [31], which reduces the efficiency of navigation or even causes failure to navigate. Combining the advantages of global path planning and local path planning, we propose a local path planning algorithm that improves the fusion of RRT and DWA [32]. The trajectory evaluation function of DWA is improved so that the unmanned vehicle follows the global path while avoiding obstacles, thus fully utilizing the shortest global path.

3.2.1. Extraction of DWA Critical Nodes by Improved RRT Algorithm

Global path planning is path planning in a static environment, while the actual working environment of unmanned vehicles is often complex and variable. To perform error-free driving, an unmanned vehicle needs to monitor the environment in which it is traveling in real time, achieve static and dynamic obstacle avoidance, and ensure that it can safely and quickly travel to the target location. The advantage of the RRT algorithm is that it can plan the shortest paths in environments with static obstacles. However, in dynamic environments, the paths generated by RRT in static environments may not be effective in avoiding obstacles. Due to the lack of global path guidance in traditional DWA algorithms, it is often challenging to obtain a desirable optimal path, especially in complex obstacle environments, and these algorithms are prone to fall into a local optimum and fail to reach the target point. Complying with traffic regulations to ensure safe navigation is crucial, but unexpected events, such as the sudden appearance of other road users or unexpected obstacles, still pose significant challenges to self-driving vehicles. Our approach integrates improved RRT and DWA algorithms to dynamically adjust the vehicle path in real time to ensure compliance with traffic regulations and effective obstacle avoidance. Our goal is to construct optimal paths that prioritize safety and efficiency without violating traffic regulations. To overcome the performance requirements of unmanned vehicle path planning for the shortest path, search efficiency, and safety, the improved RRT algorithm is fused with the DWA algorithm to realize dynamic and static navigation planning, obtaining better driving paths and higher time efficiency.

The optimized path of the improved RRT algorithm is used as the guideline of the DWA local path planning algorithm, and the global path key point is extracted as the subtarget point of the DWA algorithm. The extraction is based on the following: when the direction of the path point is consistent with the current direction of the vehicle, the path point is deleted as a redundant node, and the vehicle still travels along the current direction; if the direction is not consistent, the path point is used as the next subtarget point of the DWA algorithm. This method divides the global path into several subpaths as a guide for the DWA algorithm. Figure 10 shows the global path critical point extraction process.

Overall, by using the optimized paths of the improved RRT algorithm as guidelines for the DWA local path planning algorithm and extracting the global path key points as subtarget points of the DWA algorithm, this approach can effectively combine the optimality of global path planning with the real-time adaptability of local path planning. By taking the path points as subtarget points only when the directions are inconsistent, redundant nodes can be removed, computation can be reduced, frequent adjustments can be avoided, adaptability can be improved, path quality can be optimized, navigational efficiency can be improved, and foresight can be enhanced. This strategy not only improves the efficiency and quality of path planning but also helps to enhance the performance of the overall navigation system. The extraction process of global path key points is shown in Figure 13.

3.2.2. Improvement of the Evaluation Function

(1) In this paper, the global path key point is used in the DWA algorithm as the subtarget point of local planning; therefore, we adapt the trajectory evaluation function to the improved DWA algorithm, enhance the guidance of the target point to the speed sampling, and, at the same time, make the local planning algorithm flexible and efficient to avoid unknown obstacles to the trajectory evaluation, so the function has been improved. The improved trajectory evaluation function can be expressed as follows:

$$\left\{G(v,w)=\delta (\alpha \cdot \mathrm{heading}(v,w)+\tau \cdot {\mathrm{dist}}_{obs}(v,w)+\psi \cdot {\mathrm{dist}}_{dev}(v,w)+\gamma \cdot \mathrm{vel}(v,w))\right\}$$

(24)

As shown in Figure 14. For the azimuth subfunction heading $(v,w)$, the smaller the deviation angle $\theta$ of the orientation of the generated trajectory from the target point, the higher the rating of the trajectory.

Dist$(v,w)$ is the distance evaluation function and ${\mathrm{dist}}_{obs}(v,w)$ is the obstacle avoidance function, which indicates the minimum distance between the current trajectory endpoint and the obstacle. It is used to penalize the sampled trajectories near the obstacles to ensure the obstacle avoidance ability of the unmanned vehicle. The farther the distance, the higher the score. ${\mathrm{dist}}_{dev}(v,w)$ is the deviation function, which represents the distance between the global optimal path and the current trajectory. The higher the trajectory score, the better the trajectory.

The speed subfunction $\mathrm{vel}(v,w)$ is mainly used to evaluate the performance of the generated trajectory in terms of speed. By integrating smoothness, adaptability, and efficiency, it can be ensured that the generated trajectories not only meet the dynamic performance requirements but also provide a comfortable and efficient driving experience. Ultimately, this comprehensive evaluation method can significantly improve the overall performance and reliability of unmanned vehicle path planning.

The smoothing function $\delta$ is not obtained by simply superimposing the four subfunctions in Equation (24) but needs to be normalized and then superimposed. This is because the evaluation function is not continuous in the speed sampling space, and each simulated-trajectory calculated-obstacle distance gap is large; therefore, it will have an impact on the performance of the distance evaluation subfunction, resulting in an evaluation function of a performance indicator that is too high or too low so that the weight of the subfunctions when evaluating the trajectory in the speed sampling space is out of balance, making it necessary to carry out a normalization process of the subfunctions. In short, the purpose of the normalization process is to obtain a reasonable evaluation function, which evaluates the trajectory more reasonably. The method of normalization is that the current value of each subfunction is divided by the sum of each subfunction, and the specific processing can be expressed as follows:

$$\left\{\begin{array}{l}\mathrm{heading}(v,w)=\frac{\mathrm{heading}(v,w)}{{\displaystyle \sum _{i=1}^n\mathrm{heading}(v,w)}}\\ {\mathrm{dist}}_{obs}(v,w)=\frac{{\mathrm{dist}}_{obs}(v,w)}{{\displaystyle \sum _{i=1}^n{\mathrm{dist}}_{obs}(v,w)}}\\ {\mathrm{dist}}_{dev}(v,w)=\frac{{\mathrm{dist}}_{dev}(v,w)}{{\displaystyle \sum _{i=1}^n{\mathrm{dist}}_{dev}(v,w)}}\\ \mathrm{goal}(v,w)=\frac{\mathrm{goal}(v,w)}{{\displaystyle \sum _{i=1}^n\mathrm{goal}(v,w)}}\end{array}\right.$$

(25)

3.2.3. Adaptive Weighting Improvement

In complex and dynamic environments, dynamic windowing methods with fixed weights may encounter planning failures or lead to unreasonable paths. In this paper, we propose an adaptive weighting method that selects the combination of weights based on the distance from the current position of the unmanned vehicle to the obstacle. This enables the unmanned vehicle to better balance the relationship between the individual path planning metrics in different environments and improve the robustness and applicability of the algorithm. The specific steps are as follows:

1. If ${\mathrm{dist}}_{present}\le {\mathrm{dist}}_{warn}$, this means that the unmanned vehicle is approaching an obstacle and needs to respond to enter the safe zone. In this case, the weight value $\tau$ of the obstacle avoidance function ${\mathrm{dist}}_{obs}(v,w)$ needs to be increased, and the weight value $\psi$ of the deviation function ${\mathrm{dist}}_{dev}(v,w)$ needs to be decreased.

$$\begin{array}{l}weigh{t}_{obs}=weigh{t}_{obs}+\tau \\ weigh{t}_{dev}=weigh{t}_{fol}-\psi \end{array}$$

(26)

2. If ${\mathrm{dist}}_{present}\le {\mathrm{dist}}_{danger}$, this indicates that the current distance is within the danger distance, so the priority is to leave the area. Therefore, it is necessary to continue to weight the obstacle avoidance weight values.

$$weigh{t}_{obs}=weigh{t}_{obs}+\tau$$

(27)

3. When ${\mathrm{dist}}_{present}{>\mathrm{dist}}_{warn}$, this indicates that the unmanned vehicle is in a safe zone. To improve the tracking ability of the local path, it is necessary to increase the weight value of the deviation function ${\mathrm{dist}}_{dev}(v,w)$ and decrease the weight value of the obstacle avoidance function ${\mathrm{dist}}_{obs}(v,w)$.

$$\begin{array}{l}weigh{t}_{obs}=weigh{t}_{obs}-\tau \\ weigh{t}_{dev}=weigh{t}_{dev}+\psi \end{array}$$

(28)

In these equations, the detection distance between the current position and the obstacle is defined as ${\mathrm{dist}}_{present}$, the warning distance between the unmanned vehicle and the obstacle as ${\mathrm{dist}}_{warn}$, and the hazard distance as ${\mathrm{dist}}_{danger}$.

With this adaptive weighting method, the unmanned vehicle can dynamically adjust the weight values according to the distance between the current position and the obstacles to adapt to different environmental situations, thus producing more reasonable path planning results.

3.3. Simulation Experimental Verification and Analysis of Improved DWA Algorithm

The obstacle-avoidance performance of the DWA algorithm is tested on a two-dimensional map, as shown in Figure 15. The starting point is set to be [5,5], the single-color marking point is the end position [17,22], the black area represents obstacles, and there is a “C”-shaped obstacle in the path from the starting point to the endpoint. As shown in Figure 15a, the unmanned vehicle moves from the starting point to the endpoint, and when it reaches the area of the “C”-shaped obstacle, it falls into a dead loop until it stops there. The reason is that the unmanned vehicle can no longer search for an effective path when it is close to the “C”-shaped obstacle, and it can no longer leave the “C”-shaped obstacle. The reason is that when the unmanned vehicle approaches the “C”-shaped obstacle, it cannot search for a practical path and cannot leave the “C”-shaped obstacle, and then the path planning fails. The above experiments show that the DWA algorithm is prone to falling into the “C”-shaped obstacle dilemma and is not suitable for path planning in complex environments.

To solve the above problems, the improved DWA algorithm is used to fully utilize the global path information when driving the unmanned vehicle’s motion, i.e., the local path is generated under the guidance of the global path. As shown in Figure 15b, this fusion algorithm overcomes the shortcoming of the original dynamic window method that falls into a local optimum in the “C”-shaped obstacle map. It finally achieves the triple optimization of path length, smoothness, and safety. The green curve in the figure is the global path generated by the improved RRT algorithm, and the red curve is the motion trajectory generated by the DWA algorithm under the guidance of the global path. Comparing with Figure 15a,b, it can be seen that in complex scenes, the combination of the improved DWA algorithm and the global path planning algorithm can effectively avoid the “C”-shaped obstacles to reach the target point according to the information of the global path, and the optimal path is planned.

4. Simulation Experiment Verification and Analysis

To validate the performance of the improved RRT and DWA algorithms, comparative experiments with different algorithms are performed in Matlab R2021b software. The simulation experiments compare and verify the algorithms in terms of their adaptive ability in static scenarios and mixed static and dynamic scenarios and compare their planning efficiency as well as their planning effectiveness. Global path planning aims to plan the optimal path under typical working conditions, so this paper selects the most common driving scenarios in the actual driving of vehicles, including parking lot exit-tracking scenarios, roundabout-turn driving scenarios, intersection left-turn scenarios, and lane-change obstacle-avoidance scenarios. For this paper, we improved the simulation environment required by RRT by building a simulation scene map in Matlab and forming the boot region. Simulation experiments used the computer configuration of a 64-bit Windows 11 system with an Intel 12th i7 processor and an NVIDIA GeForce GTX 4060Ti graphics card. Considering the deviation of RRT series algorithms in each iteration, to prevent a deviation from influencing the results, we conducted 50 simulation tests with four algorithms and took the average value as the result.

4.1. Experimental Analysis of Static Simulation Scenarios

As the real road environment is full of uncertainties, even when traffic rules are observed, the sudden behavior of other road users can still affect driving safety. For example, pedestrians may suddenly enter the lane, and the vehicle in front of them may brake suddenly. To verify the effectiveness of the improved algorithm to meet the unmanned vehicle’s driving needs in daily life so that the unmanned vehicle can respond quickly in these situations, several simulation experiments were carried out using the traditional RRT algorithm, the RRT* and RRT-connect algorithms, and the improved algorithm proposed in this paper, respectively. Four different scenarios were selected: the park lot scenario, the roundabout scenario, the one-way lane obstacle-avoidance scenario, and the intersection left-turn scenario. In the simulation scenarios, the red diamonds all represent the starting position of the vehicle, i.e., the root node of the random tree; the green origins all represent the endpoint of the vehicle; and all the black shapes are obstacles. The experimental results are shown in Figure 16, where the green solid line is the traditional RRT algorithm, the dark blue solid line is the RRT*, the purple solid line is the RRT-connect, and the red solid line is the improved RRT algorithm. The performance comparison of the algorithms is shown in

Table 2. Simulation results for different driving scenarios.

Scenario	Algorithm	Path Length	Running Time	Number of Corners	Number of Iterations
Parking lot	Conventional RRT	86.46 m	4.11 s	86	2284
	RRT*	69.73 m	26.65 s	4	2000
	RRT-connect	88.38 m	33.41 s	88	1937
	The algorithm in this paper	65.61 m	0.32 s	0	96
Roundabout	Conventional RRT	18.81 m	1.93 s	22	1065
	RRT*	16.78 m	1.47 s	3	2000
	RRT-connect	20.15 m	2.29 s	18	187
	The algorithm in this paper	16.12 m	0.03 s	0	53
Intersection	Conventional RRT	19.39 m	2.16 s	42	198
	RRT*	13.52 m	4.96 s	3	1500
	RRT-connect	17.76 m	3.26 s	16	121
	The algorithm in this paper	13.44 m	0.07 s	0	74
Lane change	Conventional RRT	43.00 m	0.44 s	66	497
	RRT*	26.32 m	24.59 s	3	2000
	RRT-connect	37.92 m	9.58 s	80	400
	The algorithm in this paper	26.29 m	0.24 s	0	253

.

Scenario 1 is a parking lot scenario in which the simulation environment is a parking lot of size 50 m × 50 m, in which the black rectangles represent vehicles parked in the parking lot, all the road sections in the parking lot are unidirectional, and there is only the road section from the entrance to the exit, as shown in Figure 16a. The black dots represent pedestrians who are looking for vehicles. This scenario simulates the planned route of a car from its own parking space to the exit of the parking lot. Due to the special scene and relatively small environment, the RRT algorithm only uses objects as reference points. Here, based on the environment, the range of the obstacle is expanded, and the reservation of its contour distance is increased to ensure that no cuts or even collisions will occur because of its own contour distance and the surrounding body contour while planning the optimal driving route.

Scenario 2 is a roundabout scenario in which the simulated environment is a lane with a unidirectional width of 2.5 m and a small urban unsignalized roundabout with a diameter of 17 m. Vehicles enter the roundabout from the right side of the road below and exit at the third exit of the roundabout, as shown in Figure 16b. The black dots represent pedestrians and non-motorized vehicles crossing the intersection in this scenario.

Scenario 3 is a left-turn intersection scenario in which the simulation environment is a small unsignalized intersection consisting of an urban roadway with a width of 2.5 m on one side. Vehicles enter the intersection from the right side of the intersection, moving from left to right, to make a left turn and exit the intersection downward to continue traveling, as shown in Figure 16c. The black dots are pedestrians and non-motorized vehicles crossing the intersection.

Scenario 4 is a one-way lane obstacle-avoidance scenario, where the simulated environment is a two-lane unidirectional urban road, from left to right, with each lane having a width of 3.75 m and an intercept length of 30 m, where the black squares are the vehicles temporarily stopped or slowed down on the side of the road, as shown in Figure 16d. The black dots represent pedestrians crossing the road or small animals appearing from out of nowhere.

The following figure shows the effect of the paths planned by the four algorithms with the same conditions, where the size of the simulation environment in the parking lot scenario is 50 × 50 m, the step size is set to 1 m, and the coordinates of the start point and the target point are Xstart = [5.5, 13] and Xgoal = [46, 46]. The roundabout scenario is for a simulation environment size of 25 × 25 m with a step size of 0.5. The start and target points are Xstart = [13.5, 5] and Xgoal = [13.5, 20]. The volume of the simulation environment for the intersection left-turn scenario is 25 × 25 m. The coordinates of the root node and the target point are set to Xstart = [10.5, 5] and Xgoal = [18.5, 13.5]; the fixed step size is taken as 0.5. The size of the simulation environment for the obstacle-avoidance lane-changing scenario is 30 × 15 m, the black rectangle represents the static obstacles on the road, the road width is set to 7.5 m, the step size is 0.5, and the start and target points are Xstart = [2.5, 9.5] and Xgoal = [28, 12.5].

As can be seen from Figure 16 and Table 2, due to the complex environment with narrow space, the number of turning points and the path length are very close to and better than the RRT* algorithm, which proves that the improved RRT algorithm exceeds the best RRT* in terms of the degree of path smoothing and optimization, and at the same time, the number of sampling times and the simulation time both exceed those of the effective RRT-connect algorithm in the parking lot exit-tracking scenario in comparison In the experiment, the improved RRT algorithm compared with the remaining three algorithms reduces the time and the number of samples by 92%, 98.8%, and 99% and 95.8%, 95.2%, and 95.1%, respectively. The path cost is reduced by 24.1%, 5.9%, and 25.8%, respectively, and the number of corners is zero; the improved RRT algorithm has a substantial improvement in all four indicators. It can meet the driverless complex roadway path planning needs of unmanned complex roadways.

From Figure 16 and Table 2, it can be seen that in the comparison experiment of the roundabout turn, the improved RRT algorithm reduces the time and sampling times by 98.4%, 98%, and 98.7% and 95%, 97.4%, and 71.7%, respectively, compared to the remaining three algorithms; the path cost is reduced by 14.3%, 3.93%, and 20% respectively; and the number of corners is zero. The four indicators of the improved RRT algorithm are all greatly improved and can meet the path planning requirements of unmanned roundabout turns.

From Figure 16 and Table 2, it can be seen that in the comparison experiments of the obstacle-avoidance lane-changing scenario, the improved RRT algorithm reduces the time and the number of samples compared with the remaining three algorithms by 45.5%, 99%, and 97.5% and 49.1%, 87.4%, and 36.8%, respectively, and the path cost is reduced by 20.3%, 0.01%, and 21%, respectively. The number of corners is zero, and the four indexes of the RRT algorithm are all greatly improved, so it can meet the path planning requirements of unmanned vehicle obstacle avoidance and lane changing.

From Figure 16 and Table 2, it can be seen that the improved method proposed in this paper has apparent advantages over the remaining three algorithms in the intersection left-turn scenario in terms of the three evaluation indexes of the number of samples, planning time, and number of corners compared with the RRT algorithm, the RRT* algorithm, and the RT-connect algorithm. The time is reduced by 96.8%, 98.6%, and 97.9%, respectively; the number of samples is reduced by 63%, 95%, and 39%, respectively; the path length is reduced by 28%, 0.04%, and 19%; and the number of corners achieves the ideal 0, 63%, 95%, and 39%, respectively. The path length is reduced by 28%, 0.04%, and 19%, respectively, compared to the number of samples, and the number of corners reaches the ideal of 0. The improved RRT algorithm outperforms the remaining three algorithms in all indicators.

4.2. Analysis of Experimental Results of Static and Dynamic Fusion Simulation Scenarios

Simulation experiments were conducted to compare the performance difference between the improved DWA algorithm based on evaluation function optimization and adaptive weighting in the traditional RRT and DWA fusion algorithm and the improved RRT and DWA fusion algorithm of this paper, considering path planning in different daily driving scenarios. While international traffic regulations provide a structured framework for vehicle movement, dynamic and unexpected scenarios still occur frequently. Our approach is designed to operate within the bounds of these regulations, ensuring that the unmanned vehicle can adapt to real-time changes in the environment and avoid collisions effectively.

In order to further verify the reliability of the hybrid algorithm, temporary static and dynamic obstacles are added to the map, where the black ball is a dynamic obstacle and makes reciprocal uniform motion on both sides of the path, and other black shapes are static obstacles. Simulation comparison experiments with traditional RRT and DWA fusion algorithms and improved DWA algorithms with optimized evaluation functions are also conducted and compared to verify the planning efficiency as well as the planning effect. The experimental results are shown in Figure 17 and Figure 18, and the performance pairs are shown in

Table 3. Comparison of parking lot scenario simulation.

Scenario	Algorithm	Path Length	Running Time
Parking lot	Conventional RRT	119.68 m	36.86 s
	Improved DWA	125.40 m	33.72 s
	The algorithm in this paper	114.92 m	23.31 s

.

In order to further verify the superiority of the fusion algorithm proposed in this paper, comparative experiments with the RRT and DWA fusion algorithm, the improved DWA algorithm, and the improved fusion algorithm in this paper are conducted on the parking lot scenario map, as shown in Figure 17. As can be seen from Figure 17, all three algorithms successfully find the path from the starting point to the destination in an environment containing unknown and dynamic obstacles. However, the path planned by the RRT algorithm, as shown in Figure 17a, is not flat and is accompanied by steep turns while running a path that does not meet our daily driving requirements. Moreover, the improved DWA algorithm, shown in Figure 17b, can realize dynamic obstacle avoidance, but the path has the disadvantages of being unsafe and not smooth, and it does not meet the driving conditions. As shown in Figure 17c, the improved fusion algorithm proposed in this paper has smoother paths and safer obstacle distances with smaller and fewer turning angles, which is more suitable for unmanned vehicle driving conditions.

Figure 18 shows the linear velocity, angular velocity, and time comparison graphs, which show that the algorithm has small and gradual changes in linear and angular velocities when avoiding unknown obstacles. Meanwhile, in the area without obstacles, the linear velocity stays within a stable range, showing the stability and efficiency of this paper’s algorithm in path planning. When stable steering is required, the angular velocity should be kept within a reasonable range without frequent or drastic changes to ensure smooth steering movements and coherent paths. In the parking lot scenario, the improved algorithm in this paper decelerates when encountering sudden oncoming obstacles as well as when turning, which is more in line with driving requirements. Meanwhile, compared with the RRT and DWA fusion algorithm and the improved DWA algorithm, the magnitude of change in linear velocity and angular velocity and the algorithm time of this paper’s algorithm are significantly improved. In Table 3, the running time of the fusion algorithm proposed in this paper is reduced by 36.8% and 30.9% compared to the RRT and DWA fusion algorithm and the improved DWA algorithm, respectively. In addition, the path length is reduced by 4.8% and 8.4%, and the algorithm significantly improves the computing speed and planning efficiency with better path tracking characteristics.

To further verify the superiority of the fusion algorithm proposed in this paper, comparison experiments with the RRT and DWA fusion algorithm, the improved DWA algorithm, and the improved fusion algorithm of this paper are conducted on the map of the roundabout scenario, as shown in Figure 19. Among them, the RRT and DWA fusion algorithm in Figure 19a does not run successfully because the target point is on the opposite side of the starting point, and at the same time, there is an obstacle between the starting point and the endpoint, which causes the DWA algorithm to fall into the local optimum and fail to run. As shown in Figure 19b, although the improved DWA algorithm successfully finds the path from the starting point to the goal point in an environment containing unknown and dynamic obstacles, the path is tortuous and lengthy. As shown in Figure 19c, the improved fusion algorithm proposed in this paper has smoother paths and safer obstacle distances, smaller and fewer turning angles, and shorter paths more suitable for unmanned vehicle driving conditions.

As can be seen from Figure 20, the linear velocity of the improved fusion algorithm in this paper exhibits more excellent stability, and the angular velocity exhibits less fluctuation compared to the RRT and DWA fusion algorithm and the improved DWA algorithm, which makes the travel of the unmanned vehicle more stable and comfortable. In addition,

Table 4. Roundabout scenario simulation comparison.

Scenario	Algorithm	Path Length	Running Time
Roundabout	Conventional RRT	Slip into local optimality
	Improved DWA	23.48 m	15.98 s
	The algorithm in this paper	19.3 m	11.57 s

shows that the running time of the improved fusion algorithm in this paper is reduced by 27.6% compared to the improved DWA algorithm, respectively. In addition, the path length is reduced by 17%. In summary, utilizing the improved RRT and DWA fusion algorithm proposed in this paper not only enhances the safety of unmanned vehicle path planning but also ensures stability.

To further verify the superiority of the fusion algorithm proposed in this paper, comparative experiments with the RRT and DWA fusion algorithm, the improved DWA algorithm, and the improved fusion algorithm in this paper are conducted on the map of the intersection scenario. As shown in Figure 21, all three algorithms successfully find the path from the starting point to the goal point in the environment containing unknown and dynamic obstacles. However, the path planned by the RRT algorithm, as shown in Figure 21a, is not flat and is accompanied by steep turns while running a path that does not meet our daily driving requirements at intersections. Moreover, Figure 21b shows that although the improved DWA algorithm successfully finds a path from the starting point to the destination in an environment containing unknown and dynamic obstacles, there is a starting phase where the path is winding and too close to the opposite lane. As shown in Figure 21c, the improved fusion algorithm proposed in this paper has smoother paths and safer obstacle distances, smaller and fewer turning angles, and shorter paths. It is more compatible with unmanned vehicle driving conditions.

As can be seen from Figure 22, compared with the RRT and DWA fusion algorithm and the improved DWA algorithm, the linear velocity of the improved fusion algorithm in this paper shows more excellent stability. In contrast, the angular velocity shows less fluctuation. After successfully avoiding an obstacle, the linear and angular velocities should quickly return to the normal traveling state, showing the adaptability and efficiency of the DWA algorithm in dynamic environments. In addition,

Table 5. Comparison of intersection scenario simulation.

Scenario	Algorithm	Path Length	Running Time
Intersection	Conventional RRT	39.52 m	36.23 s
	Improved DWA	19.73 m	27.73 s
	The algorithm in this paper	13.14 m	10.96 s

shows that the running time of the improved fusion algorithm in this paper is reduced by 69.7% and 60.5% compared with the RRT and DWA fusion algorithm and the improved DWA algorithm, respectively. In addition, the path length is reduced by 50.1% and 33.4%. In summary, using the improved RRT and DWA fusion algorithm proposed in this paper not only enhances the safety of unmanned vehicle path planning but also ensures stability.

To further verify the superiority of the fusion algorithm proposed in this paper, comparative experiments with the RRT and DWA fusion algorithm, the improved DWA algorithm, and the improved fusion algorithm in this paper are carried out on the map of the obstacle avoidance lane-change scenario, as shown in Figure 23. Among them, the RRT and DWA fusion algorithm in Figure 23a does not run successfully because the target point is on the opposite side of the obstacle, which causes the DWA algorithm to fall into the local optimum and fail to run. As shown in Figure 23b, although the improved DWA algorithm successfully finds the path from the starting point to the goal point in the environment containing unknown and dynamic obstacles, the path is too long because the goal point is on the opposite side of the obstacle, which causes the improved DWA algorithm to fall into the local optimum first, but then it jumps out of the local optimum to find the goal point. As shown in Figure 23c, the improved fusion algorithm proposed in this paper has smoother paths and safer obstacle distances, avoids all dynamic static obstacles, has smaller and fewer turning angles, and has shorter paths more suitable for unmanned vehicle driving conditions.

As can be seen from Figure 24, compared with the RRT and DWA fusion algorithm and the improved DWA algorithm, the linear velocity of the improved fusion algorithm in this paper exhibits greater stability, while the angular velocity exhibits less fluctuation. In the area without obstacles, the linear velocity stays within a stable range, reflecting the stability and efficiency of this paper’s algorithm in path planning. During the obstacle avoidance process, the adjustments of linear and angular velocities are fast enough and effective enough to ensure that the obstacle avoidance maneuver is smooth without losing its smoothness.

Table 6. Comparison of lane-change scenario simulation.

Scenario	Algorithm	Path Length	Running Time
Lane change	Conventional RRT	Slip into local optimality
	Improved DWA	42.78 m	35.47 s
	The algorithm in this paper	27.02 m	16.25 s

shows that the running time of the improved fusion algorithm in this paper is reduced by 54.2% compared with the improved DWA algorithm, respectively. In addition, the path length is reduced by 36.8%. In summary, utilizing the improved RRT and DWA fusion algorithm proposed in this paper not only enhances the safety of unmanned vehicle path planning but also ensures stability.

5. Conclusions

To effectively solve the problem that unmanned vehicles are unable to adapt to unknown environments and dynamic obstacles in global path planning, as well as the problem that they are prone to fall into the local optimum in local path planning, this paper proposes an unmanned vehicle path planning method that incorporates the multi-policy improved RRT algorithm and the optimized dynamic window approach algorithm.

(1)

In this paper, the RRT algorithm is improved by introducing a goal-biased random sampling strategy, collision detection, adaptive step-size strategy, adaptive radius node screening strategy, termination criterion, and greedy strategy. The improved RRT algorithm can generate paths conforming to the vehicle motion constraints more efficiently and reduce the repeated search of explored regions, thus significantly improving the efficiency and safety of path planning.

(2)

Aiming at the problem of unreasonable path planning due to fixed weights in the DWA algorithm, this paper designs an adaptive evaluation function weighting method based on real-time obstacle distance. The optimized key nodes are used as temporary target points for local path planning to guide the local planning along the global path to realize fusion path planning.

(3)

In this paper, the effectiveness and performance advantages of the improved RRT and DWA fusion algorithm in unmanned vehicle path planning are verified by Matlab simulation. The simulation experiments cover several typical static scenarios and driving scenarios with a mixture of static and dynamic obstacles. The results show that the improved algorithm outperforms the traditional method and other improved algorithms in terms of the degree of path optimization, planning efficiency, and path smoothing and demonstrates higher safety, stability, and planning efficiency. The algorithm can effectively deal with complex environments containing temporary static obstacles and dynamic obstacles, which provides strong support for unmanned vehicle path planning applications.

At the same time, this study also has certain limitations. The algorithm proposed in this paper has only undergone simulation experiments to verify the effectiveness of the algorithm. The actual effect of the algorithm on real vehicles has yet to be verified. Therefore, the algorithm’s effectiveness applied to actual vehicles can be further verified in future work.