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Article

Research on Path Planning of a Mining Inspection Robot in an Unstructured Environment Based on an Improved Rapidly Exploring Random Tree Algorithm

by
Jingwen Wu
*,
Liang Zhao
and
Ruixue Liu
College of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an 710311, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(14), 6389; https://doi.org/10.3390/app14146389
Submission received: 6 June 2024 / Revised: 4 July 2024 / Accepted: 10 July 2024 / Published: 22 July 2024
Browse Figures
Versions Notes

Abstract

:
To ensure the safe production of mines, the intelligent trend of underground mining operations is gradually advancing. However, the operational environment of subterranean mining is intricate, making the conventional path-planning algorithm used by mining inspection robots frequently inadequate for real requirements. To safeguard the mining inspection robot, targeting the problem of low search efficiency and path redundancy in the path planning of the existing rapidly exploring random tree (RRT) algorithm in the narrow and complex unstructured environment, a path-planning algorithm combining improved RRT and a probabilistic road map (PRM) is proposed. Initially, the target area is efficiently searched according to the fan-shaped goal orientation strategy and the adaptive step size expansion strategy. Subsequently, the PRM algorithm and the improved RRT algorithm are combined to reduce the redundant points of the planning path. Ultimately, considering the kinematics of the vehicle, the path is optimized by the third-order Bessel curve. The experimental simulation results show that the proposed path-planning algorithm has a higher success rate, smoother path, and shorter path length than other algorithms in complex underground mining environments, which proves the effectiveness of the proposed algorithm.

1. Introduction

Coal mining is mainly underground mining. The environment of underground mining is complex and dangerous. In order to ensure the safe and efficient mining of coal, it is necessary to inspect the coal mine roadway regularly. The mining inspection robot can effectively prevent the occurrence of underground dangers and reduce the labor intensity of the workers. Compared with manual inspection, the mining inspection robot not only has flexibility and intelligence but also improves the accuracy and efficiency of inspection [1]. The inspection robot needs to have functions such as precise positioning, autonomous movement, and safety detection to replace manual safety inspection. Among them, autonomous movement is one of the key technologies of the mining inspection robot. This is because traditional path-planning methods are often based on structured maps, which are difficult to adapt to the complex and changeable mine environment. The roadway under the mine is a typical unstructured environment. The unstructured environment refers to the environment or scene where the robot works in an uneven surface material performance, irregular structural changes, and irregular scenes. The roadway under the mine is narrow and tortuous, and the environment is complex. Therefore, the mine inspection robot can independently plan the path in this environment, which has become the focus of many scholars [2].
Primary algorithms for path planning are categorized into conventional path-planning methods, sampling-based path-planning methods, and smart bionic algorithms. Conventional algorithms predominantly encompass the A* algorithm [3], Dijkstra algorithm [4], and the artificial potential field method [5]. The path-planning algorithms based on sampling mainly include the rapid-expansion random tree algorithm [6] and probability roadmap algorithm [7]. Intelligent bionic algorithms include the ant colony algorithm [8], lion swarm algorithm [9], etc. Owing to its probabilistic completeness, the RRT algorithm excels in handling path-planning problems within a complex unstructured environment. However, the path generated by the algorithm is often not optimal. Consequently, specialists and academics have extensively studied the path-planning problems of the RRT algorithm in complex environments.
Zhang et al. [10] proposed an adaptive target bias strategy and a regional sampling adjustment strategy for the problem that the traditional RRT algorithm does not easily converge and the sampling success rate is low in multi-obstacle scenarios. Experimental findings indicate that the improved RRT algorithm has greatly improved the running time, search times, and sampling success rate compared with the original algorithm and the other two target-driven algorithms. Xu et al. [11] proposed an SMRS-RRT algorithm for the problem of low search efficiency and excessive memory occupation of traditional RRT in complex environments with multiple obstacles. Initially, the global grid map is simplified. On this basis, the optimal path point set from the starting point to the target point is found, and the path is used as the guide path to expand through the intelligent sampling factor to obtain the intelligent sampling area. Subsequently, the iterative search is carried out in the intelligent sampling area to obtain a low-cost and collision-free path from the starting point to the target point. The outcomes of simulations indicate that the suggested algorithm significantly enhances the effectiveness of conventional RRT searches, hastens the rate of convergence, and diminishes memory usage. Luan et al. [12] suggested using DVSA-RRT to divide the sampling space using the dynamic variable sampling area formula, then selecting a particular sampling zone. Subsequently, the preliminary planning of the path is finalized through the application of collision detection, focusing on safe distance, a strategy of probabilistic target offset, and the expansion of steps across multiple levels. The outcomes of simulations reveal that this algorithm significantly diminishes the blindness and randomness in node searches relative to the initial RRT algorithm. Sun et al. [13] introduced the RRT algorithm, which utilizes adjacency extension for initial path exploration. Subsequently, strategies for identifying paths and eliminating redundant ones are employed to enhance the optimization of the chosen path. Ding et al. [14] swiftly investigated the surroundings to identify a viable route using the greedy heuristic approach for rapidly exploring random trees (EP-RRT*), subsequently expanding it to acquire a heuristic sampling zone. The process involves iterative searching within the heuristic sampling zone, which alters as the path is continuously optimized, ultimately identifying the most efficient or less effective route between the initial and final points. This algorithm enhances the rate at which nodes are used, accelerates the rate of convergence, and secures an improved path within an identical iteration count. Although the above experts and scholars have improved the path-planning problem of the RRT algorithm in complex environments from different angles, there are still some shortcomings.
This paper therefore proposes the design of a flexible wheeled inspection robot to carry out safety inspection work [15]. Targeting the problems of the complex environment and narrow roadways in underground mines, a fusion algorithm of FGA-RRT and PRM is proposed. To address the limitations of the traditional RRT algorithm, which is prone to blindness and randomness in its search strategy, a fan-shaped goal orientation strategy is proposed to guide the selection of sampling points. This is followed by an adaptive step size expansion strategy, which increases the expansion speed of the random tree in narrow channels. To prevent the RRT algorithm to generate more complex paths, the PRM algorithm and the improved RRT algorithm have been integrated, with the latter utilizing the PRM algorithm’s approach to optimizing redundant nodes. Additionally, considering the kinematics law of the robot, the path is optimized by the third-order Bessel curve, enhancing the safety of the robot in the process of autonomous movement. The experiment is conducted on the MATLAB simulation test platform, and the effectiveness of the algorithm is confirmed through comparisons with other algorithms. Finally, the improved algorithm is verified in the real-world environment.

2. Methods

2.1. Traditional RRT Algorithm

The rapidly exploring random tree algorithm is a global path-planning algorithm based on random sampling, which needs to master all environmental information and belongs to static planning. The RRT algorithm starts to expand the random tree incrementally with the starting point position as the root node while avoiding obstacles. When the nodes of the random tree expand to the area near the end point, the exploration of the state space is ended [16].
The method of extending nodes in the RRT algorithm is shown in Figure 1. xstart represents the starting point, which is added to the random tree when the algorithm begins. Next, random sampling, xrand, is performed in the map to obtain a random sampling point, and then the point xnear closest to the random sampling point is searched in the random tree. Next, the set step size is extended in the xrand direction to generate a new node xnew; then, it is detected whether there is an obstacle collision between xnear and xnew. If there is no collision, the new node is added to the random tree, and the process is repeated until the target point is found.
The RRT algorithm is a probabilistic complete sampling algorithm, which is suitable for path planning in complex unstructured scenes, which is also the biggest feature of the RRT algorithm. However, the RRT algorithm also has some limitations, mainly:
  • Strong randomness: The path generated by the RRT algorithm is based on random sampling, and the randomness is strong. The algorithm randomly scatters points in the environment map. If the scatter point is close to the target point, it can search the end point faster. If the scatter point is far away from the target point, the search efficiency is reduced.
  • Non-optimal solution: The path of finding a feasible solution by using the RRT algorithm many times may be different, and it does not guarantee that the optimal solution will be found. The RRT algorithm is affected by the different layout of obstacles between the starting point and the target point, resulting in a large difference in the quality of the planned path.
  • Poor smoothness: The random points selected by the RRT algorithm each time may lead to the discontinuity of the path, making the path turn back or turn sharply in space. As a result, the path generated by the RRT algorithm is not smooth enough visually and does not conform to the actual motion law [17].

2.2. Path-Planning Improvement

In this section, some improvement strategies are proposed for the shortcomings of the RRT algorithm. Firstly, the fan-shaped goal orientation strategy is adopted for the selection of sampling points, and then the random tree is expanded by using the exploration method of environmental adaptive step size. Then, the improved RRT algorithm is fused with the PRM algorithm. Finally, the three-order Bessel curve is used for path smoothing, which can effectively plan the safe path and realize the safe inspection of the inspection robot. Through the improvement of these aspects, the quality of the planned path is improved.

2.2.1. Fan-Shaped Goal Orientation

As a sampling-based path-planning method, the selection of sampling points has a great influence on the efficiency of the RRT algorithm. The selection of sampling points in the traditional RRT algorithm is completely random, so it has the disadvantages of blind search, low search efficiency, and being unable to handle complex environments. This study enhances the efficiency of searches by refining the selection process of sampling points through the application of a fan-shaped goal orientation approach to enlarge the random tree.
The fan-shaped goal orientation strategy takes the goal point as the reference point of the random tree expansion direction, so that each sampling can be closer to the goal point, effectively preventing the reverse search of random tree nodes, ensuring the correct direction of sampling and improving the search efficiency. Concurrently, sampling points are chosen at random within the fan-shaped area, maintaining the randomness in point selection, enabling it to seek a viable route when facing obstacles. This unique strategy significantly reduces the number of invalid sampling points caused by random sampling. And when the robot is in a complex environment, it can also make the robot quickly leave the dangerous area. This strategy not only greatly proves the efficiency of the algorithm but also ensures the adaptability of the algorithm to complex environments. The principle of the fan-shaped target orientation strategy is shown in Figure 2.
The sampling points are selected in the sector, and the selection of angle θ is fitted by the truncated standard normal distribution. Truncated normal distribution is a normal distribution that limits the range of variables. As shown in (1), the nearer the goal point, the higher the possibility of selection.
f ( θ ) = c 1 2 π e − x 2 2 ,   − 90 ∘ ≤ θ ≤ 90 ∘     0 ,           else
where c is the truncation parameter; the selection range θ is −90° to 90°.
Directly taking the goal point as the sampling point of the random tree expansion direction makes it easy to fall into a local optimum, so this paper selects the sampling point according to the probability distribution. Firstly, a semi-circular arc is made with the connection between the position and the goal point as the center of the arc, and then the sampling points are selected in the sector area according to the probability of cutting off the standard normal distribution. Then, the set step is extended in the direction of the sampling point to obtain a new extended node, xnew.
When xrand is in the left half of the sector, the coordinates of the new node, xnew, in the X and Y directions are as follows:
X n e w = X n e a r + s t e p × cos ( θ + α ) Y n e w = Y n e a r + s t e p × sin ( θ + α )
When xrand is in the right half of the sector, the coordinates of the new node, xnew, in the X and Y directions are as follows:
X n e w = X n e a r + s t e p × cos ( α − θ ) Y n e w = Y n e a r + s t e p × sin ( α − θ )
The goal-oriented approach aims to direct the extension of the random tree based on the target point, enhance the path-planning algorithm’s effectiveness in intricate environments, and elevate the quality of the planning path. The distribution of computing resources is fine-tuned to enhance global optimization potential, cut down search durations, and offer robust assistance for robotic navigation in intricate environments. This aids in enhancing the effectiveness of path-planning algorithms and the quality of path planning in intricate settings.

2.2.2. Environment-Adaptive Step Size Expansion Strategy

Most of the underground roadway environment is a narrow channel, and the step size of the conventional RRT algorithm is fixed, which limits the exploration efficiency of the random tree. Therefore, this paper proposes an environment-adaptive step size expansion strategy to improve the algorithm and adjust the step size according to the current environment. Exploring the narrow channel leads to an enlargement of the random tree expansion’s step size in this area, enabling rapid exploration of the region by the random tree.
In this paper, the bridge detection algorithm [18] is used to identify whether it is a narrow channel. The bridge detection algorithm is a heuristic algorithm for detecting whether the sampling point is in a narrow space. The main principle of the bridge detection algorithm is to identify whether it is a narrow channel by detecting the state of three sampling points: First, a line segment is randomly generated to detect the two endpoints of the line segment and the intermediate nodes. If the two endpoints are in the impassable area, and the intermediate nodes are in the free area, the intermediate nodes are detected as the sampling points in the narrow channel. As shown in Figure 3, the number 1 indicates that the bridge detection algorithm successfully identifies the narrow channel, and number 2 is the useless sampling in the obstacle.
The pseudocode of the bridge detection algorithm is as follows (Algorithm 1):
Algorithm 1: Bridge detection algorithm
1: Repeat
2: a  ← Rand();
3: if CollisionFree(a) = False then
4:    a′ ← Nearpoint(a);
5:    if CollisionFree(a′) = False then
6:        b′ ← Midpoint(aa′);
7:        if CollisionFree(b) = True then
9:           G ← Insertpoint(G, b);
10:       end
11:    end
12: End
This document utilizes the bridge detection algorithm to identify sampling locations within the narrow channel, and they are added to the narrow channel sample set G in such a cycle. In each sampling, a point, a, is randomly sampled in the space, and then the adjacent node a′ is randomly sampled. Then, taking a and a′ as the two endpoints of the bridge, the midpoint coordinate b of the bridge is calculated. Through obstacle collision detection, it is ensured that the two endpoints are collision points and the midpoint is a free point. If the conditions of the above three points are satisfied, the area where the midpoint b is located can be determined as a narrow channel, and a narrow channel detection can be completed. When the random tree searches for a narrow channel, the extended step size of the random tree is increased, so that the random tree can quickly search the region and get closer to the target point, which improves the computational efficiency.

2.2.3. Fusion of the FGA-RRT and PRM Algorithms

The improvement of the RRT algorithm solves the problem of random tree expansion, but RRT is a single-query algorithm, and the goal is to find a feasible path as soon as possible, so the planned path has more redundant nodes. This document aims to minimize the redundancy of the planned path by shortening the path through the incorporation of the PRM algorithm’s strategy.
The basic idea of PRM is to use a random network to represent the running space of the robot system and then find a feasible path in this network based on a graph search. The random network consists of a series of nodes and their connections. The nodes correspond to the robot pose without obstacle collision in space, and the connection between the two nodes corresponds to a feasible region between the two poses. The general PRM path-planning method is divided into two stages, the preprocessing stage and the search stage. In the preprocessing stage, a large number of points are evenly and randomly scattered into the configuration space C, and then the nodes in the space without obstacle collision are retained to form the node set M. Then, a local planner is used to find its adjacent nodes for each node in N and connect them to form a connection set N. In the search phase, the starting point and the target point are added to the node set M, and then the local planner finds its adjacent nodes and connects them, so that the map becomes several connected graphs. Ultimately, the graph search technique is employed to determine the most efficient route from the beginning to the goal point on the map.
The PRM algorithm obtains the optimal path by calculating the connection of random uniform nodes in the search space. The algorithm has poor completeness, the search time is long when the number of sampling points is too large, and the solution may not be found in complex scenarios. However, the RPM algorithm plans fewer redundant nodes in the path. Therefore, this paper combines the RPM and FGA-RRT algorithms to make full use of their respective advantages, learn from both, and plan a better path.
Utilizing the PRM concept, the fusion algorithm enhances the path designed by the FGA-RRT algorithm: Initially, numerous points are distributed uniformly and randomly along the path planned by the improved RRT, and then the nodes are connected to perform collision detection on the connection. If there is no collision, it is added to the path to detect whether it is a shorter path, and the shorter path is updated. The above procedure is repeated, and multiple iterations are performed until the maximum number of iterations is reached, and the optimal path at this time is output. Integrating with the PRM algorithm decreases the planned path’s inflection points and shortens its length through the optimization of the superfluous path.
The pseudocode of fusion of the FGA-RRT and PRM algorithms is as follows (Algorithm 2):
Algorithm 2: Fusion of the FGA-RRT and PRM Algorithms
1: Input: M,xstart,xgoal
2: Output: A path Γ from xstart to xgoal
3: Γ  ← Ø
4: for i = 1 to n do
5:  xrand  ← FanshapedSample(M)
6:  xnear ← near(xrand,Γ);
7:  if BridgeDetection(xrand) then
8:    xnew  ← Steer(xrand, xnear, addStepSize)
9:    if CollisionFree(xnew, xnear) then
10:    ΓaddNode(xnew)
11:    if xnew = xgoal then
12:    end if
13:    end if
14:  end if
15: end for
16: q  ← random configuration in Γ
17: for all qi∈Γ do
18:  qi ← the closest point to q chosen from Γ
19:  if CollisionFree(q, qi) then
18:    ΓaddNode(q, qi)
19:  end if
20: end for
21: Return Γ
In the fusion FGA-RRT and PRM algorithm, xstart and xgoal represent the start and goal point of the path, Γ represents the random tree, n represents the number of iterations of the algorithm, xrand represents the random sampling points in the sector area by the fan-oriented strategy, xnear represents the nearest point to xrand on the random tree, xnew represents the point obtained by xnear extending one step forward in the direction of xrand, qi denotes the random point on the initial path generated, and x denotes the point on the path closest to q.
The algorithm first determines the starting point xstart, xgoal, and the number of iterations n; initializes the random tree; and iterates through the for loop. In each step of expansion, the sampling fan-shaped target-oriented strategy first selects random sampling nodes xrand from the fan-shaped space and then uses the bridge detection algorithm to determine whether it is a narrow channel area, following by connecting the point xnear closest to xrand with a set step size for collision detection. If no collision occurs, the sampling point is added to the random tree. Finally, the PRM algorithm is integrated to optimize the path. For the random point q on Γ, the neighborhood point qi is selected according to a certain distance range, and each neighborhood point qi is judged. If q and qi have not yet formed a path, they are connected to form a path, and then collision detection is carried out. If no collision occurs, the path is retained, so as to obtain a better path, and then returned through the Return() function.

2.3. Bessel Curve Optimization

The ultimate route derived from the aforementioned algorithm is still a broken line composed of nodes, which does not conform to the kinematic law. Ignoring the curvature of the path will lead to a large tracking error when tracking the path, causing system oscillation, and even affecting the stability of the robot system. Therefore, we need to further smooth the planned path. Polynomial curves, B-spline curves, and Bessel curves are commonly used path-smoothing methods.
Because the Bessel curve has the advantages of simple control, strong description ability, and that it is easy to generate complex smooth curves, this document employs the Bessel curve technique for path smoothing. The expression of Bessel curve can be defined as follows:
q ( τ i ) = ∑ k = 0 m C m k τ i k 1 − τ i m − k P k , τ i ∈ 0 , 1
where m presents the order of the Bessel curve, q(τi) is the interpolation point at the parameter τi, C m k is the coefficient of binomial theorem, and Pk is the kth control point.
Through the value of parameter τi between [0,1], multiple interpolation points can be generated between the first control point P0 and the last control point Pm. When τi = 0, q(τi) = P0, and the starting point coincides with P0; when τi = 1, q(τi) = Pm, and the endpoint coincides with Pm; when 0 < τi < 1, the curve point is the fitting line. In this paper, the third-order Bessel curve is used for smoothing. At this time, m = 3, and its expression is as follows:
q τ i = 1 − τ i 3 P 0 + 3 τ i 1 − τ i 2 P 1 + 3 τ i 2 1 − τ i P 2 + τ i 3 P 3
where P0, P1, P2, and P3 denote four consecutive control nodes on the path to be fitted.
The third-order Bessel curve is determined by these four control nodes. The starting point of the fitting path is the first control node P0 of the third-order Bessel curve, and the end point of the fitting path is the last control node P3 of the third-order Bessel curve. The fitting result is shown in Figure 4. To prevent the smoothed path from colliding with the obstacle, only the smooth processing is performed near the inflection point of the path.
The Bessel curve mainly determines the shape of the curve by the position of the control point. By adjusting the position and number of control points, the radian and shape of the curve can be changed. The path without collision with obstacles is selected as the optimal path, and the following two points are the algorithm judgment logic:
  • The generated path has no collision after obstacle collision detection.
  • If there is more than one path that meets the previous condition, the path with the shortest length is selected.

3. Simulation and Analysis

3.1. Map Building

In this paper, the effectiveness of the FGA-RRT and PRM fusion algorithm in the confined and intricate setting of subterranean mines is shown by comparing the improved algorithm with the traditional RRT and the EP-RRT* algorithms proposed in the literature [14]. The three maps shown in Figure 5 are the maps used in this simulation experiment, which are simulated according to the partial environment of the real mine roadway. The first map is a more tortuous roadway environment, the second map is a more complex environment map of the roadway, and the third map is a roadway environment of different complexity. The simulation map size is set to 50 × 40. The black area represents the obstacle, and the white area indicates the movable space. The pink * marks the starting point, and the blue * signifies the goal point.

3.2. Analysis of the Influence of Extended Step Size

The setting of the extended step size will affect the efficiency of the improved RRT algorithm in planning the initial path. In this section, experiments are carried out by selecting different values of the step size, such as Table 1, to analyze its impact on the performance of the improved RRT algorithm. In order to test the best combination of step coefficients, the above three different experimental maps were tested. In order to avoid the contingency of the experiment, each coefficient combination was tested 30 times independently, and the time average of 30 experiments was recorded. Table 2 is the specific statistical data.
From the comparison results in Table 2 and Figure 6, it can be seen that the combination 4 has the shortest average time in the three maps. In Map 1, Map 2, and Map 3, too short or too long a step size will lead to a decrease in the efficiency of generating the initial path. This is because the random tree expansion speed will slow down, and the efficiency will be low when the step size is too short. When the step size is too long, it is difficult to select the appropriate collision-free sampling point, resulting in an increase in search time. By comparing combinations 3 and 4, increasing the step size in the narrow channel makes the algorithm more efficient. Therefore, after many experiments, combination 4 is the best parameter in the experiment.

3.3. Experimental Simulation and Analysis

3.3.1. Map 1

Figure 7 displays the outcomes of the three RRT algorithms applied in Map 1. The path marked in red represents the ultimate route, while the green signifies the starting planning path and node. The diagram illustrates that within a winding road environment, the conventional RRT algorithm, the RRT* algorithm, and the combined PRM and enhanced RRT algorithm discussed in this document are capable of converging near the intended point. However, due to the randomness of its sampling, the traditional RRT and EP-RRT* algorithms will cause the random tree to extend in all directions, sometimes even in the opposite direction to the goal point, resulting in the goal point not being able to be reached in the limited number of iterations. The degree of twist and the length of the path are higher than the enhanced algorithm proposed in this document. This paper’s enhanced algorithm adopts fan-shaped target orientation sampling, so that the nodes sampled each time are more likely to approach the location of the target point, and adopts an adaptive step size expansion strategy, which greatly improves the random tree expansion rate. Therefore, under the same number of iterations, compared with the traditional RRT algorithm, the search efficiency and accuracy are improved.
Table 3 is the experimental comparison data. The table illustrates that the enhanced algorithm presented in this study exhibits improvements in path length, path tortuosity, and the rate of planning success when contrasted with the conventional RRT algorithm and EP-RRT* algorithm. Regarding the length of paths, this paper’s enhanced algorithm shows a decrease of 15.96% and 5.31%, respectively, compared with the other two algorithms. Regarding the count of inflection points, this paper’s enhanced algorithm shows a decrease of 80.36% and 72.17% in comparison to the initial two algorithms. The reason for the optimization of the path length and the number of inflection points lies in the integration with the PRM algorithm. For the initial generated feasible path, the points on the redundant path are connected in a straight line under the premise of avoiding obstacles, and the path is optimized. In terms of planning success rate, fan-shaped target-oriented sampling is used to make each sampling node more likely to be close to the target point, which improves the search efficiency. The adaptive step size strategy is used to increase the step size of the random tree in the narrow roadway, which can quickly explore the area. Therefore, it can be seen from Table 3 that the success rate of the improved algorithm in this paper is 32.97% and 17.02% higher than that of the first two algorithms. This demonstrates the efficacy and dominance of the enhanced algorithm in the first map.

3.3.2. Map 2

Figure 8 displays the outcomes of the three RRT algorithms applied in Map 2. It can be seen from the figure that in the complex roadway environment, the roadway selected by the traditional RRT algorithm can obtain the optimal path, but its path is more tortuous, resulting in the longest path length. Because the goal of the traditional RRT algorithm is to find a feasible path, regardless of the degree of path twists and turns, the generated path is not further optimized. The EP-RRT* algorithm optimizes the initial planned path, but the effect is not good, and there are still redundant paths. In contrast to the initial pair of algorithms, this paper’s algorithm combines FGA-RRT and PRM to scatter points on the generated feasible path, traverse and optimize, find the shortest path, and find the ultimate path with the fewest inflection points and minimal path length.
Table 4 represents the comparative data for the route planning of the three algorithms in Map 2. The table illustrates that, relative to the conventional RRT algorithm and EP-RRT* algorithm, this paper’s enhanced algorithm cuts down path length optimization by 16.5% and 11.91%, respectively. Regarding turning points, this paper’s refined algorithm shows reductions of 75.35% and 72.22%, respectively, in comparison to the other two algorithms. Regarding planning success rates, this paper’s improved algorithm shows an increase of 30.52% and 10.52%, respectively, in comparison to the other two algorithms. In terms of planning success rate, the improved algorithm in this paper increases by 30.52% and 10.52%, respectively, compared with the other two algorithms. According to the comprehensive data, the fusion with the PRM algorithm can shorten the redundant path and make the generated path have fewer turning points. In contrast to the RRT and EP-RRT* algorithms, the path length has been optimized.

3.3.3. Map 3

Figure 9 displays the outcomes of the three RRT algorithms applied in Map 3. The figure illustrates that in this environment, the path deviation planned by the traditional RRT algorithm, the RRT* algorithm, and the enhanced algorithm discussed in this study is minimal, and they can quickly converge to the target point.
Table 5 represents the comparative data for the route planning of the three algorithms in Map 3. The table illustrates that the improved algorithm in this paper is compared with the conventional RRT algorithm and EP-RRT* algorithm. In terms of path length optimization, the enhanced algorithm discussed in this document has been decreased by 9.72% and 5.09%, respectively. In terms of turning points, this paper’s enhanced algorithm shows a decrease of 64.71% and 55.14%, respectively, in comparison to the other two algorithms. In terms of planning success rate, the enhanced algorithm presented in this study outperforms the other two algorithms by 8.16% and 6.12%, respectively. From the table data, because the map environment is relatively simple, the three algorithms can plan the path well, and the planned path length is less different, and the success rate is also high. In terms of path tortuosity, the enhanced algorithm introduced in this study features a reduced number of inflection points, which is more conducive to the autonomous movement of the robot.
When integrated with the evaluation of the path-planning outcomes for the three maps, the simulation experiment demonstrates that the suggested algorithm outperforms others in success, boasts a smoother path, and has a shorter path length, thereby confirming its practicality and superiority.

3.4. Bessel Curve Optimization

In order to make the generated path conform to the kinematics law of the robot system and increase the stability of the system, the generated path needs to be smoothed. The path-smoothing effect of the simulation experiment under the three maps is shown in Figure 10.
It can be seen from the figure that the third-order Bessel curve can deal well with the problem of planning-path twists and turns. Through the smooth processing of the planned path, the point of turning mutation in the path is replaced by a curve, which satisfies the kinematic law of the robot system and makes the autonomous movement of the robot more stable.

4. Real-World Experiment

4.1. Mining Inspection Robot Platform

In order to further verify the effectiveness of the path-planning algorithm of the mining inspection robot, a real-world experiment is carried out. In view of the fact that the mobile robot required in this paper mainly serves the internal channels of underground mining and takes into account the needs of inspection and some simple transportation, we choose a four-wheel differential robot with strong load, adapted to complex terrain, and is economical and efficient, as shown in Figure 11.
The hardware platform of the mining inspection robot is mainly composed of six modules. It is composed of a sensor module, drive module, power management module, total controller, input module, and human–computer interaction. The main hardware of the mining inspection robot in this experiment is introduced below:
(1)
Total controller
In this experiment, a TW-T600 industrial computer is selected as the core control unit of the robot, as shown in Figure 12. TW-T600 is developed by Tuwei Technology Co., Ltd.in Shenzhen, China. It is not only equipped with an IO port and USB port but is also equipped with a hard disk interface, network interface, and WIFI function. This experiment is equipped with a 512-core Volta GPU graphics processing unit centered on the Tensor center, which makes the visual effects of Rviz more intuitive and vivid. The equipment has excellent heat dissipation performance, mainly using aluminum alloy as the manufacturing material, and the bottom frame is pre-designed to be suitable for on-site installation. All performance meets the expected standards of this study.
(2)
Laser radar
This paper chooses RPLIDARA2 independently developed by Silan Technology Co., Ltd. in Beijing, China, as shown in Figure 13. Compared with similar two-dimensional laser radar on the market at home and abroad, this laser radar shows longer service life, lower cost, higher cost performance, and excellent stability.
(3)
Inertial measurement unit
In the experimental study, the HI219 inertial measurement unit developed by Supercore Electronic Technology Co., Ltd. in Beijing, China was selected, as shown in Figure 14. HI219 has the characteristics of low cost, high efficiency, small size, and low delay. The system adopts a new design concept and method, which encapsulates the whole system into a chip and integrates it into a circuit board. When the user is installing, there is no need to add additional expansion circuits. The installation process is simple and usually able to run continuously. Its excellent performance and efficiency can meet the needs of this experiment.
(4)
Servo driver
This study selected innovative servo drivers developed by Helishi System Integration Co., Ltd. in Beijing, China. As shown in Figure 15. The key control module of this product is composed of DSP newly developed by the TI company in the United States, which has excellent ‘dual-core’ processing function. It can not only work at low speed but also has high-speed performance. This device uses advanced full-number motor control technology to meet the needs of high-power motors. At the same time, it also has good anti-interference ability and protection performance. Encoders have taken appropriate protective measures when encountering various unexpected problems.

4.2. Experiment and Analysis

Due to the limitations of robot equipment and the experimental environment, it is impossible to carry out physical verification experiments in the actual underground mining environment. Therefore, Map 1 and Map 3 in the third-section simulation experiment are verified in the real world.

4.2.1. Simulated Environment 1

The underground mine environment is harsh, and the terrain is complex. In order to better simulate the underground mine, this experiment was carried out in a dark environment. The environment simulates Map 3 in the third section of the simulation experiment, as shown in Figure 16. The intersection of the roadway is simulated by the combination of the long frame and the white board. For the narrow feasible area in the roadway, the white board is separated into a 1.2 m wide fork road to simulate the scene through the narrow road. At the same time, cartons are set in the laboratory environment to simulate obstacles in the roadway.
As shown in Figure 17, the trajectory of the robot is displayed on the Rviz visualization platform. The red line segment is the starting point, and the actual motion path of the inspection robot is the green line. It can be seen from the path shown above that the improved optimization algorithm used in this paper can effectively plan an efficient and smooth path to avoid obstacles, so as to guide the robot to reach the preset destination successfully.
The actual path length of the inspection robot from the starting point to the end point is 12.68 m, and the time required is 36.75 s. Among them, the inspection robot has a relatively stable speed in the absence of obvious turning paths. In the turning area, due to the friction between the tire and the ground, the speed of the robot is significantly reduced during the steering process. However, in general, the robot can maintain high operating efficiency throughout the operation and can maintain good driving performance in complex environments and conditions.

4.2.2. Simulated Environment 2

Simulation environment 2 is simulated according to Map 1 in the experiment, and a complex roadway is simulated, as shown in Figure 18. The map was simulated by placing cartons and tables.
In this paper, the improved RRT and PRM algorithms are combined to write the path-planning program of the mining inspection robot, and the theoretical path-planning line under simulated environment 2 is obtained, as shown in Figure 19. It can be seen from Figure 19 that the path-planning program has obtained the shortest inspection route without collision.
The actual path length of the inspection robot from the starting point to the end point is 9.82 m, and the time required is 23.32 s. Among them, the time taken for the inspection robot to complete the overall path is significantly shorter than that of environment 1, which is due to the fact that the floor is a smoother plane, and the friction is smaller when advancing and turning, but in the actual underground mining environment, the terrain is more complex.
In this section, the performance test of the path-planning system of the mining inspection robot with different path-planning conditions was carried out under two environmental conditions. The test results show that the path-planning system of the mining inspection robot designed in this paper can quickly and accurately obtain the shortest inspection line under different environment, and the machine can complete the inspection work according to the path-planning results.

5. Conclusions

This document examines the issue where the RRT path-planning algorithm readily aligns with the local optimum, and the rate of convergence becomes sluggish when employing the underground mine inspection robot in the mine’s unstructured setting. A path-planning algorithm combining improved RRT and PRM is proposed, and the improved RRT algorithm is based on fan-shaped target orientation and environmental-adaptive step size. In contrast to the comparison algorithm, the improved RRT algorithm shortens the path length by 10.74% on average, reduces the number of inflection points by 69.99% on average, and increases the planning success rate by 17.55% on average. Simulation findings conclusively demonstrate that the overall performance of the improved RRT algorithm is better than the original algorithm and other improved algorithms in the environment of simulating some roadways. Finally, it was verified by real-world experiments. Consequently, the enhanced algorithm introduced in this document can effectively improve the optimality of trajectory selection, improve sampling efficiency and planning rate, and provide ideas for the work of underground inspection environment in narrow and complex roadways.
However, there are also shortcomings in this paper. The fusion algorithm of FGA-RRT and PRM is suitable for static-obstacle environments. However, due to the more complex internal environment of the mine in reality, there are dynamic obstacles. In future research, we can combine the dynamic obstacles and fully consider the influence of uncertain factors to analyze and verify, so as to further improve the applicability of the algorithm.

Author Contributions

Conceptualization, J.W. and R.L.; methodology, J.W.; software, J.W.; validation, J.W., R.L. and L.Z.; formal analysis, J.W.; investigation, L.Z.; resources, L.Z.; data curation, J.W., R.L. and L.Z.; writing—original draft preparation, J.W.; writing—review and editing, J.W., R.L. and L.Z.; visualization, J.W.; supervision, L.Z.; project administration, L.Z.; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (grant number: 51209167,12002251).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are available upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. The traditional RRT extended-node method.
Figure 1. The traditional RRT extended-node method.
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Figure 2. Sampling point selection principle diagram, where xrand is the sampling point, goal is the goal point, θ is the offset angle, α is the angle to the x-axis, and xnew is a new node obtained by step expansion with a certain step size.
Figure 2. Sampling point selection principle diagram, where xrand is the sampling point, goal is the goal point, θ is the offset angle, α is the angle to the x-axis, and xnew is a new node obtained by step expansion with a certain step size.
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Figure 3. Bridge detection algorithm diagram.
Figure 3. Bridge detection algorithm diagram.
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Figure 4. The fitting results of the Bessel curve.
Figure 4. The fitting results of the Bessel curve.
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Figure 5. Simulated maps. (a) Map 1; (b) Map 2; (c) Map 3.
Figure 5. Simulated maps. (a) Map 1; (b) Map 2; (c) Map 3.
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Figure 6. The average time to generate the initial path. (a) The average time of generating the initial path with different steps in Map 1; (b) the average time of generating the initial path with different steps in Map 2; (c) the average time of generating the initial path with different steps in Map 3.
Figure 6. The average time to generate the initial path. (a) The average time of generating the initial path with different steps in Map 1; (b) the average time of generating the initial path with different steps in Map 2; (c) the average time of generating the initial path with different steps in Map 3.
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Figure 7. The path-planning results of Map 1. (a) Traditional RRT algorithm; (b) EP-RRT* algorithm; (c) FGA-RRT and PRM fusion algorithm.
Figure 7. The path-planning results of Map 1. (a) Traditional RRT algorithm; (b) EP-RRT* algorithm; (c) FGA-RRT and PRM fusion algorithm.
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Figure 8. The path-planning results of Map 2. (a) Traditional RRT algorithm; (b) EP-RRT* algorithm; (c) FGA-RRT and PRM fusion algorithm.
Figure 8. The path-planning results of Map 2. (a) Traditional RRT algorithm; (b) EP-RRT* algorithm; (c) FGA-RRT and PRM fusion algorithm.
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Figure 9. The path-planning results of Map 3. (a) Traditional RRT algorithm; (b) EP-RRT* algorithm; (c) FGA-RRT and PRM fusion algorithm.
Figure 9. The path-planning results of Map 3. (a) Traditional RRT algorithm; (b) EP-RRT* algorithm; (c) FGA-RRT and PRM fusion algorithm.
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Figure 10. Third-order Bessel curve smoothing diagram. (a) Map 1; (b) Map 2; (c) Map 3.
Figure 10. Third-order Bessel curve smoothing diagram. (a) Map 1; (b) Map 2; (c) Map 3.
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Figure 11. Mining inspection robot.
Figure 11. Mining inspection robot.
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Figure 12. TW-T600 industrial computer.
Figure 12. TW-T600 industrial computer.
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Figure 13. RPLIDARA2.
Figure 13. RPLIDARA2.
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Figure 14. Inertial measurement unit.
Figure 14. Inertial measurement unit.
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Figure 15. Servo driver.
Figure 15. Servo driver.
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Figure 16. Real-world simulated environment 1. (a) Front; (b) back.
Figure 16. Real-world simulated environment 1. (a) Front; (b) back.
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Figure 17. The actual path of the robot in environment 1.
Figure 17. The actual path of the robot in environment 1.
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Figure 18. Real-world simulated environment 2. (a) Front; (b) back.
Figure 18. Real-world simulated environment 2. (a) Front; (b) back.
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Figure 19. The actual path of the robot in environment 2.
Figure 19. The actual path of the robot in environment 2.
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Table 1. Combination of different step coefficients.
Table 1. Combination of different step coefficients.
Combination123456
Non-narrow channel234456
Narrow channel454678
Table 2. The influence of different step coefficient combinations on the efficiency of the RRT algorithm.
Table 2. The influence of different step coefficient combinations on the efficiency of the RRT algorithm.
Time (s)Map 1Map 2Map 3
Combination 112.0610.539.14
Combination 29.847.648.23
Combination 39.767.517.30
Combination 46.764.697.05
Combination 511.5610.5213.52
Combination 615.9514.8617.56
Table 3. Comparison of experimental results of Map 1 planning efficiency.
Table 3. Comparison of experimental results of Map 1 planning efficiency.
AlgorithmPath-Planning LengthInflection PointsRate of Success
Traditional RRT80.5916.363%
EP-RRT*71.5211.578%
FGA-RRT and PRM fusion67.723.294%
Table 4. Comparison of experimental results of Map 2 planning efficiency.
Table 4. Comparison of experimental results of Map 2 planning efficiency.
AlgorithmPath-Planning LengthInflection PointsRate of Success
Traditional RRT79.6814.266%
EP-RRT*75.5312.685%
FGA-RRT and PRM fusion66.533.595%
Table 5. Comparison of experimental results of Map 3 planning efficiency.
Table 5. Comparison of experimental results of Map 3 planning efficiency.
AlgorithmPath-Planning LengthInflection PointsRate of Success
Traditional RRT78.1513.690%
EP-RRT*74.3410.792%
FGA-RRT and PRM fusion70.554.898%
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Wu, J.; Zhao, L.; Liu, R. Research on Path Planning of a Mining Inspection Robot in an Unstructured Environment Based on an Improved Rapidly Exploring Random Tree Algorithm. Appl. Sci. 2024, 14, 6389. https://doi.org/10.3390/app14146389

AMA Style

Wu J, Zhao L, Liu R. Research on Path Planning of a Mining Inspection Robot in an Unstructured Environment Based on an Improved Rapidly Exploring Random Tree Algorithm. Applied Sciences. 2024; 14(14):6389. https://doi.org/10.3390/app14146389

Chicago/Turabian Style

Wu, Jingwen, Liang Zhao, and Ruixue Liu. 2024. "Research on Path Planning of a Mining Inspection Robot in an Unstructured Environment Based on an Improved Rapidly Exploring Random Tree Algorithm" Applied Sciences 14, no. 14: 6389. https://doi.org/10.3390/app14146389

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