Navigation of Apple Tree Pruning Robot Based on Improved RRT-Connect Algorithm

Abstract

Pruning branches of apple trees is a labor-intensive task. Pruning robots can save manpower and reduce costs. A full map of the apple orchard with collision-free paths, which is navigation planning, is essential. To improve the navigation efficiency of the apple tree pruning robot, an improved RRT-Connect algorithm was proposed. Firstly, to address the disadvantage of randomness in the expansion of the RRT-Connect algorithm, a goal-biased strategy was introduced. Secondly, to shorten the path length, the mechanism of the nearest node selection was optimized. Finally, the path was optimized where path redundancy nodes were removed, and Bezier curves were used to deal with path sharp nodes to further reduce the path length and improve the path smoothness. The experimental results of apple orchard navigation show that the improved algorithm proposed in this paper can cover the whole apple orchard, and the path length is 32% shorter than that of the RRT-Connect algorithm. The overall navigation time is 35% shorter than that of the RRT-Connect algorithm. This shows that the improved algorithm has better adaptability and planning efficiency in the apple orchard environment. This will contribute to the automation of orchard operations and provide valuable references for future research on orchard path planning.

1. Introduction

Pruning branches is a very important part of orchard production operations. Due to the expansion of area planted with apple trees and the low level of intelligence and automation in orchards, fruit tree pruning is more time-consuming and labor-intensive [1,2]. The cost of fruit production is increasing as labor costs increase, which gradually reduces the market competitiveness of agricultural products. Automatic navigation technology of agricultural machinery is one of the core technologies of intelligent agricultural equipment and one of the solutions to the above problems. Among them, navigation path planning is the basis for achieving navigation and tracking control of agricultural machines. The lowest operating cost (e.g., total operating distance, operating time, energy consumption, etc.) is usually the goal to provide a better obstacle-free operating path for automatic navigation in the pre-operating area. Reasonable navigation path planning can reduce the total operating path, redundant coverages, and improve the operating efficiencies of agricultural machinery [3,4,5,6]. Under complex and changing operating conditions, excellent navigation planning not only increases the efficiency of operations but also contributes to their quality.

The emergence of apple tree pruning robots liberates labor, reduces production costs, and improves the competitiveness of agricultural products. Apple orchard navigation is a path-planning process based on information about apple orchards to find a path that connects the origin point to the target point while avoiding collisions with obstacles. In terms of orchard navigation, there are now mainly track navigation and human-controlled driving, with very little research on autonomous navigation. A sweet pepper harvesting robot travels along a set track in a greenhouse [7]. An apple-picking robot walks under human control in a trained orchard [8]. The mobile platform for grapevine pruning travels through the vineyard under human control and covers the vines completely [9]. Autonomous navigation in a kiwifruit orchard does not discuss obstacle avoidance but simply makes the robot cover the entire kiwifruit orchard in an ideal state without any obstacles and with a smooth surface [10]. Li et al. [11] performed navigation path planning for densely planted jujube gardens based on the joint improved A* and DWA algorithms. However, the experiment was only performed indoors, and there was no obstacle avoidance function. Therefore, apple pruning robot for orchard navigation has a wide market demand and research value.

The quality of the path, the running time of the algorithm, and the success rate of the planning are the main indicators to judge the performance of the navigation algorithms [12,13,14]. Dijkstra algorithm, A*, DWA, RRT, and genetic algorithms are some of the common classical path planning algorithms [15,16,17,18,19,20]. However, these algorithms have problems such as either long computation time, weak obstacle avoidance ability, or prone to local convergence and non-globally optimal paths, and need targeted improvements before they can be applied to the navigation of apple orchards. Dirik and Kocamaz [21] found that samples close to obstacles and paths with sharp turns in path planning do not make them effective in real-time path tracking applications. To overcome this limitation, a combination of RRT and Dijkstra algorithm was proposed. Compared to the basic RRT algorithm, due to the combination of Dijkstra and RRT, the total length of the path is reduced while the time for path planning is extended. Garip et al. [22] proposed a hybrid algorithm based on particle swarm optimization (PSO), firefly algorithm (FA), and cuckoo search (CS). The algorithm succeeded in shortening the paths and improving the path quality to some extent, but it did not smooth the paths to facilitate realistic robot walking, nor did it discuss the algorithm’s computation time, and the efficiency improvement was not persuasive enough.

The essence of path planning is the problem of obtaining an optimal or feasible solution under several constraints [23]. Among the various algorithms for motion planning, sampling-based algorithms can improve planning efficiency through sampling to avoid the complex computational problems caused by other algorithms in complex environments, such as Probabilistic Roadmap (PRM), Rapidly Exploring Random Trees (RRT), Bidirectional Random Trees (Bi-RRT), and Bidirectional Random Trees with Greedy Strategies (RRT-Connect) and other sampling-based algorithms [24,25,26].

Bi-RRT algorithm is extended by generating two trees with the origin point and the target point as root nodes. This algorithm allows the search tree to grow towards each other half of the time and grows randomly half of the time. It can speed up the execution of the algorithm, but the extension is still random. RRT-Connect introduces the idea of greedy expansion along with two-way random search. It is possible to generate a number of new nodes in succession when the direction of expansion is not random but deterministic. Greedy expansion does not stop until a collision occurs or two search trees meet. The speed of connecting the nodes of the double random tree is greatly improved. The RRT-Connect algorithm plans paths in less time and with a higher success rate than sampling-based algorithms such as PRM, RRT, and Bi-RRT. However, the randomness of the expansion is still not improved, and there are many unnecessary nodes in the path.

Some improved algorithms were proposed to address the shortcomings of the RRT-Connect algorithm. Wang et al. [27] proposed an improved RRT-Connect algorithm to accelerate the convergence of path planning, which realized the simultaneous expansion of four trees. Although the algorithm improves the efficiency and shortens the time of path planning, the quality of the planned paths is poor. Zhao et al. [28] proposed a path-planning method based on RT-Connect and dichotomy. Although this method improves the quality of paths, it does not consider the efficiency of path planning. Zhang et al. [29] proposed an improved algorithm that combined the artificial potential field method and the RRT-Connect algorithm to solve the path planning problem for UAVs in complex static environments. The path planned by the improved algorithm is close to the optimal path, but the planned path is not smooth. Some improved algorithms have been proposed to address the shortcomings of the RRT-Connect algorithm, but no improved algorithm has been proposed for the complex environment of apple orchards, where there are obstacles and narrow passages that take into account both the efficiency and the quality of the path.

To address the problems of a complex apple orchard environment with obstacles and narrow passages, which mainly rely on manual pruning and low pruning efficiency, an improved RRT-Connect algorithm is proposed to improve the navigation efficiency and quickly plan a shorter collision-free path. Firstly, to address the problem of blind search of the RRT-Connect algorithm, a goal-biased strategy was introduced to enhance the goal orientation of the algorithm in the expansion process. Secondly, to shorten the path length, the mechanism of the nearest node selection was optimized. Finally, the path was optimized where path redundancy nodes were removed, and Bezier curves were used to deal with path sharp nodes to further reduce the path length and improve the path smoothness. The feasibility, superiority, and stability of the improved RRT-Connect algorithm were tested further based on the apple orchard map.

2. Materials and Methods

2.1. RRT-Connect

The RRT-Connect algorithm expands alternately by building two random trees at the start and target points; a greedy strategy is also introduced to further accelerate the convergence speed. The RRT-Connect algorithm searches the configuration space by expanding two fast-expanding random trees simultaneously from the initial configuration and the target configuration. During each iteration, one of the random trees is expanded first, and then another random tree is attempted to expand to the new node of the current random tree expansion, and a greedy strategy is executed. The two random trees, T₁ and T_2, are expanded alternately until the two random trees meet. This expansion with enlightenment makes the tree expansion greedier and more explicit, which makes the dual-tree RRT algorithm more effective than the single-tree RRT algorithm.

As shown in Figure 1 and Figure 2, two path search trees, T₁ and T₂, were constructed at the initial point x_init and the target point x_end, respectively. A random point x_rand was generated in the C-space of the robot. The point on T₁ with the smallest Euclidean distance from x_rand was found, denoted as x_near1, with the direction pointing to x_rand. A certain step size ρ was grown in that direction, and a new point x_new1 was generated. If x_new1 did not satisfy the obstacle constraint in C-space, the point was discarded to regenerate random points; if it did, the grown branch and the new point were added to the tree. The point on T₂ with the smallest Euclidean distance from x_new1 was calculated, denoted as x_near2, with the direction which points to x_new1. A certain step size was grown in that direction, and a new point x_new2 was generated. If the collision detection was passed, x_new2 was added to T₂. At the same time, the greedy strategy subroutine was started and continued to grow in the direction of x_new1 until it stopped when it encountered an obstacle or when the closest distance between two trees was less than a threshold. If an obstacle was encountered, T₂ stopped the greedy expansion and started generating a new node at random. Then, T₁ started expanding with the current termination point of T₂ as the target point, and a greedy strategy was executed until a collision occurred or two trees met. If a collision occurred, T₁ stopped the greedy expansion and started randomly generating a new node. The SWAP function was used to exchange the two trees and to continue the sampling process described above. If the distance between the two trees was less than the connection threshold, the connection point information was returned, and the path search was completed. The collision-free paths searched by the RRT-Connect algorithm were often not optimal due to the lack of clear goal orientation of the algorithm.

2.2. Goal-Biased Strategy

The sampling of the RRT-Connect algorithm is random and lacks directionality. To enhance the orientation of the algorithm, a goal-biased strategy was introduced so that the target points had a certain probability of being sampled by random points. The process of expansion with the goal-biased strategy is shown in Figure 3. In the process of expanding without implementing the greedy strategy, there was a certain probability of generating arbitrary random points x_rand. In the search tree T₁, x_near1 was closest to the random point x_rand. A new node x_new1 was generated at a distance of one step ρ along the direction of x_rand from x_near1. There was also a certain probability that the new node x_goal1 of the search tree T₂ was selected as a random point. At this time, in the search tree T₁, x_near2 was closest to x_goal1. A new node x_new2 was generated at a distance of one step ρ in the direction of x_goal1 from x_near2. The search tree T₂ performs the goal-biased strategy expansion in a similar way to T₁.

The probability parameter threshold p was first set, which took values from 0 to 1 (excluding 0 and 1). Each time a sampling point was obtained, a probability value f was first randomly generated by the rand () function. As shown in Equation (1), when p > f, the target point was selected as the random point, and the new node grew in the direction of the target point; otherwise, the random point was expanded arbitrarily. This ensures that the path moves toward the target point with a higher probability and also prevents the node expansion from falling into a dead zone. In complex multi-obstacle areas, obstacles can be avoided, and the expansion success rate can be improved. The larger the probability parameter threshold p is, the faster the path is found. However, it may take more time to avoid when there are many obstacles. Therefore, the value of the probability parameter threshold p needs to be selected reasonably. The selection of the value of p is described in Section 3.1.1.

$$x_{rand}=\{\begin{array}{cc}\hfill x_{goal},& if p>f\\ \hfill Random,& else\end{array}$$

(1)

2.3. Optimization for the Mechanism of Nearest Node Selection

After the new node x_new was generated, the node x_min with the shortest path cost connected to x_new was found in the neighborhood with x_new as the center and radius r, and x_min was selected as the parent node of x_new instead of x_near (Figure 4). The path cost is the path length of the initial point to x_new when the search tree T₁ grows or the path length of the target point to x_new when the search tree T₂ grows. The effect of path asymptotic optimization can be achieved to further shorten the path length and improve the navigation efficiency of the pruning robot with the optimization for the mechanism of nearest node selection.

2.4. Path Optimization

The RRT-Connect algorithm was optimized by introducing the goal-biased strategy and the optimization for the mechanism of nearest node selection, which was called GSRRT-Connect. It shortens the path length, reduces the planning time, and improves the efficiency of path planning. However, there are many fold lines with sudden angle changes in the path. Some nodes do not have obstacles between them, but the trajectory is curved. This leads to the presence of many unnecessary nodes and even sharp points in the middle. It is unsatisfactory path quality. In some environments with complex obstacles, obstacle constraints lead to generating more redundant points and sharp points at turns. This situation would increase the path length and even make it difficult for the robot to track the moving path. Therefore, a smoothing method was introduced to remove redundant points and smooth the twists and turns.

2.4.1. Pruning Process

The entire generated path was pruned. The redundant intermediate nodes were removed from the path to shorten the path length, and the path could also be smoothed to some extent. As shown in Figure 5, the black fillers are obstacles. The GSRRT-Connect algorithm successfully avoided obstacles and generated a valid path which consisted of nodes q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉, q₁₀, q₁₁, q₁₂, and q₁₃. The path connected by black lines was an unpruned path, which consisted of nodes q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉, q₁₀, q₁₁, q₁₂, and q₁₃. The redundant points were removed by pruning from the original path while avoiding obstacles. q₁ and q₃ were connected. If the line between q1 and q3 collided with an obstacle, q₂ and q₄ were connected. If q₂ and q₄ were connected and did not collide with an obstacle, q₃ was deleted. q₁ and q₄ were then connected. The line between q₁ and q₄ collided with the obstacle, then q₂ and q₅ were connected. If the line of q₂ and q₅ collided with an obstacle, q₄ and q₆ were connected. If the line between q₄ and q₆ collided with an obstacle, q₅ and q₇ were connected. If the line between q₅ and q₇ did not collide with an obstacle, q₆ was deleted. Analogously, the final path connected by red lines was obtained, which consisted of nodes q₁, q₂, q₄, q₅, and q₁₃. The pruning process is shown in Figure 6. This pruning method ensures that no local minima occur in a short period of time and guarantees asymptotic optimality.

2.4.2. Bezier Curve Smoothing Method

The pruned path still has fold points. In the actual apple orchard operation, the path planning needs to conform to the kinematic and dynamic constraints of robot walking. Therefore, the planned path should satisfy the requirement of smoothness and try to ensure that the planned path is the same as the actual operation route. Bezier curves [30] are mathematical curves applied to 2D and 3D graphs. The Bezier curve is characterized by the fact that the shape of the Bezier curve changes by adjusting the control points. When the angle of the turning point on the path was less than 150°, a quadratic Bezier curve fitting was performed to make the robot advance smoothly while unnecessary energy loss is reduced at the sharp points of the path. The expression of the nth Bezier curve is:

$$P\left(t\right)={\displaystyle \sum _{i=0}^n{P}_i{B}_{i,n}\left(t\right)} \left(t\in \left[0,1\right]\right)$$

(2)

$$B_{i,n}\left(t\right)=C_n^i{t}^i{\left(1-t\right)}^{n-i}=\frac{n!}{i!\left(n-i\right)!}{t}^i{\left(1-t\right)}^{n-i} \left(i=0,1,\mathrm{\dots },n\right)$$

(3)

where P_i is the control point of the Bezier curve, t is the Bezier curve parameter, and B_i,n(t) is the Bernstein polynomial.

The quadratic Bezier curve requires 3 points to be fitted. As shown in Figure 7, the path points were q₁, q₂, q₃, q₄, and q₅, and the turning points to be fitted were q₂ and q₃. In order to keep the fitted curve consistent with the original trajectory curve, two control points, P₀ and P₁, were selected in the line segments on both sides of the turning point q₂ in accordance with the requirements of the Bezier curve. The quadratic Bezier curve was fitted to each turning point, and finally, multiple Bezier curves were stitched together to obtain a smooth path.

The GSRRT-Connect algorithm further improves the path quality via the pruning process and the Bezier curve smoothing method. The whole improved algorithm is called GSORRT-Connect.

3. Results and Discussion

3.1. Computer Simulation

In order to verify the effectiveness and superiority of the improved RRT-Connect path planning algorithm proposed in this study, the RRT-Connect algorithm, GSRRT-Connect algorithm, and GSORRT-Connect algorithm were compared and simulated by MatLab in the environment as shown in Figure 8. Maps 1, 2, and 3 are all 500 × 500 in size. Map 1 is a simple map with relatively few obstacles and is used to verify the algorithm’s ability to search in a simple environment. Map 2 has a narrow passage, which is used to verify the algorithm’s ability to pass through the narrow passage. Map 3 is a cluttered environment with many obstacles arranged, which is used to test the algorithm’s searchability in a complex environment. The initial point location is set as [20,20], and the target point location is [480,480]. The simulation for this study was performed on a Windows 10 (Microsoft Inc., Redmond, WA, USA) operating system with an Intel(R) Core(TM) i5-8400 [email protected] GHz, 8 GB GPU GeForce GTX 1070 Ti, and 16 GB RAM.

3.1.1. Optimal Probability Parameter Threshold

In the new node expansion function of the improved RRT-Connect algorithm, a goal-biased strategy was introduced with a probabilistic parameter threshold p. The value of p has a large impact on path planning. The larger the value of p is, the easier it is to sample the target point as a random point and the faster the path is found. However, it may take more time to avoid obstacles when there are many obstacles. Therefore, experiments are needed to analyze the effect of the probability parameter threshold p on the planning time and planning success rate.

Simulation tests were performed within three maps. Taking into account time, when the maximum number of iterations reaches 8000, the planning is considered as a failure if the path is still not found. The results of the simulation tests are shown in

Table 1. The effect of probability parameter thresholds on the planning time and the success rate of planning.

p	Map 1			Map 2			Map 3
	Average Time/s	Success Rate	SD 1	Average Time/s	Success Rate	SD 1	Average Time/s	Success Rate	SD 1
0.1	1.43	100%	0.1950	9.28	100%	0.4152	16.33	100%	0.7199
0.2	1.03	100%	0.1595	7.89	100%	0.3640	14.11	100%	0.6595
0.3	0.99	100%	0.1576	6.66	100%	0.2579	13.40	100%	0.5849
0.4	0.95	100%	0.1194	4.52	100%	0.0948	10.24	100%	0.4561
0.5	0.93	100%	0.1086	5.63	100%	0.1166	15.54	100%	0.6736
0.6	0.91	100%	0.0901	5.95	100%	0.1952	19.45	100%	0.8118
0.7	0.98	100%	0.1565	6.75	100%	0.2728	24.89	100%	0.8709
0.8	1.03	100%	0.1779	10.28	98%	8.0709	28.86	100%	0.9113
0.9	1.08	100%	0.2074	13.50	95%	9.3226	33.47	100%	0.9967

¹ SD: standard deviation.

.

In a simple map environment, the planning time gradually decreases when p is in the range of 0.1 to 0.6. This is because there are fewer obstacles on the map. The larger the value of p is, the easier it is to move toward the target point and the shorter the planning time is. When p is in the range of 0.6–0.9, the planning time gradually increases. This is because there are obstacles in the map located on the line between the initial point and the target point, and when the value of p is too large, it takes more time to go around those obstacles. In the simple map, the planning time is shortest as p = 0.6.

In the narrow passage map, the planning time gradually decreases when p is in the range of 0.1–0.4. This is because the value of p increases, and the target point is moved toward. Thus, the target orientation is provided. However, the randomness of the algorithm is diminished by a large value of p, which leads to the search tree being more difficult to pass through narrow passages. When the value of p is in the range of 0.4–0.9, the planning time gradually increases. When p is in the range of 0.8–0.9, the values are too large, and path planning is prone to fail. In the narrow passage map, the value of p cannot be too large. The planning time is the shortest when the value of p is 0.4.

In the complex obstacle maps, the planning success rate is 100% in all cases. This demonstrates the effectiveness of the RRT-Connect algorithm with the goal-biased strategy in complex obstacle maps. When there are too many obstacles, the value of p is too large, which leads to a great increase in planning time. This map has too many obstacles and is cluttered, so the value of p for the shortest planning time is on the small side, which is 0.4. In the apple orchard map environment, there are few obstacles, such as branches, mud blocks, stones, and plastic films on the ground, and may even cross narrow passages. Thus, the value of p is taken as 0.5.

3.1.2. Performance Comparison of a Series of Algorithms

The goal-biased strategy and the optimization for the mechanism of nearest node selection were introduced into the RRT-Connect algorithm, which is called the GSRRT-Connect algorithm. The GSRRT-Connect algorithm can find navigation paths quickly and also shorten the path length compared to the RRT-Connect algorithm. However, the path quality is not stable. There are still redundant points and spikes on the path generated by GSRRT-Connect, which are not conducive to robot walking. In this study, the smoothing process was used to optimize the paths generated by GSRRT-Connect, which reduced redundant points and spikes. This algorithm is called the GSORRT-Connect algorithm. To objectively evaluate the superiority and effectiveness of the algorithms, three algorithms, RRT-Connect, GSRRT-Connect, and GSORRT-Connect, were used for path planning within three map scenarios. The most appropriate value of p was chosen in the corresponding map mentioned in Section 3.1.1. If a path is not found when the number of iterations reaches 8000, the planning is considered to have failed. The average search time, average path length, and success rate were recorded. Figure 9, Figure 10 and Figure 11 show the results of the algorithm running within the three maps. Figure 12 and Figure 13 show the boxplots of search time and path length within the three maps, respectively.

The algorithm runs as shown in Figure 9, Figure 10 and Figure 11. The path planning from the initial point to the target point can be completed excellently by the improved RRT-Connect algorithm, and a shorter and smoother path is obtained after the path optimization process. The improved RRT-Connect algorithm is especially able to pass through narrow passages with less time and has better narrow passage capability.

As shown in

Table 2. Simulation results of three algorithms in different maps.

Method	Result	Map 1	Map 2	Map 3
RRT-Connect	Average length	828.41	834.44	1066.65
	Average time/s	1.48	23.68	17.24
	Success rate	100%	100%	100%
GSRRT-Connect	Average length	728.79	743.71	1020.48
	Average time/s	0.97	5.59	13.26
	Success rate	100%	100%	100%
GSORRT-Connect	Average length	662.93	713.02	875.55
	Average time/s	1.32	5.81	13.93
	Success rate	100%	100%	100%

, the appropriate selection of p-values results in a success rate of 100% for both algorithms. Compared with RRT-Connect, the path lengths planned by GSRRT-Connect and GSORRT-Connect are reduced by 12% and 20%, respectively, in Map 1; in Map 2, the path lengths planned by GSRRT-Connect and GSORRT-Connect are reduced by 11% and 15%, respectively; in Map 3, the GSRRT-Connect and GSORRT-Connect planned path lengths were reduced by 4% and 18%, respectively. The effectiveness of the improved RRT-Connect algorithm for path shortening is demonstrated. The GSRRT-Connect algorithm is most effective in shortening paths within simple maps, secondary in narrow passage maps, and less effective in complex maps. This is because the more effective enhancing the goal orientation of the algorithm is for path shortening in maps with fewer obstacles, and the optimization for the mechanism of nearest node selection is more likely to work.

Compared with RRT-Connect, the planning time of GSRRT-Connect is reduced by 34% in map 1, by 76% in map 2, and by 23% in map 3. The superiority of the improved RRT-Connect algorithm in reducing the planning time is proved. Especially the time through narrow passages is greatly reduced. It shows that the improved RRT-Connect algorithm has a better capability to pass narrow passages. The fewer obstacles there are within the map, the more time is reduced. It shows that the goal-biased strategy and the optimization for the mechanism of nearest node selection play their proper role.

Compared with GSRRT-Connect, the path length planned by GSORRT-Connect is reduced by 9%, 4%, and 14% in maps 1, 2, and 3, respectively. Although the planning time of GSORRT-Connect is slightly increased compared to GSRRT-Connect, GSORRT-Connect compensates for the time by shorter path length and takes less time to reach the target point. Moreover, the search space of GSORRT-Connect is a narrow region that is very close to the GSRRT-Connect path, so less computation time is required to perform additional path optimization of GSRRT-Connect. The redundant nodes were eliminated, sharp points were smoothed, and path lengths were decreased by the pruning process and Bezier curve smoothing method successfully. The reduction in path length is positively correlated with the number of obstacles. This is due to the fact that the more obstacles there are, the more redundant and sharp points there are, and the more optimization process is needed to shorten the path length.

As shown in Figure 12 and Figure 13, no outliers appear in the boxplot of the improved RRT-Connect algorithm, and the distribution results are more concentrated. It shows that the improved RRT-Connect algorithm is more stable. It is clear from the above simulation experiments that the convergence speed, the quality of the path, and stability of the RRT-Connect algorithm are effectively improved by the improved RRT-Connect algorithm in this paper.

3.2. Field Experiments in an Apple Orchard

Path planning experiments were conducted in Ma’s apple orchard in Tongzhou district, Beijing, China. The internal environment is shown in Figure 14, with a horizontal spacing of 5 m and a vertical spacing of 3 m. The apple orchard is characterized by the presence of a steel frame. This steel frame is used to build light-permeable curtains to prevent birds from pecking at the apples and can be dismantled. Removal of the steel frame from the work area is required to conduct field trials.

To avoid collision between the pruning robot and apple trees during the walking process, a radius of 0.5 m was set as an obstacle area with the apple tree plant as the center. The two-dimensional map environment is shown in Figure 15. The black area is the obstacle area, the yellow point is the location of the apple tree, and the green area is the maximum canopy area of the apple tree.

The apple tree pruning robot, as shown in Figure 16, consists of a wheeled mobile chassis equipped with a 6-degree-of-freedom Yaskawa ES165N manipulator. The working space of the manipulator is a sphere with a radius of 3 m. The apple tree has a height of 2 m and a maximum crown radius of 1.5 m, with branches starting to grow at 0.5 m above the ground. The reach of the manipulator can cover the apple tree very well. The working space of the manipulator at 2.1 m above the ground is a circular area of 2 m radius. The navigation points are selected as shown in Figure 17a,b, where the red point is the navigation point of the robot, the blue area is the working space of the manipulator, and the green area is the area covered by the branches of the apple tree. The working space of the manipulator covers the apple tree well. In order to achieve full coverage of the apple orchard by the apple tree pruning robot, the apple orchard was partitioned. As shown in Figure 17c, each inter-row area of the apple orchard was set as a separate workspace. In each workspace, red points were used as navigation target points for the pruning robot and were numbered sequentially. In one workspace, the pruning robot sequentially traversed the navigation target points in that work area in numbered order and then moved to point 1 of the next workspace and continued to traverse each navigation target point by number. The apple tree pruning robot is considered to have completed full coverage of the apple orchard until all navigation target points in the workspace are traversed in the workspace.

Two work areas were selected for path planning experiments. The apple orchard has a few obstacles, such as bricks, stones, and fallen branches on the ground. The apple orchard map environment is shown in Figure 18, where black fillers are obstacles, yellow points are apple tree locations, the blue points are the initial navigation points in one work area, the red points are the final navigation points, and the green points are the intermediate navigation points that the apple tree pruning robot needs to pass through in turn. Taking into account the apple orchard map environment, the probability parameter threshold p was chosen as 0.5. Five algorithms, RRT-Connect, GSRRT-Connect, GSORRT-Connect, Informed-RRT*-connect [31], and A*, were used to perform path-planning experiments in this map environment. The results of the total path and the path planning workspace 1, workspace 2, and between workspaces are shown in

Table 3. Path planning results for the apple orchard.

Result	Method	Total Path	Workspace 1	Workspace 2	Between Workspaces
Calculation time/s	RRT-Connect	3.32	1.95	1.29	0.08
	GSRRT-Connect	2.76	1.57	1.07	0.12
	GSORRT-Connect	5.41	2.94	2.11	0.22
	Informed-RRT*-connect	6.03	3.59	2.13	0.31
	A*	8.72	4.93	3.36	0.43
Path length	RRT-Connect	2848.82	1515.78	1257.99	75.05
	GSRRT-Connect	2360.22	1248.92	1035.09	76.21
	GSORRT-Connect	1792.78	915.78	825	52
	Informed-RRT*-connect	1845.11	961.28	825	58.83
	A*	1895.87	1014.56	825	56.31

. The coefficients of variation of path length and calculation time are shown in

Table 4. Coefficient of variation for path length and computation time.

Method	Result	Workspace 1	Workspace 2
RRT-Connect	Computation time	0.0963	0.1413
	Path length	0.0652	0.0299
GSRRT-Connect	Computation time	0.0832	0.0578
	Path length	0.0531	0.0205
GSORRT-Connect	Computation time	0.0401	0.0190
	Path length	0.0165	0
Informed-RRT*-connect	Computation time	0.0633	0.0284
	Path length	0.0201	0
A*	Computation time	0.0716	0.0294
	Path length	0.0328	0

.

The path length and operation time are increased by the randomness of the RRT-Connect algorithm. Therefore, when the RRT-Connect algorithm is improved, its randomness should be weakened.

The GSRRT-Connect algorithm has less path length and less computation time in workspace 2 than in workspace 1. This is because there are no obstacles in workspace 2. The more obstacles there are, the more time is needed to search a path within the map, and the path length increases. Compared with the path length and computation time of RRT-Connect, the GSRRT-Connect algorithm reduces 17% and 19% in workspace 1 and 18% and 17% in workspace 2, respectively. It shows that the GSRRT-Connect algorithm has stronger adaptability and search capability in the presence of obstacles. GSRRT-Connect successfully enhances the goal orientation and reduces the path length and computation time.

Compared to RRT-Connect and GSRRT-Connect, GSORRT-Connect adds a little more time to the calculation time. GSORRT-Connect compensates for a time by a shorter path length and takes less time to reach the target point. Compared to the path length of RRT-Connect and GSRRT-Connect, the GSORRT-Connect algorithm reduces the path length by 40% and 27% in workspace 1 and 34% and 20% in workspace 2, respectively. The path optimization successfully eliminates redundant nodes and reduces the path length. Compared to Informed-RRT*-connect and A*, the total path length and total computation time of GSORRT-Connect are both reduced. The superiority of the GSORRT-Connect algorithm is illustrated.

The coefficients of variation of computation time and path length for both GSRRT-Connect and GSORRT-Connect are shorter than that of RRT-Connect. This is due to the enhanced targeting and reduced randomness of the improved RRT-Connect algorithm, which is more stable. The coefficients of variation of the improved algorithm in workspace 2 are all smaller than those in workspace 1. It indicates that the stability of the improved algorithm is better in the experiment when there are fewer obstacles. The coefficient of variation of the computation time of the RRT-Connect algorithm is larger in workspace 2 than in workspace 1. This seems to be due to the slightly stronger randomness of the RRT-Connect algorithm, which lacks the constraint of a small number of obstacles in workspace 2 and explores with abandon in an obstacle-free environment. The coefficients of variation of path lengths are all smaller than the coefficients of variation of calculation times. It indicates that the paths have better repeatability. In workspace 2, the coefficient of variation of path length for GSORRT-Connect is 0. It indicates that the optimized path obtained multiple times is the same path, which is likely to be the shortest path in workspace 2. Compared to Informed-RRT*-connect and A*, GSORRT-Connect has a lower coefficient of variation. This demonstrates that the GSORRT-Connect algorithm possesses better stability.

The inter-working area path is the path from the final navigation point in workspace 1 to the initial navigation point in workspace 2. The path length planned by the GSORRT-Connect algorithm is 1790.78, which is 37% shorter than that of the RRT-Connect algorithm. The improved RRT-Connect algorithm effectively improves the convergence speed, path quality, and stability in terms of overall path, workspace 1, workspace 2, and inter-work area paths. The experimental results show that the improved algorithm of this study has better adaptability and planning efficiency in the apple orchard environment.

The route diagram of path planning for the GSORRT-Connect algorithm is shown in Figure 19, where the blue line segment, red line segment, and green line segment are the planned paths of the robot in workspace 1, workspace 2, and between workspaces, respectively. As can be seen from Figure 19, the planned path traverses each navigation point in turn from the starting navigation point in workspace 1 and has a low path complexity to achieve full coverage of the apple orchard by the apple tree pruning robot.

The GSORRT-Connect algorithm, RRT-Connect algorithm, Informed-RRT*-connect algorithm, and A* algorithm were used to conduct orchard navigation experiments in an apple orchard environment, as shown in Figure 20.

The maximum walking speed of the pruning robot is 0.5 m·s⁻¹. The path lengths covered by the four algorithms and the time required by the pruning robot to complete the navigation and success rate in the two workspaces are shown in

Table 5. Navigation experiment data.

Algorithm	Path Length/m	Time/s	Success Rate
GSORRT-Connect	72.63	174	92.31%
RRT-Connect	106.95	267	73.01%
Informed-RRT*-connect	74.91	186	88.46%
A*	77.02	201	80.77%

. When the robot is unable to avoid obstacles, the navigational planning is considered a failure.

The coverage path, which is planned by the GSORRT-Connect algorithm, is 32% shorter compared to the RRT-Connect algorithm. The navigation time of the GSORRT-Connect algorithm is 174 s, which is 35% shorter than the RRT-Connect algorithm. The path length and navigation time of the GSORRT-Connect algorithm are both less than the corresponding data of the Informed-RRT*-connect algorithm and the A* algorithm. The success rate of all algorithms is not 100%, probably because the ground is not flat or the position information of the obstacles is not precise enough, while the paths planned are too close to the obstacles, which leads to the robot not being able to avoid obstacles. The GSORRT-Connect algorithm has the highest success rate of the four algorithms. This is because the GSORRT-Connect algorithm is characterized by asymptotic optimality, and most of the paths planned are close to the optimal path. Most of the navigation paths planned by the GSORRT-Connect algorithm have similarities, so the success rate is relatively high. It is further demonstrated that the global path planning method with the improved RRT-Connect algorithm proposed in this study effectively improves the global path planning efficiency of the apple tree pruning robot.

This study investigates the autonomous navigation of an apple tree pruning robot in an apple orchard to improve operational efficiency. However, apple tree pruning is selective pruning. In addition to the pruning robot traversing each apple tree, the end-effector of the pruning robot should also selectively prune branches on each apple tree. The combination of the two can greatly improve operational efficiency and reduce the labor requirement. Therefore, the path planning for selectively pruning branches of apple trees will be further investigated in the future. In addition, another important issue in the apple orchard is the removal of oversized fruit (only one should be left in the cluster, and it is the best). The issue has similarities with selective pruning of apple tree branches. In the future, this problem can be solved by drawing on the research experience of selective pruning of apple tree branches.

4. Conclusions

To improve the navigation efficiency of the apple tree pruning robot in an orchard located in a plain area, an improved RRT-Connect algorithm was proposed. To address the problem of blind search of the RRT-Connect algorithm, a goal-biased strategy was introduced to enhance the goal orientation of the algorithm in the expansion process. To shorten the path length, the mechanism of the nearest node selection was optimized. Finally, the path was optimized where path redundancy nodes were removed, and Bezier curves were used to deal with path sharp nodes to further reduce the path length and improve the path smoothness. Navigation efficiency and the quality of the path are both improved.

The effects of probability parameter thresholds on planning time and planning success were analyzed. Then, the optimal probability parameter threshold p was chosen as 0.6, 0.4, and 0.4 for simple, narrow passage, and complex environments, respectively. The simulation test results show that the path length is significantly shortened, and the path is smooth and continuous after the path smoothing process is used. The planning efficiency and quality of the paths of the basic RRT-Connect algorithm and the improved RRT-Connect algorithm were compared. The experiments show that the improved RRT-Connect algorithm has shorter planning time and higher quality and stability of paths.

Field experiments were conducted in the apple orchard. The improved RRT-Connect algorithm proposed in this paper can achieve full coverage of apple orchards by apple tree pruning robots with paths that are 32% shorter than the RRT-Connect algorithm. The overall navigation time is 35% shorter than that of the RRT-Connect algorithm. The path length and navigation time of the GSORRT-Connect algorithm are both less than the corresponding data of the Informed-RRT*-connect algorithm and the A* algorithm. The GSORRT-Connect algorithm had the highest success rate. It indicates that the improved algorithm has better adaptability and planning efficiency in the apple orchard environment.

In summary, the path planning method with the improved RRT-Connect algorithm proposed in this study effectively improves the navigation efficiency of the apple tree pruning robot.