Robot Navigation in Forest Management Based on Graph

This paper reports on an application of robotics to the management of a trees intended for eventual harvest. Such management requires periodic cutting extraneous growth around the trees. We proposes the trajectory computation for guidance of the robot in the forest is carried out based on a weighted undirected graph G with trees as vertices. The graph to be used in the navigation system is ( ) , the line graph of G. The vertices of ( ) represent the midpoints of the edges of and the midpoints of each tree pair. The ( ) would be safety paths for the robot pass through. Our robot was able to follow a part of the trajectory computed in experimental forest, thus demonstrating the feasibility of forest maintenance by an autonomous.


Introduction
The application of robotics in management of forest resources is well-established [1].Especially, improvements in Simultaneous Localization and Mapping (SLAM) techniques allow for the automatic creation of a precise forest inventory that includes individual tree locations trunk diameters, and tree height [2,3].Such these applications have been introduced to increase productivity, enhance safety and in some cases, to compensate for the lack of available forest workers.However, there are not so many discuss the automation about a work with travelling on a rough terrain.Particularly, eliminate weed plants work aimed at promoting the growth of trees must be periodic performed.Currently, it have been done manually.Such work have being placed large labor on the employees, so it is expected that introducing the autonomous land vehicle in forest management.[4].This paper reports an application of robotics to the maintenance of trees and forest intended for eventual harvest.The weeding robot our focused is required to have a mechanism for weeding, and traveling in the forest without damage to the tree.Navigation is most challenging part of this process.A navigation system is requires 1) localization, 2) path planning and 3) path-following with obstacle avoidance.This paper assumes that the localization is achieved by using GPS, and mentions regard for the path planning method and the path-following with obstacle avoidance behavior.In the path planning, we propose using trees consisting a forest as a landmark.Trees are resources that the subjects of management, its location will unchanged in long period of time.Trees are resources that the subjects of management, its location will unchanged in long period of time.Using a SLAM techniques or a identify locations of each tree by GPS will allow for utilizing in a navigation system.There are not many changes in short term, so the landmark based map would be created at low labor.Therefore, in this research, we made the landmark based map in advance of the robot entrances into the forest.Therefore，in this research, we made the landmark based map in advance of the robot entrances into the forest.The map contains only position information of each tree without other objects (i.e.rocks or any obstacles).The path planning is performed by a graph consisted by the individual trees as vertices.We have been developed the robot having reactive pathfollowing with obstacle avoidance behavior system.We show how it can be done and report on an experiment using our method in the setting of a small experimental forest located on the campus of the Kyushu Institute of Technology.

Computing the trajectory based on graph
Computation of a trajectory in a forest to make it follow the robot would be facilitated by treating the tree as vertices in a graph.Trees can be represented by a graph = ( , where is the set of vertices and is the set of edges [5]．A vertex represents an individual tree, and and edge ∈ joining vertices and represents a path between trees．The graph used in the robot's trajectory is ( the line graph of .A line graph is a graph having vertices that correspond one-toone to edges in G, and connected two vertices of line graph corresponding to adjacent two edges [6] ． In constructing the trajectory, we superimposed the natural geometry over the line graph, considering the position of the vertices of L(G) to be the midpoints of the edges of G．If the case of G with an Eulerian property, all vertices in G have even degrees, and an Euler circuit can be found.In addition, a Hamilton circuit can be used to represent the vertices in the line graph corresponding to the order to follow the edges in the Eulerian graph [6,7].To ensure the existence of Hamiltonian circuit in ( the graph will be made to be Eulerian.Any line of sight path between two trees can define an edge of so there are sufficiently many choices of edges to allow for obtaining an Eulerian graph.Every pair of trees between which there is an unobstructed path in the forest that would allow the robot to navigate safety could contribute an edge. In large scale forest applications it might be advisable to divide the trees into sections and treat each one separately.Criteria for subdividing the forest would naturally include section sizes, location of robot staging areas, and terrain issues such as steepness and presence of potential obstacles (e.g., rocks).For example, there were 3000 trees in the forest, it could be subdivided into 150 clusters each containing 20 trees.Such a subdivision would allow for simplifying the computation of the robot's trajectory.We created a set of graphs containing several trees as vertices, and created a high-level graph consisted these as vertices, as shown in Fig. 1.

Forestry Robotic System "SOMA"
The autonomous robot "SOMA" shown in Fig. 2 is built on the platform of an All-Terrain Vehicle (ATV).An ATV was chosen for its robust design for outdoor use in rough terrain.The power source is 90cc gasoline engine.The throttle, brake lever and steering are controlled by DC motors to propel the robot.The weeding operation is realized by a specialized mechanism attached to the front of the ATV.Included sensors are RTK-GPS for localization，IMU in order to measurement the robot's heading，rotary encoder to measure the velocity，and RGB-D camera is to recognize an surrounding external situation．The final dimensions of the robot are 0.9×1.4× 1.2m (Width × Length × Height).It is sufficiently smaller than a standard planting interval (2.5m), and allows for the robot to enter the interior of a forest.

Autonomous Moving System
The overview of the system is shown in Fig. 3.In this research, the robot moves on two dimensional plane, and its state vector in the discrete time is represented by = [ , , ].Here, , represent a location of the robot obtained by RTK-GPS, and is the robot's heading measured by IMU.The control input is represented by = [ , ], is steering angle and is a moving velocity．Each actuator control systems are built on another CPU in order to improve development efficiency.The navigation system is consisted by three subsystems as follows.
External situation recognition Search secure trajectories Determine the control input for path following Each subsystem are described below.

External Situation Recognition
The robot recognizes the external situation via the point cloud obtained from the RGB-D camera.We are using R200 (Intel Corporation) for our vision system.Figure 4 shows the procedure from the point cloud to the obstacle recognition around the robot.First, after acquiring the point cloud, performing the noise remove processes.Then each three-dimensional point is projected on the xz plane.Next, the clustering process of points is performed based on euclidean distance between each point, finally, obstacle boundaries approximated to rectangular are obtained.

Search secure trajectories based on State Space Sampling
After recognition the external situation, searching secure trajectories capable avoiding collision with obstacles is performed based on State Space Sampling method.State Space Sampling method creates a set of terminal state vector on an arc around the robot, and a set of control input allowing for reach to these state vectors are also computed [10].The searching space of it is defined by a shape parameter .The details of the procedure of sampling the terminal state vectors and are see [8].In this research, as shown in Fig. 5, The set of control input [ , … , ] that ensured safety is extracted via applying State Space Sampling to the local coordinate of the robot.

Determine the control input for path following
Pure Pursuit algorithm [9] is used make the robot follow the desired path based on graph described in Section 2. In each discrete time, the destination point is set on an edge in desired paths.The control input which the robot could follow the path is obtained, however it is not always output because of the obstacle avoidance behavior is high priority more than path-following.In many situations, obstacles exist surrounding the robot.Therefore, the robot should be took detour and return to paths.In the system, the final control input to propel the robot is determined by the cost function shown in Eq. ( 1) and ( 2).

Experimental results
The experimental forest on the campus of the Kyushu Institute of Technology consists of 39 trees spread over a 35×35 meter square.There are no objects other than trees.The maximum degree of slope is about 5°.
Based on these dimensions and the width of the path between trees, an undirected graph was developed, as shown in Fig. 6.The adjacencies represent pairs of trees at a line-of-sight distance from each other.We created three graphs using by trees having label shown in Table .1 as for graphs of lower layers.As shown the experimental results (Fig. 8), the robot traverses around each graph in low layer, and performed transition between the graph and adjacent graph of its.These suggests it is feasible The result suggest it is feasible that the robot will be able to traverse a whole of forest by subdividing to small scale region and based on reactive motion control.

Conclusion
In this paper reported we have demonstrated the feasibility of designing an autonomous forestry robot to service trees meant for eventual harvest.A paths for an autonomous robot to follow can be computed based on graph from initial geographic map of trees in a forest.In the future work, we will improve the accuracy of pathfollowing to decline the error between trajectories and desired paths.

Table 1 .
Trees used in each graph