# Collision-Free Motion Planning of a Six-Link Manipulator Used in a Citrus Picking Robot
## 5 Conclusions  
To improve the efficiency and success rate of the intelligent citrus-picking robot, the motion planning problem of a manipulator--which was the core component of the citrus-picking robot--was studied in-depth, and a novel improved APF algorithm was proposed by improving the models of potential fields and forces of APF and designing some optimization strategies, which greatly reduced the calculation amount of its application in the process of motion planning of a manipulator. In this paper, the ETS method is used to model the kinematics of the EC63M manipulator, and the Jacobian matrix of each point on the manipulator relative to the base coordinate frame can be obtained easily by this model. The improved and original algorithms were both used to carry out the motion of the EC63M manipulator mounted on the intelligent citrus-picking robot. Compared with the original method, the improved one reduced the operation time by 54.89% and the total joint error by 45.41%. Therefore, the improved APF in this paper can not only  
Figure 16: The trajectory curves in picking simulation of the ICPR. (**a**) Joint trajectory of EC63M during picking stage; (**b**) Joint trajectory of EC63M during releasing stage; (**c**) Joint trajectory of EC63M during initialization stage.  
Figure 17: Experiment results of IAPF applied to ICPR. (**a**) Picking pose 1; (**b**) Picking pose 2; (**c**) Picking pose 3.  
effectively avoid the problems of the local minimum trap but also the target position not reachable problem existing in APF. Concisely, the improved APF has stronger real-time and accuracy performance. Furthermore, because the working environment of a citrus-picking robot is too complex, this paper used the PSE method to model the target citrus tree. The experimental results show that the PSE method can effectively reduce the calculation amount of motion planning for collision detection. Therefore, the improved APF mentioned in this paper is better than the original algorithm, concerning both real-time performances and the accuracy of the citrus picking robot. This paper presents the PSE method of the target citrus tree but does not explain the general situation for any other citrus tree, which will be the next research goal of our project team. In this experiment, we did not consider the impact on the branch directly attached to the fruit when detaching the citrus fruit from it and the optimal picking orientation of the gripper, and these matters will be part of our forthcoming research as well.  
Conceptualization, Z.T.; Methodology, Z.T.; Software, Z.T. and H.X.; Validation, Z.T., L.X. and H.X.; Formal analysis, Z.T., Y.W. and H.X.; Investigation, Z.T., Y.W. and Z.K.; Resources, L.X., Y.W. and Z.K.; Data curation, L.X.; Writing--original draft preparation, Z.T.; Writing--review and editing, Z.T., L.X. and Y.W.; Visualization, Z.T.; Supervision, L.X. and Y.W.; Project administration, Z.T. and L.X.; Funding acquisition, X.L. and Z.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Key R&D project of Science and Technology Department of Sichuan Province on Research and Development of an Intelligent Citrus Picking Robot, grant number 2020 YFN0025; Sichuan Provincial Department of Education Research on Key Technology of Manipulator Arm Motion Control of Citrus Picking Robot, grant number 2021 JDRC0091.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to restrictions of privacy and morality.  
The authors would like to thank the anonymous reviewers and the editor, whose comments and suggestions greatly improved this paper.  
The authors declare no conflict of interest.