# Collision-Free Motion Planning of a Six-Link Manipulator Used in a Citrus Picking Robot
###### Abstract  
This paper presents the results of a motion planning algorithm that has been used in an intelligent citrus-picking robot consisting of a six-link manipulator. The real-time performance of a motion planning algorithm is urgently required by the picking robot. Within the artificial potential field (APF) method, the motion planning of the picking manipulator was basically solved. However, the real-time requirement of the picking robot had not been totally satisfied by APF because of some native defects, such as the large number of calculations used to map forces into torques by the Jacobian matrix, local minimum trap, and target not reachable problem, which greatly reduce motion planning efficiency and real-time performance of citrus-picking robots. To circumvent those problems, this paper proposed some novel methods that improved the mathematical models of APF and directly calculates the attractive torques in the joint space. By using the latter approach, the calculation time and the total joint error were separately reduced by 54.89% and 45.41% compared with APF. Finally, the novel algorithm is presented and demonstrated with some illustrative examples of the citrus picking robot, both offline during the design phase as well as online during a realistic picking test. citation: [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Collision-Free Motion Planning of a Six-Link Manipulator Used in a Citrus Picking Robot. _Appl. Sci._**2021**, _11_, 11336. [[https://doi.org/10.3390/appl12311336](https://doi.org/10.3390/appl12311336)]([https://doi.org/10.3390/appl12311336](https://doi.org/10.3390/appl12311336))  
Academic Editor: [PERSON]  
Received: 8 November 2021  
Accepted: 25 November 2021  
Subscribed: 30 November 2021  
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**Published in: 11 July 2021  
process motion planning problems, and the related algorithms include RRT*, Informed-RRT, RRT-Connect, and so on. RRT gives a path in the workspace by randomly walking and continuously expanding its leaf nodes. This process will not end till the leaf nodes spread throughout the whole workspace, so this algorithm usually takes a long time and is not suitable for a picking robot because of the real-time requirement. Generally, RRT has a good effect on the motion planning problem of mobile vehicles, but it is not feasible to directly use RRT for a manipulator in Cartesian space, because a manipulator cannot be regarded as a single particle. Therefore, some scholars proposed to adopt RRT to carry out motion planning in the configuration space (C-space) of manipulators, in which a point represents a single configuration instance. RRT divides C-space into free and obstructed space and carries out motion planning in the free space. Because a picking robot works in an unstructured and greatly complex environment with many obstacles, the C-space construction of a manipulator would take an extremely long time. From the existing literature, PRM and A* algorithms also need to build C-space, so RRT, PRM, and A* cannot meet the real-time requirements of a picking robot. The neural network algorithm not only needs a long time to train itself, but also has higher requirements on hardware, so it cannot be used for real-time motion planning of a picking robot as well. APF was firstly proposed by [PERSON] [23] in 1986 and was applied to real-time dynamic obstacle avoidance motion planning of a manipulator, PUMA560, and a mobile vehicle. APF plans the motion by building a virtual potential field in the workspace which is a Cartesian space, in which moving objects are affected by two kinds of forces--attractive force, and repulsive force--and avoid crashing into obstacles during the process of moving from the initial to the target position. Different from global planning algorithms such as RRT and PRM, APF is a local motion planning algorithm with low algorithm complexity, low dependence on computer resources, and strong real-time performance.