# Collision-Free Motion Planning of a Six-Link Manipulator Used in a Citrus Picking Robot
###### Abstract
However, APF has problems such as local minimum trap (LMT) [24; 25] and target not reachable problem (TNRP) [26]. LMT means that when the object has not reached the target position, the gradient of the potential field of APF disappears, then the resultant force becomes zero, and the object in the potential field no longer can reach the target position, which is the main problem and shortcoming of APF. TPNR refers to that when there is an obstacle near the target position, the attraction is far less than the repulsive force, and the object in the potential field cannot overcome the repulsive force to reach the target position under the action of the attractive force. TPNR is caused by the gradual loss of attractive force near the target position which is another main problem and shortcoming of APF. [PERSON], [PERSON] et al. [27] designed a non-minimum speed algorithm to improve APF, and the improved APF can effectively avoid the occurrence of the LMT. [PERSON], [PERSON] et al. [28] proposed a water sink model for path planning of planar robots aiming at solving LMT. Although the above studies have effectively avoided the LMT, the application object is a mobile vehicle rather than a manipulator, so it cannot be directly applied to a picking robot for real-time motion planning. A large number of scholars have also carried out lots of relevant studies on the application of APF in manipulators. [PERSON], [PERSON] et al. [26] improved the repulsive force calculation function of APF and combined it with the cosine adaptive genetic algorithm. Motion planning for the end effector of a 5-DOF manipulator needed 8.72 and 8.31 s respectively in conventional and LMT conditions, and the time was reduced by 51.6% and 53.85% compared with the original APF. [PERSON], [PERSON] et al. [20] took 103.421 s to carry out path planning for a dual-manipulator in a static environment based on the potential field of velocity, and the time was 16.85% less than that of APF. [PERSON], [PERSON] et al. [29] improved the APF algorithm based on the Jacobian matrix and carried out path planning for a 7-DOF manipulator to avoid spherical and cylindrical obstacles respectively, which both took 7 s, and the single iteration took 1.925 and 2.5 ms respectively. [PERSON] [30] combined RRT with APF and proposed a velocity potential field method for obstacle avoidance motion planning of manipulators based on virtual target points. It could effectively avoid falling into LMT, but the path planning for a planar 3-DOF manipulator took at least 4.15 s. [PERSON], [PERSON] et al. [31] improved the attractive potential field calculation formula of APF by introducing a Cartesian space boundary, but it took more than 5 s for path planning of self-designed 9-DOF manipulator to get very close to the target configuration. Although the above studies successfully applied APF to path planning of manipulators and effectively avoided the emergence of LMT, LMT, and TPNR were not considered at the same time. In addition, due to the high real-time requirements of a picking robot on the motion planning algorithm, the above research results are all time-consuming and cannot meet the real-time requirements of picking robots. Because of the problems mentioned above, this paper improved the calculation model of both potential fields and forces of APF respectively, and directly calculated the attractive torques in the joint space of a manipulator when planning the motion of a manipulator and proposed a novel improved APF (IAPF) which can effectively reduce the calculation time of motion planning for manipulators and avoid LMT and TPNR problems at the same time. Finally, the correctness and effectiveness of IAPF in manipulators were verified by some illustrative experiments both in the design and realistic picking phase.