# Position Selection and Collision-Free Path Planning for Fruit Picking Robots
## 1 Introduction
An algorithm called TO-RRT was proposed in [22], combining RRT and APF, utilizing a node-first search strategy to prevent the local minima problems caused by APF and employing the regression superposition algorithm to minimize computation time. The proposed algorithm was used for a citrus-picking robot. In [23], the IAPF was proposed, which is based on an artificial potential function incorporated with a sigmoid function element to avoid local minima. Despite various developments in orchard mapping, fruit detection, path planning and automated systems over the past 30 years, currently developed harvesting robots are considered less practical than manual harvesting in most applications [24]. Significant research has been conducted on fruit harvesting robots; however, the question of where a harvesting robot should be positioned to efficiently harvest a fruit or a cluster of fruits has been overlooked. In [25], a fully integrated system was implemented for autonomous citrus harvesting, but positioning it for harvesting specific target fruits still relied on manual intervention. The positioning of harvesting robots has not been sufficiently studied, as it often relies on manual placement by humans [26], is constrained by pre-defined and highly structured environments, such as planar orchards [27], or excludes target fruits that are inaccessible due to fixed robot bases locations and limited approach angles [28]. Placing robots in appropriate positions not only reduces the risk of harvesting failure and collisions with obstacles but also shortens path generation time [29]. Furthermore, it is inefficient to move the entire robot each time harvesting takes place, in contrast to manipulating the harvest from a fixed position [30]. The efficiency of the harvesting process can be increased by maximizing the number of fruits harvested from a single location with arm motions alone. This paper proposes a new approach to selecting an optimal position of a harvesting robot and the orientation of end-effector for harvesting multiple fruits based on an inverse reachability map. Pre-determining the position of the mobile manipulator and the orientation of the end-effector enables efficient harvesting of as many fruits as possible from a single position, without the need to move the entire system. With the proposed scheme, the success rate of harvesting can be increased, since it takes into account the manipulator workspace and obstacles in advance. This paper also proposes an algorithm for collision-free path planning for robot systems called the model predictive artificial potential field (MPAPF). Typically, path planning for a manipulator using APF involves calculating the gradient of the potential function acting on the end-effector and computing the torques applied to each joint using the manipulator Jacobian matrix. Alternatively, a grid-based method is employed, moving the end-effector to the point with the lowest potential value in the vicinity. These methods have a limitation in that it is difficult to account for the manipulator workspace or joint limits because the path planning is performed in the end-effector space. In MPAPF, by planning the path in joint space, singularities can be avoided and joint limits can be easily considered. Furthermore, the potential field is formed for multiple points on the manipulator, so MPAPF can avoid collisions between the entire manipulator and obstacles. Additionally, the risk of falling into a local minimum is reduced due to the complexity of the potential field. The positioning and path planning assumes that the locations of the tree and fruit are known in advance. The entire harvesting process was implemented in a simulator with a model of an orchard, and collision-free paths in complex environments were verified in experiments. The main contributions of this paper as follows:  
1. A new method to select the position of the robot base and the orientation for approaching a target fruit of the end-effector is proposed for increased efficiency and reduced risk of failure in harvesting. 2.