Combinatorial Optimization and Performance Analysis of a Multi-arm Cartesian Robotic Fruit Harvester—Extensions of Graph Coloring

A mobile melon robotic harvester consisting of multiple Cartesian manipulators, each with three degrees of freedom, is being developed. In order to design an optimal robot in terms of number of arms, manipulator capabilities, and robot speed, a method of allocating the fruits to be picked by each manipulator in a way that yields the maximum harvest has been developed. Such a method has already been devised for a multi-arm robot with 2DOF each. The maximum robotic harvesting problem was shown there to be an example of the maximum k-colorable subgraph problem (MKCSP) on an interval graph. However, for manipulators with 3DOF, the additional longitudinal motion results in variable intervals. To overcome this issue, we devise a new model based on the color-dependent interval graph (CDIG). This enables the harvest by multiple robotic arms to be modeled as a modified version of the MKCSP. Based on previous research, we develop a greedy algorithm that solves the problem in polynomial time, and prove its optimality using induction. As with the multi-arm 2DOF robot, when simulated numerous times on a field of randomly distributed fruits, the algorithm yields a nearly identical percentage of fruit harvested for given robot parameters. The results of the probabilistic analysis developed for the 2DOF robot was modified to yield a formula for the expected harvest ratio of the 3DOF robot. The significance of this method is that it enables selecting the most efficient actuators, number of manipulators, and robot forward velocity for maximal robotic fruit harvest.