The paper presents results of research on inverse kinematics algorithms to be used in a functional model of a cucumber harvesting robot consisting of a redundant manipulator with one prismatic and six rotational joints (P6R). Within a first generic approach, the inverse kinematics problem was reformulated as a non-linear programming problem and solved with a generic algorithm. Solutions were easily obtained, but the considerable calculation time needed to solve the problem prevented on line implementation. To circumvent this problem, a second, less generic approach was developed consisting of a mixed numerical-analytic solution of the inverse kinematics problem exploiting the particular structure of the P6R manipulator. This approach facilitated rapid and robust calculation of the inverse kinematics of the cucumber harvester. During the early stages of the cucumber harvesting project, this inverse kinematics algorithm was used to off-line evaluate the ability of the robot to harvest cucumbers using 3D-information of a cucumber crop obtained in a real greenhouse. Thereafter, the algorithm was employed successfully in a functional model of the cucumber harvester to determine if cucumbers were hanging within the reachable workspace of the robot and to determine a collision-free harvest posture to be used for motion control of the manipulator during harvesting.
van Henten, E. J., Schenk, E. J. J., van Willigenburg, L. G., Meuleman, J., & Barreiro, P. (2008). Collision-free inverse kinematics of a 7 link cucumber picking robot. Acta Horticulturae, 801, 579-586. https://doi.org/10.17660/ActaHortic.2008.801.65