Inverse kinematics of a 5-DOF hybrid manipulator

Control of any robotic system cannot be executed without a preliminary solution of the inverse kinematic problem. This problem implies determining the control actions of the actuators required to perform a given motion trajectory and embedded into the control system. The current study considers the inverse kinematics of a hybrid (parallel-serial) manipulator with five degrees-of-freedom (5-DOF). The article first briefly describes the manipulator structure, which includes 3-DOF parallel and 2-DOF serial parts, and then explains an algorithm for solving the inverse kinematics. The algorithm relies on the product-of-exponentials (PoE) formula applied to an equivalent manipulator with a serial structure. The proposed algorithm results in a closed-form solution with no assumptions about the manipulator geometry. A case study confirms the algorithm correctness. The method for solving the inverse kinematic problem can be adapted for other hybrid manipulators.