Globally optimal inverse kinematics method for a redundant robot manipulator with linear and nonlinear constraints

This paper presents a novel inverse kinematics global method for a redundant robot manipulator performing a tracking maneuver. The proposed method, based on the choice of appropriate initial joint trajectories that satisfy the kinematic constraints to be used as inputs for a multi-start optimization algorithm, allows for the optimization of different integral cost functions, such as kinetic energy and joint torques norm, and can provide solutions with a variety of constraints, both linear and nonlinear. Furthermore, it is suitable for multi-objective optimization, and it is able to find multiple optima with minimal input from the user, and to solve cyclic trajectories. Problems with a high number of parameters have been addressed providing a sequential version of the method based on successive stages of interpolation. The results of simulations with a three-Degrees-of-Freedom (DOF) redundant manipulator have been compared with a solution available in the literature based on the calculus of variations, thus leading to the validation of the method. Moreover, the effectiveness of the presented method has been shown when used to solve problems with constraints on joint displacement, velocity, torque, and power.