A Novel Algebraic Inverse Kinematics Based Approach to Gaze Control in Humanoid Robots

The vision system of humanoid robots is one of the essential components that allow them to do complex activities. This has led to numerous studies on artificial gaze stabilization, many of which are based on biological vision system reflexes. The gaze stabilization solution includes image capture and processing, inverse kinematics, and feedback control to achieve the desired gaze behavior. Generally, the multi-solution problem of finding the desired gaze direction and the inverse kinematics problem of finding the desired joints are solved by using cost functions and numerical solvers. This results in disadvantages that include long processing time, uncertain number of iterations, and risk of numerical instability. In this work, an alternative algebraic method is introduced by exploiting the cascading structure of the neck and eye. By using direct equations instead of numerical solving, the multi-solution and inverse kinematics problems are solved utilizing the geometrical structure and the proposed virtual configurations. Moreover, a sliding mode controller is designed to move the neck-eye joints to their desired positions. The developed scheme is simulated in the MATLAB/SIMULINK environment. Results for various scenarios show that the system can effectively gaze at different stationary and moving targets, showing human-like gaze behavior. In terms of timing, the desired gaze direction is quickly achieved and stabilized, whereas the neck-eye system dynamics stay longer. For one of the simulation cases presented, it took 0.3 seconds to achieve the desired gaze direction for the dynamics of more than 1 second.