The Natural Gradient as a control signal for a humanoid robot

This paper presents Natural Gradient Control (NGC), a control algorithm that efficiently estimates and applies the natural gradient for high-degree of freedom robotic control. In contrast to the standard task Jacobian, the natural gradient follows the direction of steepest descent with respect to a parameterized model with extra degrees of freedom injected. This procedure enables NGC to maneuver smoothly in regions where the task Jacobian is ill-conditioned or singular. NGC efficiently estimates the natural gradient using only forward kinematics evaluations. This sampling-based algorithm prevents the need for gradient calculations and therefore allows great flexibility in the cost functions. Experiments show NGC can even use statistics of rendered images as part of the cost function, which would be impossible with traditional inverse kinematics approaches. The advantages of NGC are shown on the full 41-degree upper body of an iCub humanoid, in simulation and on a real robot, and compared to a Jacobian-based controller. Experiments show that the natural gradient is robust and avoids common pitfalls such as local minima and slow convergence, which often affects the application of Jacobian-based methods. Demonstrations on the iCub show that NGC is a practical method that can be used for complex movements.