Complete analytical inverse kinematics for NAO

The design of complex dynamic motions for humanoid robots is achievable only through the use of robot kinematics. In this paper, we study the problems of forward and inverse kinematics for the Aldebaran NAO humanoid robot and present a complete, exact, analytical solution to both problems, including a software library implementation for realtime onboard execution. The forward kinematics allow NAO developers to map any configuration of the robot from its own joint space to the three-dimensional physical space, whereas the inverse kinematics provide closed-form solutions to finding joint configurations that drive the end effectors of the robot to desired target positions in the three-dimensional physical space. The proposed solution was made feasible through a decomposition into five independent problems (head, two arms, two legs), the use of the Denavit-Hartenberg method, and the analytical solution of a non-linear system of equations. The main advantage of the proposed inverse kinematics solution compared to existing approaches is its accuracy, its efficiency, and the elimination of singularities. In addition, we suggest a generic guideline for solving the inverse kinematics problem for other humanoid robots. The implemented, freely-available, NAO kinematics library, which additionally offers center-of-mass calculations, is demonstrated in two motion design tasks: basic center-of-mass balancing and pointing to the ball.