Complete Analytical Forward and Inverse Kinematics for the NAO Humanoid Robot

Articulated robots with multiple degrees of freedom, such as humanoid robots, have become popular research platforms in robotics and artificial intelligence. Such robots can perform complex motions, including the balancing, walking, and kicking skills required in the RoboCup robot soccer competition. The design of complex dynamic motions is achievable only through the use of robot kinematics, which is an application of geometry to the study of arbitrary robotic chains. This thesis studies the problems of forward and inverse kinematics for the Aldebaran NAO humanoid robot and presents for the first time a complete analytical solution to both problems with no approximations, including an implementation of a software library for real-time 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 closedform solutions to finding joint configurations that drive the end effectors of the robot to desired points in the three-dimensional 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 compared to existing numerical approaches is its accuracy, its efficiency, and the elimination of singularities. The implemented NAO kinematics library, which additionally offers centerof-mass calculation, is demonstrated in two motion design tasks: pointing to the ball and basic balancing. The library has been integrated into the software architecture of the RoboCup team “Kouretes” and is currently being used in various motion design problems, such as dynamic balancing, trajectory following, dynamic kicking, and omnidirectional walking.