Generalized humanoid leg inverse kinematics to deal with singularities

We present here a simple technique of inverse kinematics to be used for humanoid legs. This technique has two advantages. First it permits to manage the stretched-legs space boundary singularities encountered with the classical inverse kinematics that uses a whole Jacobian matrix for all leg joint angle variations. This leg singularity configuration always appears when the humanoid robot has to get from the standing position with both legs stretched to a knee flexed position and vice-versa. Second the technique is independent of the convention of angle orientation at the hips and at the ankles. Therefore it does not require the specific solving for hip and ankle joint angles of the rotation matrix equations in the case of analytical geometric methods. The inverse kinematics proposed here is based on geometrical calculations to get knee coordinates, and on the decomposition of inverse leg kinematics, i.e. inverse kinematics at the hip for the one part, and inverse kinematics at the ankle for the other part. This calculation assumes that the leg has six rotary degrees of freedom, three at the hip, one at the knee, and two at the ankle. The orientation of rotary joints at the hip and at the ankle can be arbitrary.