2. Robot geometry

2.1 Transformation matrix and parameterization

The description in space of a humanoid robot composed of m bodies considered as rigid and with n degrees of freedom requires 6 + n variables. The first six describe the position and orientation relative to a fixed Galilean reference frame F _g of one of its m bodies, which is chosen as the reference body. The other n variables describe the configuration of its joints. If the number 6 + n is minimal, the variables used to describe the humanoid robot are called "generalized coordinates". The coordinate system linked to joint j is denoted F _j . Unlike the fixed-base manipulator robot, the reference frame F ₀ ...