Input and output transformations for a space robot modeled with quaternions

This paper describes a procedure for obtaining the dynamical model of a space robot in a form that is useful for simulation. The differential equations of motion of the space robot are derived using a constrained Lagrangian approach to mechanics. Quaternions are utilized to model rotation which gives rise to generalized forces that are in the direction of the quaternion elements. A transformation is presented which transforms realizable torques into these abstract forces. The form of a complete model with both realizable inputs and measurable outputs is described.