We consider a flier as an articulated system consisting of the basic body (the torso) and several branches (head, arms and legs), as shown in Figure 1. Let there be independent joint motions described by joint-angles vector (the terms joint coordinates or internal coordinates are often used). The basic body needs six coordinates to describe its spatial position: , where defines the position of the mass center and are orientation angles (roll, pitch, and yaw). Now, the overall number of degrees of freedom (DOF) for the system is , and the system position is defined by
Unconstrained (free flier) and constrained system
We now consider the drives. It is assumed that each joint motion has its own drive – the torque . Note that in this analysis there is no drive associated to the basic-body coordinates X (this is a real situation with humans and humanoids in “normal” activities, however, in space activities – actions like repairing a space station, etc. – reactive drives are added, attached to the torso; the proposed method for simulation can easily handle this situation). The vector of the joint drives is , and the extended drive vector (N-dimensional) is ; zeros stand for missing basic-body drives.
The dynamic model of the flier has the general form:
Dimensions of the inertial matrix and its submatrices are: , , , , and . Dimensions of the column vectors containing centrifugal, Coriolis’ and gravity effects are: , , and .