An approach to posture control of free-falling twin bodies using differential flatness

Often, electronics and packages must be prevented from damages resulting from awkward falls. The goal of this paper is to explore how actuators and control can be used to reorient bodies during free fall. It is well known that motion of a free-falling body or a set of interconnected bodies is characterized by the principle of conservation of angular momentum. The governing angular momentum equations are nonholonomic, i.e., are non-integrable rate equations. In this paper, we assume that the falling system consists of twin bodies interconnected by a hinge joint. One of the twin bodies is designated as the primary body which needs to be reoriented during fall. The secondary body is connected to the primary body by a hinge joint, similar to a protective cover on a cell phone. The relative angle between the twin bodies is actively controlled. In addition, two rotors are mounted on the primary body with axes orthogonal to the axis of the hinge between the twin bodies. The goal of this study is to use the framework of differential flatness to compute trajectories for the hinge joint and the two rotors so that the twin bodies achieve prespecified orientations at the end of the free fall.