Position and attitude tracking for a formation of three agents

In this paper we consider a trajectory tracking control problem for a multi-agent formation consisting of three agents. The agents provide a high level representation of three manipulators that have grasped a rigid object. More precisely, the agents´ positions represent the end-effectors´ grasp points. The agents are modelled by single integrators, and are designed to move the object such that it is located at a particular position with a particular attitude in a particular time, i.e. position and attitude tracking. The object rigidity is modelled by requiring that the agents should remain at constant relative distances from each other, reducing their three degrees of freedom each to a total of six translational and rotational degrees of freedom for the whole formation. The formation of agents is shown to be equivalent to a rigid body. The position tracking problem is solved using a standard technique whereas the attitude tracking problem is solved by adopting and adapting a recently developed approach.