Error propagation and formation structure design using dual quaternion algebra

By utilizing a new mathematical tool, i.e., unit dual quaternion and its logarithmic norm, the problem of error propagation and its upper bound on rotation and translation in one path of a rooted tree in 3-dimensional space is studied. For prescribed angular and distance error thresholds, a maximum depth of the rooted tree is obtained correspondingly, which can be used to guide the structure design for formations. Finally, the maximum depth condition is validated by simulations on the USARSim platform with quad-rotor formations.