Kinematic Analysis of Quadrotors with Manufacturing Errors

We discuss the problem of calibrating quadrotors fabricated using inexpensive printing techniques used by the do-it-yourself community. Although it is easy to create prototypes rapidly, the rotor axes and positions in these prototypes may not be according to specifications. In such a case, operating the motors at the nominal speeds will not result in stable hovering. The fundamental equations that govern hovering are similar to those encountered in objects suspended with cables in that they couple the position and orientation variables with the forces required for equilibrium. We develop the kinematics and statics and derive the conditions for stable equilibrium with a numerical example to illustrate the basic ideas and point to approaches in which adaptation through software can rectify shortcomings in inexpensive manufacturing processors.