On Challenges in Coordinate Transformation for Using a High-Gain Multi-Output Nonlinear Observer

This paper considers the design of a multi-output high gain observer for a vehicle trajectory tracking application. The high gain observer approach offers the advantages of guaranteed feasibility and global stability with just one constant observer gain for this application. The challenges of transforming the vehicle dynamic model into the required companion form for applying the high gain observer technique are addressed. Transforming a traditional kinematic model to companion form is found to result in an increased number of states. Instead, a coordinate transformation that allows for varying velocity and varying slip angle is shown to be appropriate. The high gain observer methodology for a dynamic system with multiple outputs is presented and the calculation of the Lipschitz constant for the vehicle tracking application is discussed.