Newton–Euler Modeling and Control of a Multi-copter Using Motor Algebra $$\mathbf{G}^+_{3,0,1}$$

Abstract

In this work the dynamic model and the nonlinear control for a multi-copter have been developed using the geometric algebra framework specifically using the motor algebra $$G^+_{3,0,1}$$. The kinematics for the aircraft model and the dynamics based on Newton-Euler formalism are presented. Block-control technique is applied to the multi-copter model which involves super twisting control and an estimator of the internal dynamics for maneuvers away from the origin. The stability of the presented control scheme is proved. The experimental analysis shows that our non-linear controller law is able to reject external disturbances and to deal with parametric variations.