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.

中文翻译：

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使用马达代数$$ \ mathbf {G} ^ + _ {3,0,1} $$ G3,0,1 +的多直升机牛顿-欧拉建模与控制

在这项工作中，已经使用几何代数框架，特别是使用电机代数\（G ^ + _ {3,0,1} \）开发了多直升机的动力学模型和非线性控制。介绍了飞机模型的运动学和基于牛顿-欧拉形式主义的动力学。块控制技术被应用于多直升机模型，该模型涉及超级扭曲控制和内部动力估计器，用于远离原点的机动。证明了所提出控制方案的稳定性。实验分析表明，我们的非线性控制器定律能够拒绝外部干扰并处理参数变化。