Immersion and Invariance-Based Adaptive Controller for Quadrotor Systems
针对惯性参数不确定的四旋翼系统，提出一种浸入与不变性自适应控制器，通过分层框架和饱和反步法实现轨迹跟踪，并保证质量与惯性张量估计的渐近收敛。
This paper develops a novel immersion and invariance (I&I)-based adaptive controller for nonlinear underactuated quadrotor systems subject to uncertain inertial parameters. The objective is to drive the quadrotor to accurately track a reference trajectory. The controller synthesis is based on a hierarchical framework. First, the solution to the trajectory tracking problem is transformed to stabilizing its corresponding error system asymptotically. Second, to avoid singularity in the command attitude extraction, a saturated backstepping control strategy with smooth hyperbolic tangent functions is developed to synthesize a command force in the position loop, where an I&I adaptive methodology is introduced to update the mass estimation. The I&I adaption guarantees the asymptotic convergence of the mass estimation to its actual value. Third, in the attitude loop, the projection algorithm is used to update the inertial tensor estimations, which enables the estimations to be maintained within a prescribed range. Then, a rotation matrix-based applied torque with an initial condition constraint is synthesized. It is proven that, with appropriate control parameters, the proposed controller guarantees the asymptotic stability of the error system and then the trajectory tracking of the quadrotor is achieved. Finally, numerical simulations are given to verify and highlight the performance of the proposed controller.