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Hybrid Certainty Equivalence Control of Rigid Bodies With Quaternion Measurements

机译：四元数测量的刚体混合确定性等价控制

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摘要

In this technical note, we solve the control problem of rigid bodies with only quaternion measurements for all initial rotations and angular velocities. The proposed solution is based on the theory of cascades using any switching certainty equivalence controller satisfying certain assumptions along with an in the large hybrid observer. The equilibrium point of the proposed observer in closed loop with the rigid body dynamics is proven to be -exponentially stable in the large i.e., we prove that the equilibrium point is stable and that the error states converge exponentially fast towards the origin for initial rotations and angular velocities. Until now, stability results for quaternion-based observers have typically only been valid for a bounded set of initial conditions. To overcome this issue, our observer design is based on dynamic scaling and switching logic. Furthermore, we show that the origin of the proposed switching certainty equivalence controller in closed loop with the hybrid observer is asymptotically stable in the large for all available initial conditions associated with the quaternion space. Simulation results for the proposed scheme are presented with the particular case of the PD controller, revealing that all states converge as expected from our theoretical findings.
机译：在本技术说明中，我们仅对所有初始旋转和角速度进行四元数测量即可解决刚体的控制问题。所提出的解决方案基于级联理论，该级联理论使用满足某些假设的任何开关确定性等效控制器以及大型混合观测器中的。证明了所提出的具有刚体动力学的闭环观测器的平衡点在大范围内是-指数稳定的，即，我们证明了平衡点是稳定的，并且对于初始旋转，误差状态以指数方式快速收敛到原点，并且角速度。到目前为止，基于四元数的观测器的稳定性结果通常仅对有限的一组初始条件有效。为了克服这个问题，我们的观察器设计基于动态缩放和切换逻辑。此外，我们表明，在与四元数空间相关的所有可用初始条件下，带有混合观测器的闭环拟议切换确定性等效控制器的起源在大范围内渐近稳定。针对PD控制器的特殊情况，提出了该方案的仿真结果，表明所有状态都按照我们的理论发现进行了收敛。

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