This paper investigates the practical considerations for implementing an underactuated transverse function-based control law using only two reaction wheels. Previous investigations into transverse functions have looked at implementing these control laws for the underactuated problem but have yet to fully consider what may be required to run these control laws long term for a realistic mission and have primarily dismissed the increased control efforts needed from the remaining actuators. This paper first shows the effects of neglecting momentum dumping for both the transverse function approach and a previously published Singular Nonlinear Quaternion (SNLC) –based controller. This paper then outlines a control strategy using magnetic torque devices to dump momentum and help maintain the conditions needed to maintain the assumptions used by these underactuated systems. With adequately sized magnetic torque-based angular momentum management techniques, both the SNLC and Transverse function-based approaches produce acceptable results. However, the Transverse function-based method allows for a systematic setting of the allowable error bound, a desirable trait in a potentially compromised system where a trade-off in performance could extend the system’s longevity. The paper then investigates improving the transverse function methods by minimizing the control effort the remaining wheels need by slowly changing the setpoint of the desired error bound when the desired orientation is far from the current orientation. This strategy helped power consumption on the wheels and allowed large manoeuvres before the remaining actuators became saturated. Transverse function-based controllers also perform well with uncertain spacecraft parameters, as shown through a Monte Carlo analysis.

中文翻译：

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在欠驱动反作用轮控制航天器上使用横向函数方法的实际考虑


本文研究了仅使用两个反作用轮实现欠驱动横向函数的控制律的实际考虑。以前对横向功能的研究着眼于针对驱动不足的问题实施这些控制定律，但尚未充分考虑长期运行这些控制定律以执行实际任务可能需要什么，并且主要忽略了其余执行器所需的增加控制工作。本文首先展示了忽略动量转储对横向函数方法和之前发表的基于奇异非线性四元数 （SNLC） 的控制器的影响。然后，本文概述了一种使用磁扭矩装置来释放动量并帮助维持维持这些欠驱动系统使用的假设所需的条件。借助适当大小的基于磁扭矩的角动量管理技术，SNLC 和基于横向函数的方法都能产生可接受的结果。然而，基于 Transverse 函数的方法允许系统地设置允许的误差边界，这在可能受损的系统中是一个理想的特性，因为性能的权衡可能会延长系统的使用寿命。然后，本文研究了改进横向函数方法的方法，当所需方向远离当前方向时，通过缓慢改变所需误差边界的设定值来最大限度地减少剩余车轮所需的控制工作。这种策略有助于消耗车轮的功率，并允许在剩余的执行器饱和之前进行大型操作。基于横向函数的控制器在不确定的航天器参数下也表现良好，如蒙特卡洛分析所示。