本研究基於多軸機器手臂的建模與鑑別，並分析最小平方法在有擾動下的影響，並且可以發現條件數以及觀測矩陣有擾動下會影響到估測結果，而且因機器手臂有干涉問題，必須設計軌跡在閉迴路下進行激發，則會設計最佳激發軌跡針對條件數以及物理限制，利用計算力矩法實現此軌跡，接著獲得角度以及力矩並進行系統鑑別，而在鑑別中需要加速度項，而加速度為位置微分兩次，量化誤差會因此而放大，會遇到觀測矩陣含有巨大的擾動，所以本文提供了最小差距濾波器 (minimum difference filter, MDF)並針對量化雜訊做設計，可以有效的將雜訊抑制，得到雜訊較小的加速度，並對其進行系統鑑別，因摩擦引想在低速段有顫振的現象，故使用權重最小平方法，獲得的等效參數在進行驗證。

This research is based on the modeling and identification of multi-axis robotic arms, and analyzes the influence of the least square method under disturbances, and it can be found that disturbances in the condition number and the observation matrix will affect the estimation results, and the robot arm has interference problems , The trajectory must be designed for excitation in a closed loop, and the optimal excitation trajectory will be designed according to the condition number and physical limitations. The calculated torque method is used to achieve this trajectory. Then the angle and torque are obtained and the system is identified. The acceleration term is required in the identification. The acceleration is differentiated twice by the position. The quantization error will be amplified and the observation matrix will contain huge disturbances. Therefore, this article provides a minimum difference filter (MDF) and is designed for quantization noise, which can be effective The noise is suppressed, and the acceleration with less noise is obtained, and the system is identified, due to friction, there is chatter in the low speed range, so the weighted least square method is used and the obtained equivalent parameters are being verified.

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