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求解方程RaRx=RxRb的四元数几何研究

DOI: 10.11834/jig.20100615

Keywords: 手眼标定,四元数几何,旋转方程,条件数

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Abstract:

机器人手眼标定通常要解一个旋转方程[WTHX]R?aR?x[WTBZ]=[WTHX]R?xR?b[WTBZ],求解该方程有很多方法,其中利用四元数的方法最为简洁实用。但一般的四元数求解侧重应用,缺乏几何意义的对照,也没有全面分析方程各种解的情况。为了提高机器人手眼标定的效率和精度,在深入研究求解该方程的四元数几何方法的基础上,详细而严格地论证了各种情况下方程的解,不仅给出了四元数矩阵分析与几何解释的有趣对照,而且仿真验证了该算法的正确性。仿真实验表明,了解方程各种解的情形以及几何意义将有助于降低求解的条件数和提高标定的效率,此外,该研究对于发展四元数几何分析也有很大的意义。

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