提出1-自由度有理连杆的运动规划算法，实现精准轨迹控制。
Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages
- 用对偶四元数表示有理运动，推导正向运动学公式
- 设计高精度数值逆运动学求解方法，支持平滑轨迹生成
- 适用于4到7关节机制，无需额外几何分析，适合机器人应用
本研究提出一套针对单自由度（DoF）有理单回路机构的轨迹规划算法。基于对偶四元数对有理运动的表示，给出了正向运动学的解析公式、一种数值逆运动学求解算法，并实现了驱动关节轨迹生成。提出一种基于高斯-牛顿搜索的单参数逆运动学新方法。此外，通过弧长重参数化，实现了工具的平稳等距运动。该通用方法适用于具有4至7个关节、具备有理运动特性的单自由度机构，无需额外几何分析。实验在实验室平台上验证了其有效性。
原文摘要 · Abstract (English)
This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree of freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for performing smooth equidistant travel of the tool is provided by applying arc-length reparameterization. This general approach can be applied to one-DoF mechanisms with four to seven joints characterized by a rational motion, without any additional geometrical analysis. An experiment was performed to demonstrate the usage in a laboratory setup.
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