提出基于螺旋理论的快速可靠逆运动学求解器，解决Franka机械臂冗余问题
GeoFIK: A Fast and Reliable Geometric Solver for the IK of the Franka Arm based on Screw Theory Enabling Multiple Redundancy Parameters
- 用螺旋理论建模整机几何，提前计算雅可比矩阵
- 可处理所有奇异性，支持多种冗余变量配置
- 实测速度与鲁棒性优于现有先进求解器
现代机器人应用需要快速、稳健且一致的逆运动学（IK）求解器，并能提供全部解。当前广泛用于机器人研究的Franka机械臂具有7个自由度，其逆运动学不仅因1自由度冗余而复杂，还受腕部和肘部存在连杆偏移的影响。由于这种复杂性，现有文献中的Franka IK求解器在实际应用中均未达到满意效果。为此，本文提出GeoFIK（几何型Franka IK），一种解析式逆运动学求解器，支持使用不同关节变量来处理冗余。该方法利用螺旋理论描述机器人整体几何结构，可在计算关节角前预先获得雅可比矩阵，所有奇异性均可被识别并妥善处理。作为几何信息应用的示例，文中提供以旋转角度为自由变量的求解器。通过多项实验验证了GeoFIK在速度、鲁棒性和可靠性方面优于两种先进求解器。
原文摘要 · Abstract (English)
Modern robotics applications require an inverse kinematics (IK) solver that is fast, robust and consistent, and that provides all possible solutions. Currently, the Franka robot arm is the most widely used manipulator in robotics research. With 7 DOFs, the IK of this robot is not only complex due to its 1-DOF redundancy, but also due to the link offsets at the wrist and elbow. Due to this complexity, none of the Franka IK solvers available in the literature provide satisfactory results when used in real-world applications. Therefore, in this paper we introduce GeoFIK (Geometric Franka IK), an analytical IK solver that allows the use of different joint variables to resolve the redundancy. The approach uses screw theory to describe the entire geometry of the robot, allowing the computation of the Jacobian matrix prior to computation of joint angles. All singularities are identified and handled. As an example of how the geometric elements obtained by the IK can be exploited, a solver with the swivel angle as the free variable is provided. Several experiments are carried out to validate the speed, robustness and reliability of the GeoFIK against two state-of-the-art solvers.
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