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Globally Optimal Solution to Inverse Kinematics of 7DOF Serial Manipulator
arXiv - CS - Symbolic Computation Pub Date : 2020-07-24 , DOI: arxiv-2007.12550
Pavel Trutman (CIIRC), Safey El Din Mohab (SU), Didier Henrion (LAAS), Tomas Pajdla (CIIRC)

The Inverse Kinematics (IK) problem is to nd robot control parameters to bring it into the desired position under the kinematics and collision constraints. We present a global solution to the optimal IK problem for a general serial 7DOF manipulator with revolute joints and a quadratic polynomial objective function. We show that the kinematic constraints due to rotations can all be generated by second-degree polynomials. This is important since it signicantly simplies further step where we nd the optimal solution by Lasserre relaxations of non-convex polynomial systems. We demonstrate that the second relaxation is sucient to solve the 7DOF IK problem. Our approach is certiably globally optimal. We demonstrate the method on the 7DOF KUKA LBR IIWA manipulator and show that we are able to compute the optimal IK or certify in-feasibility in 99 % tested poses.

中文翻译:

7DOF串行机械手逆运动学全局最优解

逆运动学 (IK) 问题是在运动学和碰撞约束下找到机器人控制参数,使其进入所需位置。我们为具有旋转关节和二次多项式目标函数的通用串行 7DOF 机械手提供了最优 IK 问题的全局解决方案。我们表明由于旋转引起的运动学约束都可以由二次多项式生成。这很重要,因为它显着简化了我们通过非凸多项式系统的拉塞尔松弛找到最优解的进一步步骤。我们证明第二次松弛足以解决 7DOF IK 问题。我们的方法无疑是全球最优的。
更新日期:2020-07-27
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