逆运动学作为低秩欧氏距离矩阵的完备化
Inverse Kinematics as Low-Rank Euclidean Distance Matrix Completion
摘要：
大多数逆运动学（IK）算法在由关节角度定义的配置空间中搜索解。然而，许多机器人的运动学也可以用刚性连接点之间的距离来描述，这些距离共同形成了欧几里得距离矩阵。这种替代的几何描述的运动学揭示了一个优雅的等效IK和低秩矩阵完成的问题。我们使用这种连接来实现一种新的黎曼优化为基础的解决方案，以IK为各种关节式机器人与对称关节角度的约束。
英文摘要：
The majority of inverse kinematics (IK) algorithms search for solutions in a configuration space defined by joint angles. However, the kinematics of many robots can also be described in terms of distances between rigidly-attached points, which collectively form a Euclidean distance matrix. This alternative geometric description of the kinematics reveals an elegant equivalence between IK and the problem of low-rank matrix completion. We use this connection to implement a novel Riemannian optimization-based solution to IK for various articulated robots with symmetric joint angle constraints.
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