The isotropic compliance property is examined in the Special Euclidean Group SE(3) in the case of redundant manipulators. The redundancy problem is solved by means of the QR decomposition of the transposed Jacobian matrix, and the compliance property is achieved by means of active stiffness regulation. Thanks to the defined control matrices, the control system realizes the isotropy condition. The local optimization of the joint torques is discussed. In particular, the joint control torques work is minimized obtaining an analytic solution through a Lyapunov equation. The proposed approach is applied to a 7R and to a 9R serial manipulator, and verified by means of multibody dynamics simulations.

中文翻译：

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冗余机械手中的主动各向同性合规性

在冗余操纵器的情况下，在特殊欧几里得组SE（3）中检查了各向同性顺应性。通过转置的雅可比矩阵的QR分解解决了冗余问题，并通过主动刚度调节实现了顺应性。由于定义了控制矩阵，控制系统实现了各向同性条件。讨论了关节扭矩的局部优化。尤其是，通过Lyapunov方程获得的联合解析扭矩最小。所提出的方法适用于7R和9R串行操纵器，并通过多体动力学仿真进行了验证。