This paper analyzes operational space dynamics for redundant robots with un-actuated joints and reveals their highly nonlinear dynamic impacts on operational space control (OSC) tasks. Unlike conventional OSC approaches that partly address the under-actuated system by introducing rigid grasping or contact constraints, we deal with the problem even without such physical constraints which have been overlooked, yet it includes a wide range of applications such as free-floating robots and manipulators with passive joints or unwanted actuation failure. In addition, as an intuitive application example of the drawn result, an OSC is formulated as an optimization problem to alleviate the dynamics disturbance stemmed from the un-actuated joints and to satisfy other inequality constraints. The dynamic analysis and the proposed control method are verified by a number of numerical simulations as well as physical experiments with a 7-degrees-of-freedom robotic arm. In particular, we consider joint actuation failure scenarios that can be occurred at certain joints of a torque-controlled robot and practical case studies are performed with an actual redundant robot arm.

本文分析了具有未驱动关节的冗余机器人的操作空间动力学，并揭示了它们对操作空间控制 (OSC) 任务的高度非线性动态影响。与通过引入刚性抓取或接触约束部分解决欠驱动系统的传统 OSC 方法不同，即使没有被忽视的物理约束，我们也可以处理该问题，但它包括广泛的应用，例如自由浮动机器人和具有被动关节或意外驱动故障的机械手。此外，作为绘制结果的直观应用示例，将 OSC 公式化为优化问题，以减轻源自未驱动关节的动力学干扰并满足其他不等式约束。动态分析和所提出的控制方法通过大量数值模拟以及 7 自由度机械臂的物理实验得到验证。特别是，我们考虑了可能在扭矩控制机器人的某些关节处发生的关节驱动故障场景，并使用实际的冗余机器人手臂进行了实际案例研究。