This paper provides stability analysis of a robust interaction control, nonlinear bang–bang impact control, for one degree-of-freedom robot manipulators. The interaction controller takes advantages of robot joint’s friction that is not helpful for constrained space control usually, has no need to change gains throughout the tasks requiring free space motion, constrained motion, and the transition between the two, and needs virtually no information on robot dynamics for its design and implementation. Despite these advantages, to date, there was no complete and formal proof of its stability, hindering its practical use for interaction tasks requiring robots’ frequent contact with various environments, including humans. A sufficient stability condition was derived based on the L_∞ space analysis with its physical implications. Stability condition was found to be only dependent on the intentional time delay for the online lumped robot dynamics estimation and the inertia estimation accuracy and was not dependent on the passive environment properties and disturbances. Interestingly, in the case of the nonlinear bang–bang impact control, joint frictions helped stabilize the robot during the transition from free space to constrained space.

中文翻译：

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具有非结构化环境的单自由度机器人的鲁棒交互控制的稳定性

本文为一自由度机器人操纵器提供了鲁棒的交互控制，非线性爆炸冲击控制的稳定性分析。交互控制器利用了机器人关节的摩擦力，这通常对约束空间的控制没有帮助，不需要在需要自由空间运动，约束运动以及两者之间的过渡的整个任务中更改增益，并且几乎不需要机器人的任何信息其设计和实施的动力学。尽管具有这些优点，但迄今为止，还没有完整和正式的证据表明其具有稳定性，从而阻碍了其在需要机器人经常与包括人类在内的各种环境进行接触的交互任务中的实际使用。足够的稳定性条件是基于所导出的大号_∞空间分析及其物理意义。发现稳定性条件仅取决于在线集总机器人动力学估计的故意时间延迟和惯性估计精度，而不取决于被动环境特性和干扰。有趣的是，在非线性爆炸冲击控制的情况下，在从自由空间到受约束空间的过渡过程中，关节摩擦有助于稳定机器人。