The presence of faulty or underactuated manipulators can disrupt the end-effector formation keeping of a team of manipulators. Based on two-link planar manipulators, we investigate this end-effector formation keeping problem for mixed fully- and under-actuated manipulators with flexible joints. In this case, the underactuated manipulators can comprise of active-passive (AP) manipulators, passive-active (PA) manipulators, or a combination thereof. We propose distributed control laws for the different types of manipulators to achieve and maintain the desired formation shape of the end-effectors. It is achieved by assigning virtual springs to the end-effectors for the fully-actuated ones and to the virtual end-effectors for the under-actuated ones. We study further the set of all desired and reachable shapes for the networked manipulators' end-effectors. Finally, we validate our analysis via numerical simulations.

翻译：故障或欠驱动机械臂的存在会破坏机械臂团队的末端执行器编队保持。基于两连杆平面机械臂，我们研究了混合全驱动与欠驱动柔性关节机械臂的末端执行器编队保持问题。在这种情况下，欠驱动机械臂可包含主动-被动（AP）型机械臂、被动-主动（PA）型机械臂，或两者的组合。我们针对不同类型的机械臂提出了分布式控制律，以实现并维持末端执行器的期望编队形状。该方法通过对全驱动机械臂的末端执行器分配虚拟弹簧，以及对欠驱动机械臂的虚拟末端执行器分配虚拟弹簧来实现。我们进一步研究了网络化机械臂末端执行器所有可达且期望的编队形状集合。最后，通过数值仿真验证了我们的分析。