We present three classes of distributed formation controllers for achieving and maintaining the 2D/3D formation shape of manipulator end-effectors to cope with different scenarios due to availability of modeling parameters. We firstly present a distributed formation controller for manipulators whose system parameters are perfectly known. The formation control objective is achieved by assigning virtual springs between end-effectors and by adding damping terms at joints, which provides a clear physical interpretation of the proposed solution. Subsequently, we extend it to the case where manipulator kinematic and system parameters are not exactly known. An extra integrator and an adaptive estimator are introduced for gravitational compensation and stabilization, respectively. Simulation results with planar manipulators and with seven degree-of-freedom humanoid manipulator arms are presented to illustrate the effectiveness of the proposed approach.

翻译：我们提出了三类分布式编队控制器,用于实现和维护2D/3D型操纵机终端效应元件的形成形状,以应对由于具备模型参数而出现的不同情况;我们首先为完全知道系统参数的操纵机组首次提供一个分布式编队控制器;通过在终端效应器之间分配虚拟弹簧和在联合点添加阻隔条件来实现编队控制目标,从而对拟议解决办法提供明确的物理解释;随后,我们将其扩大到对操纵机动和系统参数不完全了解的情况;为重力补偿和稳定性分别采用了额外的集成器和适应性估计器;与平流操纵机和七度自由人体操纵器模拟结果,以说明拟议方法的有效性。