In this paper, cooperative robotic manipulators under uncertain base coordinate are investigated. The coordinate uncertainties result in biases of cooperative robotic dynamics, which involve horizontal and vertical translational errors in the task space and rotational errors in the joint space. To the best of our knowledge, uncertainties in the base coordinate system of cooperative robotic manipulators have drawn little attention in existing literature. To solve this problem, this paper presents an adaptive robust controller for the synchronized control of two cooperative robotic manipulators. An adaptive neural network associated with base coordinate parameter adaption law is proposed to estimate the cooperative system parameters given unknown system dynamics and base coordinate uncertainties. A synchronization-factor-based robust slide mode controller is then derived to stabilize the target position and internal force between the cooperative manipulators. Mathematical proof and numerical experiments under various conditions are conducted. The results demonstrate the satisfactory and effective convergences of both the cooperative robotic trajectory and internal force despite of uncertainties in the base coordinate system.

本文研究了不确定基坐标下的协作机器人机械手。坐标不确定性导致协作机器人动力学的偏差，其中涉及任务空间中的水平和垂直平移误差以及关节空间中的旋转误差。据我们所知，协作机器人机械手的基本坐标系中的不确定性在现有文献中很少引起关注。为了解决这个问题，本文提出了一种自适应鲁棒控制器，用于两个协作机器人机械手的同步控制。提出了一种与基坐标参数自适应律相关的自适应神经网络，用于在未知系统动力学和基坐标不确定性的情况下估计协同系统参数。然后推导出基于同步因子的鲁棒滑动模式控制器，以稳定协作机械手之间的目标位置和内力。进行了各种条件下的数学证明和数值实验。结果表明，尽管基础坐标系存在不确定性，但协作机器人轨迹和内力的收敛效果令人满意且有效。