Cartesian Sliding PID Control Under Jacobian Uncertainty of Robotics Hands: Executing Transition Tasks

R. García-Rodríguez, Vicente Parra‐Vega
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Abstract

The necessity to make complex tasks have increased in many robotics systems such as cooperatives robots or robotics hands. When each robot execute free and constrained motion tasks involves change into dynamics for rigid contact. At the time of impact regime the derivative of the velocity vector is not well-defined, therefore it is difficult to design controller for transition task. The trivial approach to avoid the impact is presented commuting consistently ODE- and DAE-based controller to insure formally zero contact velocity, -at any given arbitrarily time and for any initial condition. One way to circumvent this, it is to know exactly the commuting time to guarantee zero contact velocity such that impulsive dynamics will not arise and stable transition can be obtained. The novelty of our approach is characterized in the fact that very fast decentralized Cartesian cooperative tracking is obtained without using the model of the robot nor exact knowledge of inverse Jacobian. The model-free sliding PD force controller is used to compensate nonlinear dynamics of each robot and the residual error dynamics is finally canceled by a chattering-free Cartesian sliding mode to guarantee convergence of position and force tracking errors. It is important notice that inverse kinematics are avoided by synthesized Cartesian, rather than joint error sliding surfaces, thus the commuting manifold does not depend on the Jacobian, therefore, the system is robust against Jacobian uncertainty. Simulations study of two robots manipulating a constrained object shows that system is robust under parametric uncertainty of robots
机器人手部雅可比不确定性下的笛卡尔滑动PID控制:执行过渡任务
在许多机器人系统中,如协作机器人或机械手,完成复杂任务的必要性增加了。当每个机器人执行自由和约束运动时,任务涉及到刚性接触的动力学变化。在冲击状态下,速度矢量的导数不明确,给过渡任务的控制器设计带来困难。提出了一种避免冲击的简单方法,即在任意给定的任意时间和任何初始条件下,交换一致的基于ODE和基于dae的控制器以确保接触速度为零。解决这一问题的一种方法是,精确地知道通勤时间,以保证零接触速度,从而不会产生脉冲动力学,并获得稳定的过渡。该方法的新颖之处在于在不使用机器人模型和精确的逆雅可比矩阵知识的情况下,实现了快速的分散笛卡尔协同跟踪。采用无模型滑动PD力控制器对各机器人的非线性动力学进行补偿,最后通过无抖振的笛卡尔滑模消除残余误差动力学,保证位置和力跟踪误差的收敛性。需要注意的是,利用合成的笛卡儿坐标而不是关节误差滑动曲面避免了逆运动学,因此交换流形不依赖于雅可比矩阵,因此系统具有抗雅可比矩阵不确定性的鲁棒性。对两个机器人操纵约束对象的仿真研究表明,系统在机器人参数不确定性下具有鲁棒性
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