基于凯恩方程的机械臂固定时间滑模控制

Fixed-Time Sliding Mode Control of Manipulators Based on Kane's Equation

针对存在未建模动态和随机干扰等因素影响下的机械臂轨迹跟踪控制问题,提出了一种新型非奇异固定时间滑模控制策略。首先,利用凯恩方程和虚功原理,推导了n自由度机械臂的动力学方程;然后,由固定时间稳定理论设计了新型固定时间滑模面,结合6R机械臂的凯恩动力学模型,针对机械臂的模型参数不确定性和外界干扰,设计了非奇异固定时间滑模控制器,并基于Lyapunov理论证明了系统的稳定性;最后的数值仿真表明,所设计的控制器能保证系统状态的收敛不依赖于初始条件,并具有更快的收敛速率和更短的收敛时间以及良好的鲁棒性。

A new nonsingular fixed-time sliding mode control method is proposed for the trajectory tracking control of the manipulator under the influence of such factors as unmodeled dynamics and random interferences.Firstly, the dynamic equation of the n degree-of-freedom manipulator is derived by using Kane’s equation and virtual work principle.Secondly, a new fixed-time sliding mode surface is designed based on the fixed-time stability theory.Combined with 6 R manipulator’s Kane dynamics model, a non-singular fixed-time sliding mode controller is designed aiming at the uncertainty of model parameters and external interferences of the manipulator.The stability of the system is proved by using Lyapunov method.Numerical simulation shows that the designed controller can ensure that the convergence of the system state is independent of the initial conditions, and it has faster convergence rate, shorter convergence time and good robustness.