基于POE的动力学建模与快速非奇异终端滑模控制  

Dynamic Modeling Based on POE and Non-singular Terminal Sliding Mode Control

作　　者：陈庆诚[1] 朱世强[1] Rajat Mittal 张学群[1] 

机构地区：[1]浙江大学流体动力与机电系统国家重点实验室,杭州310027 [2]曼尼帕大学曼尼帕工学院

出　　处：《农业机械学报》2015年第6期310-318,共9页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家自然科学基金创新研究群体资助项目(51221004);浙江省自然科学基金资助项目(LY13E050001);杭州市重大科技创新资助项目(20132111A04)

摘　　要：结合旋量指数积形式(POE)和凯恩方程的优点,提出了一种具有明显几何意义的高效动力学建模方法,并以此为基础提出机器人系统的快速非奇异终端滑模控制算法。凯恩方程中的偏速度选择为基于旋量理论描述的合适的物体雅可比矩阵,并以此定义其他动力学模型参数表达方式,且在'钱江一号'串联机器人上进行建模实例验证。基于该动力学模型,为了改善传统滑模控制的有限时间收敛特性,保证全局控制非奇异性,提出了一种快速全局非奇异终端滑模控制,通过构造带状态高次项的滑模面函数,得到全局非奇异控制,并保证系统从任意状态到达滑模面的时间和在滑模上到达平衡点的时间均为有限且快速收敛,通过李雅普诺夫函数证明了其稳定性,并结合对比实验,验证了该方法在机器人系统中的鲁棒性和有效性。To compact the dynamic analysis and improve the computation efficiency,the advantages of Kane＇s equations and the product of exponential（ POE） formulas were combined based on screw theory to propose a new effective dynamic modeling of robot manipulator with explicit geometric significance,and based on this dynamic model,a non-singular terminal sliding mode control was presented to achieve better performance. The velocity Jacobian matrix was addressed in the product of exponential form by introducing the screw theory,and the partial velocity of Kane＇s equations was selected specifically from the suitable velocity Jacobian matrix. Then a dynamic modeling example based on Kane＇s equations and screw theory was established,which led to be less complicated compared with other typically dynamic methods. With the proposed dynamic equations of serial robot manipulator,a fast non-singular terminal sliding mode（ FNTSM） control was presented by introducing an improved fast non-singular terminal sliding mode surface,which was designed to ensure the fast convergence in global system state whether it was near to equilibrium or far away from the equilibrium. Then the stability analysis of the proposed method was performed by using Lyapunov stability theory. Finally, comparative experiments were implemented to demonstrate the effectiveness and robustness of the proposed approach.

关 键 词：动力学建模 凯恩方程 指数积 滑模控制 

分 类 号：TP242.2[自动化与计算机技术—检测技术与自动化装置]