Title：Kinematics and Dynamics HessianMatrices of Manipulators Based on Screw Theory
Author：ZHAO Tieshi, GENG Mingchao, CHENYuhang, LI Erwei, YANG Jiantao
Abstract：The complexity of the kinematicsand dynamics of a manipulator makes it necessary to simplify the modelingprocess. However, the traditional representations cannot achieve this becauseof the absence of coordinate invariance. Therefore, the coordinate invariantmethod is an important research issue. First, the rigid-body acceleration, thetime derivative of the twist, is proved to be a screw, and its physical meaningis explained. Based on the twist and the rigid-body acceleration, theacceleration of the end-effector is expressed as a linear-bilinear form, andthe kinematics Hessian matrix of the manipulator(represented by Lie bracket) isdeduced. Further, Newton-Euler’s equation is rewritten as a linear-bilinearform, from which the dynamics Hessian matrix of a rigid body is obtained. Theformulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work, the dynamics Hessian matrix of theparallel manipulator is gotten and the detailed dynamic model is derived. Anindex of dynamical coupling based on dynamics Hessian matrix is presented. Inthe end, a foldable parallel manipulator is taken as an example to validate thededuced kinematics and dynamics formulae. The screw theory based method cansimplify the kinematics and dynamics of a manipulator, also the correspondingdynamics Hessian matrix can be used to evaluate the dynamical coupling of amanipulator.
摘要：在汽车动力学理论的基础上,通过对基于集成起动机/发电机(Integratedstarter/Generator,ISG)的中度混合动力汽车(Medium hybrid electric vehicle,Medium-HEV)的系统效率进行瞬时优化计算,得到ISG型中度混合动力汽车控制策略,确定控制策略中三个关键系数:电池电量切换阈值XSC,发动机充电曲线系数Xe_chg和发动机关闭曲线系数Xe_off,以及它们的取值范围。在Matlab/Simulink仿真平台下,建立ISG型中度混合动力汽车整车仿真模型,将电池电量变化值△SC折算为等效油耗,以ISG型中度混合动力系统综合油耗最小为优化目标优选三个系数的取值,从而确定ISG型中度混合动力系统动力源的匹配和优化控制策略。仿真结果表明,与传统汽车相比,ISG型中度混合动力汽车的油耗降低了36.95%,明显提高了中度混合动力系统燃油经济性。
