Dynamic Modeling, Trajectory Planning And Vibration Suppressing Of The Spatial Flexible Manipulator

With the rapid development of the aerospace industry and increasing demands foraerospace applications, more and more tasks in space need to be completed with the help ofspace manipulators, such as construction and operation of the station. In the spaceapplications, due to the limitation of launch costs and energy and the requirement of spaceoperation, the redundant flexible manipulator with light structure, low energy consumption,great payload-to-manipulator-weight ratio and rapid response, has been highly valued andwidely used.The field of spatial flexible manipulator essentially belongs to the category of offlexible multibody system dynamics, which has always been one of the hot and difficultsubjects. The conventional flexible multibody system dynamics methods based on theassumptions of small deformation and little rotation, can not satisfy the requirement ofprecise modeling for light aircrafts. The combination of the Absolute Nodal CoordinateFormulation (ANCF) describing flexible bodies and the Natural Coordinate Formulation(NCF) describing rigid bodies, can form the rigid-flexible multibody system dynamicsmethod called the Absolute-Coordinate-Based (ACB) method, which is suitable for themodeling of multibody system with large deformation. The flexible joints and flexible linksare widely used in spatial flexible manipulators. These two flexible aspects will causevibration at different levels. Meantime, trajectory planning needs to be completed beforethe manipulator performs tasks. It is significant if trajectory planning and vibrationsuppressing can be combined, which is called trajectory planning for vibration suppressing.This dissertation presents a problem-oriented research, based on the ACB method, inorder to deal with trajectory planning and vibration suppressing of the spatial flexiblemanipulators. The major contributions of the dissertation can be summarized as follows.1) Some simple formulations are proposed to impose torsional torque on NCF elements.The driving torque imposed on the manipulator joint modeled by NCF can be obtainedwith these formulations. The inverse kinematics of NCF is analysed, and the physicalmeaning of the inherent and joint constraints of NCF elements are explained. Some simple formulations are proposed to calculate the driving torque between two NCFelements with relative motion. This method can be used in the inverse dynamics of themanipulator.2) Based on the continuum mechanics theory, finite element method and matrix analysistheory, the elastic force and its Jacobian matrix of the three-dimensional ANCF beamelement of two nodes is derived in detail. And this method can be expanded to otherANCF elements.3) The specialized stiffness test equipment developed by our research group is used totest the torsional stiffness of some typical flexible joints. The test data is fitted andthen three typical models of flexible joints are put forward, including linear stiffnessmodel, nonlinear stiffness model and nonlinear stiffness with clearance model.4) For the point-to-point and rest-to-rest motion in the joint space, a new function basedon Fourier cosine series with one redundant coefficient is proposed to plan the jointtrajectory. By designing the redundant coefficient, the optimal trajectory can beobtained to suppress the residual vibration of the flexible manipulator. Based on thistrajectory function, particle swarm optimization (PSO) is introduced to optimize thecoefficient, the residual vibration can be more effectively suppressed.5) Both the forward kinematics and inverse kinematics of the redundant manipulator areanalyzed and the inverse kinematics algorithm is discussed. The simulation isconducted on the three-link manipulator, and the algorithm accuracy is verified. Usingthe manipulator redundancy and optimizing the self-motion with PSO, the residualvibration can be effectively reduced and the end-effector trajectory along the given oneis ensured simultaneously.6) Both the forward kinematics and inverse kinematics of the spatial manipulator of sevenDOF (degrees of freedom) are derived in detail, including homogeneous transformationmatrix and Jacobian matrix. Two typical forms of motion including rectilinear motionand circular motion of the manipulator end-effector are analyzed. Trajectory planningof these two kinds of motions are given in detail. These two trajectory planningmethods are verified effectively by performing simulations, and the obtained trajectory,velocity and acceleration are all smooth and continuous.