Research On Robot Dynamics Modeling And Trajectory Planning Based On Dual Quaternion

With the development of science and technology,robots have been widely used in various fields.When a robot completes a task,the accuracy of the robot is one of the important indicators affecting the quality of the robot work.Therefore,the establishment of accurate kinematics and dynamics model is the basis for the robot to accomplish the task with high quality.Based on this,this thesis makes a research on the dynamic modeling and trajectory planning of robots based on dual quaternion.This thesis studies the kinematics and dynamics modeling methods of robots by using dual quaternion as mathematical tools.And on this basis,this thesis makes a research on the trajectory planning of robots.The main contents and work of this thesis are as follows:Firstly,the forward kinematics modeling method of multi-degree-of-freedom robot based on dual quaternion is discussed and compared with the kinematics model established by exponential product formula.Aiming at inverse kinematics,all existing types of sub-problems are summarized and introduced,and the sub-problems is also discussed.The selection of reference points and the principle of distance invariance in sub-problems are discussed in depth.The intersection points of interior lines and surfaces in space are analyzed for the extended form of two-axis sub-problems.Aiming at the problem of difficult combination of joint variables of robots,the existing sub-problems are reclassified and a decomposition calculation method for robot inverse kinematics is provided based on dual quaternions.Secondly,a dynamic modeling method based on dual quaternion and Kane's equation is proposed based on Darren Bell principle.The Jacobian matrix of the robot is deduced by describing the process of screw motion with dual quaternion,and the pseudo-velocity applied to Kane's equation is combined.The dual quaternion of active force,inertia force,partial velocity,generalized active force and generalized inertia force are defined,which simplifies the dynamic modeling process.Then,combined with the dual quaternion robot forward kinematics modeling,the robot trajectory planning in the joint space is carried out.At the same time,the inverse kinematics solution of the sub-problem is combined with the trajectory planning in the robot Cartesian space.And the trajectory planning in the joint space and Cartesian space of the robot is completed.In order to realize the pose control of the robot,an error control model based on dual quaternion is proposed,and the generalized proportional control rate is used to control the pose of the robot.Finally,through a three-degree-of-freedom robot dynamics experiment,the simulation results show that the dynamic modeling method is effective.The trajectory planning of afour-degree-of-freedom robot in joint space and Cartesian space is simulated and experimented.The experimental results show that the forward kinematics modeling of the robot based on dual quaternion and the inverse kinematics solving method based on inverse sub-problems are effective.