Trajectory Planning For 3-DOF Permanent Magnet Spherical Motor

Three degree of freedom(3-DOF)permanent magnet spherical motor is a kind of electromechanical energy conversion device which has the advantages of novel structure,high integration and multiple degree of freedom movement,and can be used widely.But the study of the permanent magnet spherical motor is still in the theoretical research and such as experimental stage,and trajectory planning,motion control,many other issues needs to be solved.In this paper,the kinematic and dynamic characteristics of 3-DOF permanent magnet spherical motor are analyzed by using the screw theory.Firstly,the kinematic characteristics of 3-DOF permanent magnet spherical motor is analyzed with spiral motion and POE index method,and the inverse and positive kinematics solution are founded,as well as the speed Jacobi matrix of 3-DOF spherical permanent magnet motor.Using the Kaine equation and the screw theory,the driving torque for 3-DOF permanent magnet spherical motor is obtained,and the dynamic model of 3-DOF permanent magnet spherical motor is established.Secondly,Using a variety of methods make a deep research on trajectory planning problem for 3-DOF spherical permanent magnet motor.Using S curve acceleration and deceleration method,three spline method and B spline method for 3-DOF spherical permanent magnet motor trajectory planning and simulate all of this methods respectively on the same path.Analyzed and studied the trajectories of different trajectory planning methods,and compare the performance of different methods trajectories.Finally,the minimum jerk trajectory planning method improving the performance of permanent magnet spherical motor is proposed,with minimum of jerk square integral is carried out fluctuation as the objective of smooth performance.Using genetic algorithm get the global optimization with the minimum jerk objective and the corresponding time node vectors,and the minimum jerk trajectory is obtained.The feasibility and effectiveness of the proposed method are verified by simulation experiments.