Trajectory Planning Of Permanent Magnet Spherical Motor Based On Different Optimal Targets

Permanent magnet spherical motor as a driving mechanism to complete the three-dimensional space movement,which can effectively simplify the complexity of the system and improve the dynamic and performance system's static,has a wide range of applications.However,the permanent magnet spherical motor is still in the exploratory stage,and some progress has been made in trajectory planning and motion control.However,it is still far from practical application and further research is still needed.In this paper,the operating principle of three degrees-of-freedom permanent magnet spherical motor is analyzed firstly,and the forward kinematic model of the rigid-body motor with a single rigid body and the sliding rail support system is established.The three-degrees-of-freedom permanent magnet spherical motor speed transformation Jacobian matrix.Then according to the law of moment of momentum,the rotor dynamic equation of the motor is established and transformed into the standard form of Lagrange equation.It provides an important theoretical basis for the follow-up study of trajectory planning and trajectory tracking control of three-DOF permanent magnet spherical motor.Secondly,this paper uses a variety of mathematical methods to deeply study the trajectory planning problem of three degrees-of-freedom permanent magnet spherical motor.First of all,taking the minimum time as the optimization target,the continuous trajectory of three degrees of freedom permanent magnet spherical motor is respectively calculated by S curve,exponential curve,trigonometric curve,cubic spline,B spline and NURBS,planning.The motion trajectory is represented as a series of key points.The key points are connected by the above six planning methods,and the angular velocity is used as the constraint condition.The maximum of various angular velocity curves Splicing can get a comprehensive angular velocity curve,solve the optimal solution,the last simulation.Finally,a multi-objective trajectory planning method for a three-DOF permanent magnet spherical motor is proposed in this paper.In this method,two performance indexes of time and shock are optimized objective function.Five times of non-uniform rational B-spline curve interpolation position sequence are used to convert the kinematic constraints into non-uniform rational B-spline curves to control vertex constraints.Considering velocity,Kinematic constraints of acceleration and shock ensure that acceleration is continuous and start-stop speed,acceleration and jerk can be set.The sequence quadratic programming method is used to solve the optimal time nodes of movement,and then the trajectory satisfying the constraints and performance indexes is planned.At last,simulation is carried out.