A simplified model of inverse kinematics of permanent magnet spherical motor

Abstract

The inverse kinematics of permanent magnet spherical motor is the basis of dynamic control, motion analysis and trajectory planning. However, inverse kinematics is actually a solving problem of a set of strong coupling and nonlinear equations. The analytic solution is more complicated. In this paper, the inverse kinematics problem of permanent magnet spherical motor is solved by particle swarm optimization and gradient projection method respectively, and the performance of the two methods is compared. Aiming at the shortcomings of calculating the inverse kinematics, a simple model of inverse kinematics is proposed by using the idea that the sine and cosine can be linearized when the Euler angle is infinite, the model reduces the coupling degree of the equations and simplifies the complexity of constructing the feasible descent direction. The relationship between the rotation variable and the solution time and the precision of the solution is analyzed, and the effectiveness of the simplified model is verified.