Path Tracking using WKB Approximation

This paper introduces a new approach for robot path tracking based on the WKB approximate analytical solution of time-varying ordinary differential equations. An open-loop control is chosen for the system and an expression is obtained for the linearized perturbation dynamics around the nominal trajectory corresponding to the open-loop control. The WKB solution of the linearized dynamics is used to choose state error feedback coefficients to guarantee stability. The new approach is applied to a 2-DOF manipulator example.