Norm optimal iterative learning control for general spatial path following problem

This paper takes the advantage of iterative learning control (ILC) to solve spatial path following problems with high tracking accuracy. The concept of spatial path tracking is first introduced by defining a varying reference profile, which specifies the speed along the path. The task description of ILC is extended to incorporate the scope of spatial tracking by enabling its reference profile as a changing variable. Hence, a spatial ILC algorithm with monotonic convergence properties is derived, which updates the input signal and reference profile simultaneously by solving a minimum norm problem. This optimization problem is further reformulated into a second order cone programming (SOCP) problem by linear approximation, and the global optimal solution can be obtained. Based on a gantry robot model, numerical tests are undertaken to demonstrate the feasibility of the proposed algorithm.