Constrained minimum-time trajectory generation for a laboratory-scale magnetic-levitation system

In this paper we present a method to generate minimum-time constrained trajectories for a magnetic-levitation (Maglev) system. The Maglev model is a differentially flat system, and as such it has the useful property that the input and the state trajectories can be completely characterised by the so-called flat output. We propose a B-splines parameterisation for the flat output, and the corresponding parameterisation for the performance output, the states, and the inputs. Using this parameterisation the problem of minimum-time constrained trajectory planning is cast into a feasibility-search problem in the spline control-points space, in which the constraint region is characterised by a polytope. A close approximation of the minimum-time trajectory is obtained by systematically searching the end-time that makes the constraint polytope to be minimally feasible. Experimental results, validating the method on a laboratory real system, are presented.