Flatness-based minimum-time trajectory generation for constrained linear systems using B-Splines

In this paper we discuss minimum-time trajectory generation for input-and-state constrained continuous-time LTI systems in the light of the notion of flatness and B-splines parameterisation. Flat systems have the nice property that the input and the state trajectories can be completely characterised by the so-called flat output. We propose a splines parameterisation for the flat output, and the corresponding parameterisations 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 splines control-point 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.