Optimal trajectory generation for polynomial nonlinear systems with guaranteed constraint satisfaction using B-splines

This contribution extends the results from [1], in which optimal trajectories for linear systems are determined using a B-spline parameterization of the flat output of the system. Semi-infinite bounds on system states or inputs are imposed using the convex hull property of B-splines, yielding simple linear constraints on the spline coefficients which guarantee constraint satisfaction over the support of the spline. This method provides an alternative to gridding the constraint, which is commonly used for solving optimal control problems but does not provide any guarantees for feasibility in between grid points.