Constrained trajectory synthesis via quasi-interpolation

In this article we introduce QuITO — Quasi-Interpolation based Trajectory Optimization, a direct multiple shooting algorithm to solve a class of constrained nonlinear minimum energy optimal control problems. This technique is based on the theory of approximate approximations – a quasi-interpolation scheme. We parameterize the control trajectory using the quasi-interpolation formula, and we discretize the optimal control problem using the collocation points on a uniform cardinal grid, thereby transcribing the optimal control problem (OCP) into a nonlinear program (NLP). Several examples are provided to show the numerical fidelity of the algorithm.