On-Board Near Optimal Flight Trajectory Generation using Deferential Flatness

Abstract

An optimal explicit guidance law that maximizes terminal velocity is developed for a reentry vehicle to a fixed target. The equations of motion are reduced with differential flatness approach and acceleration commands are related to trajectory's parameters. An optimal trajectory is determined by solving a real-coded genetic algorithm. For online trajectory generation, optimal trajectory is approximated. The approximated trajectory is compared with the pure proportional navigation, and genetic algorithm's solutions. The near optimal terminal velocity solution compares very well with these solutions. The approach robustness is examined by Monte Carlo simulation. Other advantages such as trajectory representation with minimum parameters, applicability to any reentry vehicle configuration and any control scheme, and Time-to-Go independency make this guidance approach more favorable.

Optimal trajectory generation and robust flatness–based tracking control of quadrotors

“…Since the quadrotor has a nonlinear model, indirect methods have been used only for a few examples, ie, the one being examined by Hehn et al Direct methods are developed while avoiding the disadvantages of the two‐point limit value resolution, by converting the path optimization problem into a nonlinear programming (NLP) problem, which can be solved using an NLP solver such as spare nonlinear optimizer (SNOPT) . The principle of the direct method is to approximate the state and control variable by utilizing curvilinear functions such as B‐splines, Bezier, the pseudospectral, and Hermit polynomials . Accordingly, the parameters of these curves represent the decision variable of the optimization problem.…”