Euler–Lagrange as Pseudo-metric of the RRT algorithm for optimal-time trajectory of flight simulation model in high-density obstacle environment

Abstract

SUMMARYThis paper introduces a solution to the problem of steering an aerodynamical system, with non-holonomic constraints superimposed on dynamic equations of motion. The proposed approach is a dimensionality reduction of the Optimal Control Problem (OCP) with heavy path constraints to be solved by Rapidly-Exploring Random Tree (RRT) algorithm. In this research, we formulated and solved the OCP with Euler–Lagrange formula in order to find the optimal-time trajectory. The RRT constructs a non-collision path in static, high-dense obstacle environment (i.e. heavy path constraint). Based on a real-world aircraft model, our simulation results found the collision-free path and gave improvements of time and fuel consumption of the optimized Hamiltonian-based model over the original non-optimized model.