Computing feasible trajectories for constrained maneuvering systems: the PVTOL example

TL;DR

This paper presents an optimal control strategy for computing feasible trajectories of nonlinear constrained systems, demonstrated on a simplified aircraft model, combining dynamic embedding, constraint relaxation, and novel optimization methods.

Contribution

It introduces a new trajectory planning approach for constrained nonlinear systems using dynamic embedding and optimization, specifically applied to the PVTOL model.

Findings

Successfully computes feasible trajectories for PVTOL

Demonstrates the method's capability to handle constraints

Provides insights into system capabilities within the operating region

Abstract

In this paper we provide an optimal control based strategy to explore feasible trajectories of nonlinear systems, that is to find curves that satisfy the dynamics as well as point-wise state-input constraints. The strategy is interesting itself in understanding the capabilities of the system in its operating region, and represents a preliminary tool to perform trajectory tracking in presence of constraints. The strategy relies on three main tools: dynamic embedding, constraints relaxation and novel optimization techniques, introduced in [10,12], to find regularized solutions for point-wise constrained optimal control problems. The strategy is applied to the PVTOL, a simplified model of a real aircraft that captures the main features and challenges of several "maneuvering systems".