Reachability as a Unifying Framework for Computing Helicopter Safe Operating Conditions and Autonomous Emergency Landing

TL;DR

This paper introduces a grid-free numerical method using Hamilton-Jacobi equations to efficiently compute safe helicopter operating conditions and autonomous emergency landing trajectories, even in complex flight scenarios.

Contribution

It presents a novel trajectory optimization approach that avoids exponential scaling of traditional grid-based methods for high-fidelity helicopter models.

Findings

Successfully computes safe landing trajectories from any initial condition.

Efficiently determines unsafe operating regions without spatial discretization.

Applicable to various flight conditions, including non-cruise scenarios.

Abstract

We present a numeric method to compute the safe operating flight conditions for a helicopter such that we can ensure a safe landing in the event of a partial or total engine failure. The unsafe operating region is the complement of the backwards reachable tube, which can be found as the sub-zero level set of the viscosity solution of a Hamilton-Jacobi (HJ) equation. Traditionally, numerical methods used to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension, which is problematic for the high-fidelity dynamics models required for accurate helicopter modeling. We avoid the use of spatial grids by formulating a trajectory optimization problem, where the solution at each initial condition can be computed in a computationally efficient manner. The proposed method is shown to compute an autonomous landing trajectory from any operating condition, even in non-cruise flight conditions.