Optimal Take-off under Fuzzy Clearances

TL;DR

This paper introduces a hybrid obstacle avoidance system combining optimal control with fuzzy logic to adaptively handle safety constraints for unmanned aircraft, aiming for real-time performance and regulatory compliance.

Contribution

It develops a novel three-stage fuzzy rule system integrated into optimal control to adapt obstacle clearances based on aviation safety standards.

Findings

Achieved near real-time trajectory computation within 2-3 seconds per iteration.

Demonstrated the feasibility of fuzzy-enhanced optimal control for obstacle avoidance.

Identified software limitations affecting constraint enforcement in current toolboxes.

Abstract

This paper presents a hybrid obstacle avoidance architecture that integrates Optimal Control under clearance with a Fuzzy Rule Based System (FRBS) to enable adaptive constraint handling for unmanned aircraft. Motivated by the limitations of classical optimal control under uncertainty and the need for interpretable decision making in safety critical aviation systems, we design a three stage Takagi Sugeno Kang fuzzy layer that modulates constraint radii, urgency levels, and activation decisions based on regulatory separation minima and airworthiness guidelines from FAA and EASA. These fuzzy-derived clearances are then incorporated as soft constraints into an optimal control problem solved using the FALCON toolbox and IPOPT. The framework aims to reduce unnecessary recomputations by selectively activating obstacle avoidance updates while maintaining compliance with aviation procedures. A proof of concept implementation using a simplified aircraft model demonstrates that the approach can generate optimal trajectories with computation times of 2,3 seconds per iteration in a single threaded MATLAB environment, suggesting feasibility for near real time applications. However, our experiments revealed a critical software incompatibility in the latest versions of FALCON and IPOPT, in which the Lagrangian penalty term remained identically zero, preventing proper constraint enforcement. This behavior was consistent across scenarios and indicates a solver toolbox regression rather than a modeling flaw. Future work includes validating this effect by reverting to earlier software versions, optimizing the fuzzy membership functions using evolutionary methods, and extending the system to higher fidelity aircraft models and stochastic obstacle environments.