Optimal Take-off under Fuzzy Clearances

TL;DR

This work addresses safe UAV take-off under dynamic obstacles by combining Optimal Control under clearance with a three-stage Takagi-Sugeno-Kang FRBS that modulates obstacle constraints through outputs $R_i$, $U_i$, and Activation and integrates these as soft constraints in the Falcon.m/IPOPT optimization framework. The key contribution is an interpretable, regulation-informed decision layer that adapts constraint radii and urgency in real time to reduce recomputation while preserving aviation safety standards. Empirical results on a simplified aircraft model show near real-time performance with notable speed ($2$ to $3$ seconds per iteration) but reveal a solver regression where the Lagrangian penalty remained identically zero with recent software versions, suggesting a toolbox compatibility issue rather than a modeling failure. The authors propose future work including reverting to earlier software versions, optimizing fuzzy membership functions via evolutionary methods, extending to higher-fidelity aircraft models and stochastic environments, and benchmarking against alternative anti-collision approaches, to validate scalability and robustness for real-world deployment.

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.

Figures (12)

• Figure 1: Object Type Membership
• Figure 2: Object Size Membership
• Figure 3: Object Distance Membership
• Figure 4: Object Closing-rate Membership
• Figure 5: Constraint Radius Membership