Heteroscedastic Bayesian Optimization-Based Dynamic PID Tuning for Accurate and Robust UAV Trajectory Tracking

TL;DR

HBO-PID addresses UAV trajectory tracking under nonlinear, coupled quadrotor dynamics by fusing a cascaded PID controller with heteroscedastic Bayesian optimization. The method models input-dependent noise variance with a GP-based surrogate, updating the noise predictions via a parametric form $ u(oldsymbol{ ext{Xi}})=z\exp\big(\boldsymbol{\beta}^\top \rho(\boldsymbol{\text{Xi}})\big)+\zeta$ and using Expected Improvement to guide parameter search. A two-stage, phased optimization scheme first rapidly reduces large tracking errors and then fine-tunes gains to minimize residuals, particularly angular errors. Experiments in simulation and on a real UAV show HBO-PID achieving substantial reductions in position and angular errors (e.g., up to 42.9% and 78.4% on ellipse trajectories) over SOTA baselines, validating improved accuracy and robustness in dynamic environments.

Abstract

Unmanned Aerial Vehicles (UAVs) play an important role in various applications, where precise trajectory tracking is crucial. However, conventional control algorithms for trajectory tracking often exhibit limited performance due to the underactuated, nonlinear, and highly coupled dynamics of quadrotor systems. To address these challenges, we propose HBO-PID, a novel control algorithm that integrates the Heteroscedastic Bayesian Optimization (HBO) framework with the classical PID controller to achieve accurate and robust trajectory tracking. By explicitly modeling input-dependent noise variance, the proposed method can better adapt to dynamic and complex environments, and therefore improve the accuracy and robustness of trajectory tracking. To accelerate the convergence of optimization, we adopt a two-stage optimization strategy that allow us to more efficiently find the optimal controller parameters. Through experiments in both simulation and real-world scenarios, we demonstrate that the proposed method significantly outperforms state-of-the-art (SOTA) methods. Compared to SOTA methods, it improves the position accuracy by 24.7% to 42.9%, and the angular accuracy by 40.9% to 78.4%.

Figures (7)

• Figure 1: Overall algorithm framework and controller parameter optimization, we first divide the trajectory tracking into two phases and use heteroskedastic Bayesian optimization to search for the optimal PID parameters in each phase to adaptively obtain the best parameter configuration for the current trajectory.
• Figure 2: Example of error estimation $\hat{e}$ with Gaussian Process regression, showing predicted error with homoscedastic and heteroscedastic variances.
• Figure 3: Tracking results of different algorithms on three trajectories, ellipse on the left, four-leaf clover in the center, and spiral trajectory on the right. As shown by the red arrows, our method is consistently closer to the reference trajectory in all three trajectories.
• Figure 4: Tracking error of using different noise models.
• Figure 5: Tracking error of using different optimization strategies.