Online Learning-Enhanced High Order Adaptive Safety Control

TL;DR

The paper addresses safety guarantees for complex robotic systems under unknown time-varying perturbations by enhancing high-order control barrier functions with online knowledge-based neural ODE residual learning (NODE-HO-aCBF). It integrates a nominal dynamics model with a neural residual learned online, updating a safe control via a $100\,\text{Hz}$ QP that accounts for the residual through Lie-derivative terms of the learned dynamics. The authors demonstrate both simulations (with a double integrator and obstacle avoidance) and physical experiments on a $38\,\text{g}$ nano quadrotor under $18\,\text{km/h}$ wind, showing improved safety performance and adaptability compared to baseline HO-aCBF and HOCBF controllers. The approach is data-efficient due to the hybrid KNODE structure and online updates, enabling real-time safety maintenance in dynamic, uncertain environments with potential extensions to probabilistic guarantees and swarm scenarios.

Abstract

Control barrier functions (CBFs) are an effective model-based tool to formally certify the safety of a system. With the growing complexity of modern control problems, CBFs have received increasing attention in both optimization-based and learning-based control communities as a safety filter, owing to their provable guarantees. However, success in transferring these guarantees to real-world systems is critically tied to model accuracy. For example, payloads or wind disturbances can significantly influence the dynamics of an aerial vehicle and invalidate the safety guarantee. In this work, we propose an efficient yet flexible online learning-enhanced high-order adaptive control barrier function using Neural ODEs. Our approach improves the safety of a CBF-certified system on the fly, even under complex time-varying model perturbations. In particular, we deploy our hybrid adaptive CBF controller on a 38g nano quadrotor, keeping a safe distance from the obstacle, against 18km/h wind.

Figures (7)

• Figure 1: A 38$\unit{g}$ nano quadrotor tracks a circular trajectory while keeping a safe distance from the obstacle, against an $18\unit{km/h}$ wind. The safety is improved on-the-fly, i.e., the quadrotor moves further away from the obstacle after experiencing the wind once.
• Figure 2: The picture depicts the system overview of our NODE-HO-aCBF framework. The safety control solves the NODE-HO-aCBF QP, which uses the most recently trained model, at $100\unit{Hz}$ to certify the desired control. The state and control input data are stored in an online queue for training. The hybrid adaptation module combines a nominal model with a learning-based term that approximates the unknown residual dynamics online.
• Figure 3: Qualitative result of our algorithms compared to baseline controllers with the presence of external residual dynamics. The blue dot represents the initial state, and the red dot represents the current reference. The Gray sphere is the forbidden region. Top left: "Attractive" residual, Top right: "Repulsive" residual, Bottom left: "Time-varying" residual from $0$-$20\unit{s}$, Bottom right: "'Time-varying" residual from $20$-$40\unit{s}$.
• Figure 4: Qualitative comparison between baseline HO-aCBF controller with different settings. "Attractive" residual (on the left), and "Time-varying" residual (on the right) are applied in experiments.
• Figure 5: The top views (first row) and the side views (second row) of $60\unit{s}$ trajectories using different safety controllers in the physical experiments. The red arrows indicate the location and direction of the wind.

Theorems & Definitions (3)

• Definition 1: Relative degree khalil2002nonlinear
• Definition 2: HOCBFs xiao2021hightan2021high
• Theorem 1: tan2021high