Resilient Estimator-based Control Barrier Functions for Dynamical Systems with Disturbances and Noise

TL;DR

This work tackles safety in path planning under disturbances and measurement noise by marrying a resilient estimator with a stochastic control barrier framework. The proposed RE-CBF framework uses Itô-based barrier conditions and disturbance estimates from a resilient estimator to compute a safe control input $u_s$ that remains close to a nominal input $u$ while ensuring the state stays inside the safe set $\mathcal{S}$. Key contributions include (i) a stochastic CBF optimization that accounts for process noise and measurement noise, (ii) a resilient estimator that estimates disturbance $d_k$ online to correct state estimates, and (iii) a quadrotor testing pipeline validated via simulations and real indoor flights demonstrating safety guarantees in the presence of disturbances and noise. The approach advances practical safety for autonomous systems in uncertain environments by providing provable safety mechanisms that integrate estimation and barrier-based control, with direct applicability to aerial robots and similarly modeled dynamical systems.

Abstract

Control Barrier Function (CBF) is an emerging method that guarantees safety in path planning problems by generating a control command to ensure the forward invariance of a safety set. Most of the developments up to date assume availability of correct state measurements and absence of disturbances on the system. However, if the system incurs disturbances and is subject to noise, the CBF cannot guarantee safety due to the distorted state estimate. To improve the resilience and adaptability of the CBF, we propose a resilient estimator-based control barrier function (RE-CBF), which is based on a novel stochastic CBF optimization and resilient estimator, to guarantee the safety of systems with disturbances and noise in the path planning problems. The proposed algorithm uses the resilient estimation algorithm to estimate disturbances and counteract their effect using novel stochastic CBF optimization, providing safe control inputs for dynamical systems with disturbances and noise. To demonstrate the effectiveness of our algorithm in handling both noise and disturbances in dynamics and measurement, we design a quadrotor testing pipeline to simulate the proposed algorithm and then implement the algorithm on a real drone in our flying arena. Both simulations and real-world experiments show that the proposed method can guarantee safety for systems with disturbances and noise.

Figures (5)

• Figure 1: An illustrative control diagram of RE-CBF method implementing on a quadrotor drone.
• Figure 2: World coordinate and body fixed coordinate of Crazyflie and Euler angles defined in these coordinates
• Figure 3: 2D trajectories of PD nominal controller and the resilient estimator-based CBF controller that avoid a super ellipsoid obstacle. The quadrotor flies around the target while avoiding an obstacle with the help of the RE-CBF.
• Figure 4: 3D space trajectories of the nominal PD controller and the RE-CBF controller inside a box area. We also plot the zoom-in trajectories in the area where $r_x, r_y\in [-1.6, -1.3]$m and $r_z \in [-2, 8]$m.
• Figure 5: Figures of flying arena, quadrotor and final rsults.

Theorems & Definitions (4)

• Definition 1
• Theorem 1
• Definition 2
• Definition 3