Quadrotor Stabilization with Safety Guarantees: A Universal Formula Approach

TL;DR

This work tackles quadrotor safe stabilization under obstacle avoidance with limited onboard computation. It introduces a universal formula inspired by Sontag's universal formula to fuse $CLF$-based stabilization and $CBF$-based safety constraints without solving onboard optimization. The method is strengthened with ISS/ISSf to handle disturbances and a projection-based approach to enforce input constraints, including a log-sum-exp barrier approximation to consolidate multiple barrier functions. Through simulations and real-world experiments, the authors demonstrate substantially faster onboard computation while maintaining provable stability and safety, enabling practical deployment on resource-constrained quadrotors.

Abstract

Safe stabilization is a significant challenge for quadrotors, which involves reaching a goal position while avoiding obstacles. Most of the existing solutions for this problem rely on optimization-based methods, demanding substantial onboard computational resources. This paper introduces a novel approach to address this issue and provides a solution that offers fast computational capabilities tailored for onboard execution. Drawing inspiration from Sontag's universal formula, we propose an analytical control strategy that incorporates the conditions of control Lyapunov functions (CLFs) and control barrier functions (CBFs), effectively avoiding the need for solving optimization problems onboard. Moreover, we extend our approach by incorporating the concepts of input-to-state stability (ISS) and input-to-state safety (ISSf), enhancing the universal formula's capacity to effectively manage disturbances. Furthermore, we present a projection-based approach to ensure that the universal formula remains effective even when faced with control input constraints. The basic idea of this approach is to project the control input derived from the universal formula onto the closest point within the control input domain. Through comprehensive simulations and experimental results, we validate the efficacy and highlight the advantages of our methodology.

Figures (11)

• Figure 1: Quadrotor coordinate frames: System conversion with $\mathcal{W}$ and $\mathcal{B}$ denoting world and body frames, respectively.
• Figure 2: An approximation of multiple barrier functions: The areas shaded in red represent the unsafe regions defined by the three barrier functions, while the blue regions correspond to the approximated barrier function.
• Figure 3: Control schematic of the quadrotor.
• Figure 4: A graphical interpretation of the projection idea.
• Figure 5: Simulation - The environment settings and safe tracking performances of four different algorithms.

Theorems & Definitions (15)

• Definition 1
• Definition 2
• Definition 3
• Lemma 1
• Theorem 1
• Remark 1
• Remark 2
• Lemma 2
• proof
• Lemma 3