Quadrotor Stabilization with Safety Guarantees: A Universal Formula Approach

TL;DR

This paper presents a fast, analytical control strategy for quadrotor stabilization that guarantees safety and obstacle avoidance without relying on computationally intensive optimization, incorporating robustness to disturbances and input constraints.

Contribution

It introduces a universal formula-based control approach inspired by Sontag's formula, integrating CLFs, CBFs, ISS, and input projection for real-time safe quadrotor control.

Findings

Effective obstacle avoidance demonstrated in simulations

Real-world experiments confirm fast onboard computation

Enhanced disturbance robustness through ISS and ISSf integration

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.