Navigating the Noise: A CBF Approach for Nonlinear Control with Integral Constraints

TL;DR

This paper introduces a novel control approach using constraint-based methods for nonlinear systems with integral constraints, demonstrated on quadrotors emitting noise, with potential applications in environmental and biological monitoring.

Contribution

It extends control barrier functions to handle trajectory-based integral constraints and proposes efficient over-approximations for constraints over lines and sets.

Findings

Successful simulation validation of the proposed control strategies.

Effective management of noise emission and obstacle avoidance in quadrotor trajectories.

Potential applicability to diverse fields like microscopy and pollution control.

Abstract

Many physical phenomena involving mobile agents involve time-varying scalar fields, e.g., quadrotors that emit noise. As a consequence, agents can influence and can be influenced by various environmental factors such as noise. This paper delves into the challenges of controlling such agents, focusing on scenarios where we would like to prevent excessive accumulation of some quantity over select regions and extended trajectories. We use quadrotors that emit noise as a primary example, to regulate the trajectory of such agents in the presence of obstacles and noise emitted by the aerial vehicles themselves. First, we consider constraints that are defined over accumulated quantities, i.e functionals of the entire trajectory, as opposed to those that depend solely on the current state as in traditional Higher order Control Barrier Functions (HOCBF). Second, we propose a method to extend constraints from individual points to lines and sets by using efficient over-approximations. The efficacy of the implemented strategies is verified using simulations. Although we use quadrotors as an example, the same principles can equally apply to other scenarios, such as light emission microscopy or vehicle pollution dispersion. The technical contribution of this paper is twofold.