Noncooperative Herding With Control Barrier Functions: Theory and Experiments

Abstract

In this paper, we consider the problem of protecting a high-value unit from inadvertent attack by a group of agents using defending robots. Specifically, we develop a control strategy for the defending agents that we call "dog robots" to prevent a flock of "sheep agents" from breaching a protected zone. We take recourse to control barrier functions to pose this problem and exploit the interaction dynamics between the sheep and dogs to find dogs' velocities that result in the sheep getting repelled from the zone. We solve a QP reactively that incorporates the defending constraints to compute the desired velocities for all dogs. Owing to this, our proposed framework is composable i.e. it allows for simultaneous inclusion of multiple protected zones in the constraints on dog robots' velocities. We provide a theoretical proof of feasibility of our strategy for the one dog/one sheep case. Additionally, we provide empirical results of two dogs defending the protected zone from upto ten sheep averaged over a hundred simulations and report high success rates. We also demonstrate this algorithm experimentally on non-holonomic robots. Videos of these results are available at https://tinyurl.com/4dj2kjwx.

Distributed Multirobot Control for Non-Cooperative Herding

“…In this section, we show two approaches to solve Problem 1, building on our previously proposed centralized algorithm [9]. Define a safety index h(•) : R 2 −→ R that quantifies the distance of S i from P:…”

“…where the jacobians are defined as J S ji := ∇ x S j f i (x) and J D li := ∇ x D l f i (x) Note that (10) contains the velocity terms of all dogs. In [9], we leveraged this observation to obtain a linear constraint on the velocity of all dogs collectively for preventing sheep S i from breaching P:…”

“…In this section, we show the results obtained by performing robot experiments by implementing the distributed algorithms of section 4.1 and section 4.2. Additionally, we also present more experimental results for our prior centralized algorithm from [9] (because at the time, we did not have as many robots). We conduct these experiments in our lab's multi-robot arena, which consists of a 14ft × 7ft platform with multiple Khepera IV robots and eight Vicon cameras for motion tracking.…”

“…We conduct these experiments in our lab's multi-robot arena, which consists of a 14ft × 7ft platform with multiple Khepera IV robots and eight Vicon cameras for motion tracking. Although Khepera robots have unicycle dynamics, [9] consists of a technique to convert the single-integrator dynamics (assumed for dogs and sheep) to linear and angular velocity commands for the robots.…”

“…In our prior work [9], we developed a centralized algorithm to solve this problem using control barrier functions. In this work, a) we provide more experimental validation of the centralized algorithm, b) propose two distributed algorithms, and c) provide simulations and experiments to validate these algorithms.…”