Multi Robot Control for Non-Cooperative Herding using Control Barrier Functions

Abstract

Control Barrier Functions (CBFs) have emerged as a powerful theoretical tool for designing controllers with provable safety guarantees. This work presents a novel methodology that leverages CBFs to synthesize controllers for the problem of protecting a high-value unit from inadvertent attack by a group of non-cooperative agents using defending robots. Specifically, we develop a control strategy for the defending agents that we call ``dog robots" to prevent the non-cooperative agents, i.e., a flock of ``sheep agents" from breaching a protected zone. The sheep agents have no knowledge about the presence of the high-value unit and follow flocking dynamics to reach their goal. We take recourse to CBFs 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.

Furthermore, we address a crucial limitation of existing CBF-based controllers that usually fail to respect the control input's limits, resulting in undesirable outcomes. Imposing these limits by capping the control input could compromise the safety guarantees offered by CBFs, and incorporating them as constraints in the optimization process often leads to infeasibility. To overcome these challenges, we propose a two-step cascaded optimization method. We parameterize the CBF and then compute their values that ensure that CBFs yield solutions, if they exist, within the control limits without compromising safety or feasibility. The performance and efficacy of our cascaded control approach are thoroughly evaluated through extensive simulations in the aforementioned multi-robot scenarios. We also experimentally demonstrate all the above algorithms using Khepera IV robots in a laboratory environment. Overall, this work contributes to advancing multi-robot coordination by providing a framework built on Control Barrier Functions, offering provable safety guarantees while addressing crucial challenges in controller design.