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Robotic Shepherding in Cluttered and Unknown Environments using Control Barrier Functions

Mahmoud Hamandi, Farshad Khorrami, Anthony Tzes

TL;DR

This work tackles guiding a noncooperative herd of robot-sheep using a small team of robot-dogs to a goal in cluttered unknown environments. It introduces an optimization-based controller built on Control Barrier Functions to enforce a moving protected region around a reference trajectory and to impose obstacle and inter-agent collision avoidance, yielding linear inequality constraints on dog velocities. The approach integrates centralized LiDAR-based environment mapping, frontier exploration, and skeletal path planning to compute safe trajectories, solved via a quadratic program that respects dog speed limits. Through obstacle-free, cluttered, and maze-like simulations, the method demonstrates reliable confinement of the herd, smooth dog-driven trajectories, and robust re-planning in unknown spaces.

Abstract

This paper introduces a novel control methodology designed to guide a collective of robotic-sheep in a cluttered and unknown environment using robotic-dogs. The dog-agents continuously scan the environment and compute a safe trajectory to guide the sheep to their final destination. The proposed optimization-based controller guarantees that the sheep reside within a desired distance from the reference trajectory through the use of Control Barrier Functions (CBF). Additional CBF constraints are employed simultaneously to ensure inter-agent and obstacle collision avoidance. The efficacy of the proposed approach is rigorously tested in simulation, which demonstrates the successful herding of the robotic-sheep within complex and cluttered environments.

Robotic Shepherding in Cluttered and Unknown Environments using Control Barrier Functions

TL;DR

This work tackles guiding a noncooperative herd of robot-sheep using a small team of robot-dogs to a goal in cluttered unknown environments. It introduces an optimization-based controller built on Control Barrier Functions to enforce a moving protected region around a reference trajectory and to impose obstacle and inter-agent collision avoidance, yielding linear inequality constraints on dog velocities. The approach integrates centralized LiDAR-based environment mapping, frontier exploration, and skeletal path planning to compute safe trajectories, solved via a quadratic program that respects dog speed limits. Through obstacle-free, cluttered, and maze-like simulations, the method demonstrates reliable confinement of the herd, smooth dog-driven trajectories, and robust re-planning in unknown spaces.

Abstract

This paper introduces a novel control methodology designed to guide a collective of robotic-sheep in a cluttered and unknown environment using robotic-dogs. The dog-agents continuously scan the environment and compute a safe trajectory to guide the sheep to their final destination. The proposed optimization-based controller guarantees that the sheep reside within a desired distance from the reference trajectory through the use of Control Barrier Functions (CBF). Additional CBF constraints are employed simultaneously to ensure inter-agent and obstacle collision avoidance. The efficacy of the proposed approach is rigorously tested in simulation, which demonstrates the successful herding of the robotic-sheep within complex and cluttered environments.
Paper Structure (18 sections, 1 theorem, 32 equations, 7 figures, 1 algorithm)

This paper contains 18 sections, 1 theorem, 32 equations, 7 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Modeling
  3. Problem Statement and Assumptions
  4. CBF Overview & Frontier Exploration
  5. Control Barrier Functions
  6. Environment Mapping and Path Computation
  7. Optimization Based Controller
  8. Sheep herding CBF
  9. Obstacle avoidance CBF
  10. Agent collision avoidance CBF
  11. Objective Function Formulation
  12. Overall Herding Approach
  13. Simulation Studies
  14. Obstacle-Free Herding
  15. Cluttered and Unknown Environment Herding
  16. ...and 3 more sections

Key Result

Proposition 1

Constraint sheep_herding_CBF_all is guaranteed to have a solution if $n=m$ and in the absence of the other constraints eq:full_dog_obstalces, eq:full_dog_repulsion and the dogs' velocity limits $\bar{u}$.

Figures (7)

  • Figure 1: Overview of the sheep herding algorithm.
  • Figure 2: Objective function components.
  • Figure 3: Herding in an obstacle-free environment.
  • Figure 4: Herding in a small-size cluttered space.
  • Figure 5: Collective sheep herd position and orientation (top). Desired and actual heading $h^d(t)$, $h(t)$ of the sheep swarm (bottom).
  • ...and 2 more figures

Theorems & Definitions (1)

  • Proposition 1