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One Ring to Rule Them All: Constrained Distributional Control for Massive-Scale Heterogeneous Robotic Ensemble Systems

Andres Arias, Wei Zhang, Haoyu Qian, Jr-Shin Li, Chuangchuang Sun

TL;DR

The paper tackles safe, scalable control of massive heterogeneous robotic ensembles under state and environmental constraints. It introduces a moment kernel transform that maps ensemble dynamics into a moment space, enabling a single shared controller to enforce polyhedral constraints and obstacle avoidance, with STL specifications incorporated for complex tasks. The approach yields explicit moment-space representations of polyhedra and obstacles, and demonstrates both simulation and hardware validation (unicycles and QCar 2) for constrained tasks like box/polyhedral confinement and obstacle-rich environments. This work advances scalable, constraint-aware orchestration of large robotic populations by unifying dynamics, constraints, and task specifications in moment space.

Abstract

Ensemble control aims to steer a population of dynamical systems using a shared control input. This paper introduces a constrained ensemble control framework for parameterized, heterogeneous robotic systems operating under state and environmental constraints, such as obstacle avoidance. We develop a moment kernel transform that maps the parameterized ensemble dynamics to the moment system in a kernel space, enabling the characterization of population-level behavior. The state-space constraints, such as polyhedral waypoints to be visited and obstacles to be avoided, are also transformed into the moment space, leading to a unified formulation for safe, large-scale ensemble control. Expressive signal temporal logic specifications are employed to encode complex visit-avoid tasks, which are achieved through a single shared controller synthesized from our constrained ensemble control formulation. Simulation and hardware experiments demonstrate the effectiveness of the proposed approach in safely and efficiently controlling robotic ensembles within constrained environments.

One Ring to Rule Them All: Constrained Distributional Control for Massive-Scale Heterogeneous Robotic Ensemble Systems

TL;DR

The paper tackles safe, scalable control of massive heterogeneous robotic ensembles under state and environmental constraints. It introduces a moment kernel transform that maps ensemble dynamics into a moment space, enabling a single shared controller to enforce polyhedral constraints and obstacle avoidance, with STL specifications incorporated for complex tasks. The approach yields explicit moment-space representations of polyhedra and obstacles, and demonstrates both simulation and hardware validation (unicycles and QCar 2) for constrained tasks like box/polyhedral confinement and obstacle-rich environments. This work advances scalable, constraint-aware orchestration of large robotic populations by unifying dynamics, constraints, and task specifications in moment space.

Abstract

Ensemble control aims to steer a population of dynamical systems using a shared control input. This paper introduces a constrained ensemble control framework for parameterized, heterogeneous robotic systems operating under state and environmental constraints, such as obstacle avoidance. We develop a moment kernel transform that maps the parameterized ensemble dynamics to the moment system in a kernel space, enabling the characterization of population-level behavior. The state-space constraints, such as polyhedral waypoints to be visited and obstacles to be avoided, are also transformed into the moment space, leading to a unified formulation for safe, large-scale ensemble control. Expressive signal temporal logic specifications are employed to encode complex visit-avoid tasks, which are achieved through a single shared controller synthesized from our constrained ensemble control formulation. Simulation and hardware experiments demonstrate the effectiveness of the proposed approach in safely and efficiently controlling robotic ensembles within constrained environments.

Paper Structure

This paper contains 19 sections, 1 theorem, 24 equations, 8 figures.

Table of Contents

  1. INTRODUCTION
  2. Related works
  3. Problem Formulation
  4. Ensemble system formulation of robot populations
  5. Moment kernel reduction of ensemble systems
  6. Moment kernel transform of ensemble systems
  7. Moment kernelized unicycle ensembles
  8. Constrained Ensemble Control: Transforming constraints from state space to moment space
  9. Polyhedral region exploration
  10. Moment kernelization of polyhedra
  11. Constrained control of unicycle ensembles
  12. Obstacle avoidance
  13. Moment system under Signal Temporal Logic (STL)
  14. SIMULATION RESULTS
  15. Steering an ensemble of unicycles within a box constraint
  16. ...and 4 more sections

Key Result

Theorem 1

pant2017smooth For a signal $x$ with domain $E$ s.t. $x : E \rightarrow \mathbb{R}$ and STL formula $\varphi$, if $\rho_{\varphi}(x, t) < 0$ then $\varphi$ is not satisfied by $x$ at time $t$, and if $\rho_{\varphi}(x, t) > 0$ then $x$ satisfies $\varphi$ at $t$. If $\rho_{\varphi}(x, t) = 0$ is inc

Figures (8)

  • Figure 1: Broadcasting shared control to an ensemble of heterogeneous robots parameterized by $\beta$.
  • Figure 2: The second-order Legendre polynomial is given by $\phi_2(\mu) = \tfrac{1}{2}(3\mu^2 - 1)$, with roots at $\mu_1 = -\tfrac{1}{\sqrt{3}}$ and $\mu_2 = \tfrac{1}{\sqrt{3}}$, defined over $-1=\mu_l \leq \mu \leq \mu_u=1$.
  • Figure 3: Higher order Legendre polynomials, defined over $-1=\mu_l \leq \mu \leq \mu_u=1$.
  • Figure 4: Comparison between unconstrained and box-constrained trajectories.
  • Figure 5: Comparison between unconstrained and polyhedron-constrained trajectories.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Example 1
  • Example 2
  • Theorem 1
  • Example 3