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Safe Distributed Learning-Enhanced Predictive Control for Multiple Quadrupedal Robots

Weishu Zhan, Zheng Liang, Hongyu Song, Wei Pan

TL;DR

The paper addresses safe, scalable formation control for multiple quadrupedal robots in unknown environments, tackling stability and collision avoidance under dynamic obstacles and changing team structures. It introduces a distributed DMPC framework with Control Lyapunov Functions for formation stability and decentralized Safety via Control Barrier Functions, augmented by SAPIE for permutation-invariant encoding of dynamic neighbor information. Neural-network based CBFs are trained with a combined loss and integrated with a low-latency DDS-based communication layer, plus an event-triggered deadlock resolver to maintain motion in constrained spaces. Validation includes high-fidelity NVIDIA Omniverse Isaac Sim digital twins and real-world experiments on the XG platform, demonstrating real-time feasibility, robust deadlock handling, and effective collision avoidance. These results indicate practical potential for large-scale swarm deployment of legged robots in unstructured environments.

Abstract

Quadrupedal robots exhibit remarkable adaptability in unstructured environments, making them well-suited for formation control in real-world applications. However, keeping stable formations while ensuring collision-free navigation presents significant challenges due to dynamic obstacles, communication constraints, and the complexity of legged locomotion. This paper proposes a distributed model predictive control framework for multi-quadruped formation control, integrating Control Lyapunov Functions to ensure formation stability and Control Barrier Functions for decentralized safety enforcement. To address the challenge of dynamically changing team structures, we introduce Scale-Adaptive Permutation-Invariant Encoding (SAPIE), which enables robust feature encoding of neighboring robots while preserving permutation invariance. Additionally, we develop a low-latency Data Distribution Service-based communication protocol and an event-triggered deadlock resolution mechanism to enhance real-time coordination and prevent motion stagnation in constrained spaces. Our framework is validated through high-fidelity simulations in NVIDIA Omniverse Isaac Sim and real-world experiments using our custom quadrupedal robotic system, XG. Results demonstrate stable formation control, real-time feasibility, and effective collision avoidance, validating its potential for large-scale deployment.

Safe Distributed Learning-Enhanced Predictive Control for Multiple Quadrupedal Robots

TL;DR

The paper addresses safe, scalable formation control for multiple quadrupedal robots in unknown environments, tackling stability and collision avoidance under dynamic obstacles and changing team structures. It introduces a distributed DMPC framework with Control Lyapunov Functions for formation stability and decentralized Safety via Control Barrier Functions, augmented by SAPIE for permutation-invariant encoding of dynamic neighbor information. Neural-network based CBFs are trained with a combined loss and integrated with a low-latency DDS-based communication layer, plus an event-triggered deadlock resolver to maintain motion in constrained spaces. Validation includes high-fidelity NVIDIA Omniverse Isaac Sim digital twins and real-world experiments on the XG platform, demonstrating real-time feasibility, robust deadlock handling, and effective collision avoidance. These results indicate practical potential for large-scale swarm deployment of legged robots in unstructured environments.

Abstract

Quadrupedal robots exhibit remarkable adaptability in unstructured environments, making them well-suited for formation control in real-world applications. However, keeping stable formations while ensuring collision-free navigation presents significant challenges due to dynamic obstacles, communication constraints, and the complexity of legged locomotion. This paper proposes a distributed model predictive control framework for multi-quadruped formation control, integrating Control Lyapunov Functions to ensure formation stability and Control Barrier Functions for decentralized safety enforcement. To address the challenge of dynamically changing team structures, we introduce Scale-Adaptive Permutation-Invariant Encoding (SAPIE), which enables robust feature encoding of neighboring robots while preserving permutation invariance. Additionally, we develop a low-latency Data Distribution Service-based communication protocol and an event-triggered deadlock resolution mechanism to enhance real-time coordination and prevent motion stagnation in constrained spaces. Our framework is validated through high-fidelity simulations in NVIDIA Omniverse Isaac Sim and real-world experiments using our custom quadrupedal robotic system, XG. Results demonstrate stable formation control, real-time feasibility, and effective collision avoidance, validating its potential for large-scale deployment.

Paper Structure

This paper contains 20 sections, 1 theorem, 19 equations, 9 figures.

Table of Contents

  1. Problem Formulation
  2. Quadruped Robot Model
  3. Problem Statement
  4. DISTRIBUTED CONTROLLER DESIGN
  5. MPC With CLF Constraints
  6. SAPIE for Dynamic Neighborhood Adaptation
  7. SAPIE-CBF Based on Neural Networks
  8. Deadlock Resolution
  9. SIMULATIONS AND EXPERIMENTS
  10. System Design
  11. Quadruped robot
  12. Digital Twins in NVIDIA Omniverse Isaac Sim
  13. Simulated Experiments
  14. Simulation Setup
  15. Scenario 1: Safe Navigation in Obstacle Dense Environment
  16. ...and 5 more sections

Key Result

Lemma 1

When the optimal cost function $J_{\text{CLFs }}\left(\hat{\boldsymbol{u}}_i\right)$ reaches zero, the CLF constraint becomes slack, indicating that the dynamics of the system inherently drives the formation error $\boldsymbol{e}_{\mathcal{N}_i}$ to zero, ensuring stability without additional contro

Figures (9)

  • Figure 1: Quadruped robots cooperative formation and collision avoidance.
  • Figure 2: Exemplary scenarios of communication graphs with (a) N = 3 and (b) N = 5. The arrows represent the directions of information exchange among robots. Communications are instantaneously exchanged between neighboring robots at each step.
  • Figure 3: Overview of the presented approach. Left: The distributed control architecture for each quadruped robot combines an MPC-CLF optimizer for formation stability with an SAPIE-CBF Neural Networks for safety enforcement. The SAPIE module processes variable neighbor configurations through a permutation-invariant encoding mechanism, while the event-triggered mechanism resolves potential deadlocks. Right: Multirobot environment validation showing the seamless transition from digital twin simulation to physical deployment, demonstrating the effectiveness of our framework in both simulated and real-world scenarios.
  • Figure 4: The digital twin of XG, an autonomous quadrupedal robot, shown operating in two simulated environments (Office and Warehouse). These high-fidelity simulations facilitate robust development and Sim2Real transfer.
  • Figure 5: Evolution of the XG quadrupedal robot platform. From left to right: Engineering schematic showing the mechanical design and joint placement; Digital twin model implemented in NVIDIA Isaac Sim for high-fidelity simulation; Standard XG robot hardware implementation; XG Black variant with modified chassis configuration for enhanced payload capacity and experimental deployments.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Remark 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4: CBFames2016control
  • Definition 5
  • Definition 6: minniti2021adaptive
  • Lemma 1
  • proof