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ADMM-Based Distributed MPC with Control Barrier Functions for Safe Multi-Robot Quadrupedal Locomotion

Yicheng Zeng, Ruturaj S. Sambhus, Basit Muhammad Imran, Jeeseop Kim, Vittorio Pastore, Kaveh Akbari Hamed

Abstract

This paper proposes a fully decentralized model predictive control (MPC) framework with control barrier function (CBF) constraints for safety-critical trajectory planning in multi-robot legged systems. The incorporation of CBF constraints introduces explicit inter-agent coupling, which prevents direct decomposition of the resulting optimal control problems. To address this challenge, we reformulate the centralized safety-critical MPC problem using a structured distributed optimization framework based on the alternating direction method of multipliers (ADMM). By introducing a novel node-edge splitting formulation with consensus constraints, the proposed approach decomposes the global problem into independent node-local and edge-local quadratic programs that can be solved in parallel using only neighbor-to-neighbor communication. This enables fully decentralized trajectory optimization with symmetric computational load across agents while preserving safety and dynamic feasibility. The proposed framework is integrated into a hierarchical locomotion control architecture for quadrupedal robots, combining high-level distributed trajectory planning, mid-level nonlinear MPC enforcing single rigid body dynamics, and low-level whole-body control enforcing full-order robot dynamics. The effectiveness of the proposed approach is demonstrated through hardware experiments on two Unitree Go2 quadrupedal robots and numerical simulations involving up to four robots navigating uncertain environments with rough terrain and external disturbances. The results show that the proposed distributed formulation achieves performance comparable to centralized MPC while reducing the average per-cycle planning time by up to 51% in the four-agent case, enabling efficient real-time decentralized implementation.

ADMM-Based Distributed MPC with Control Barrier Functions for Safe Multi-Robot Quadrupedal Locomotion

Abstract

This paper proposes a fully decentralized model predictive control (MPC) framework with control barrier function (CBF) constraints for safety-critical trajectory planning in multi-robot legged systems. The incorporation of CBF constraints introduces explicit inter-agent coupling, which prevents direct decomposition of the resulting optimal control problems. To address this challenge, we reformulate the centralized safety-critical MPC problem using a structured distributed optimization framework based on the alternating direction method of multipliers (ADMM). By introducing a novel node-edge splitting formulation with consensus constraints, the proposed approach decomposes the global problem into independent node-local and edge-local quadratic programs that can be solved in parallel using only neighbor-to-neighbor communication. This enables fully decentralized trajectory optimization with symmetric computational load across agents while preserving safety and dynamic feasibility. The proposed framework is integrated into a hierarchical locomotion control architecture for quadrupedal robots, combining high-level distributed trajectory planning, mid-level nonlinear MPC enforcing single rigid body dynamics, and low-level whole-body control enforcing full-order robot dynamics. The effectiveness of the proposed approach is demonstrated through hardware experiments on two Unitree Go2 quadrupedal robots and numerical simulations involving up to four robots navigating uncertain environments with rough terrain and external disturbances. The results show that the proposed distributed formulation achieves performance comparable to centralized MPC while reducing the average per-cycle planning time by up to 51% in the four-agent case, enabling efficient real-time decentralized implementation.
Paper Structure (12 sections, 1 theorem, 24 equations, 5 figures, 1 table)

This paper contains 12 sections, 1 theorem, 24 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Problem Formulation
  5. ADMM-based DMPC with CBF Constraints
  6. Proposed ADMM-based DMPC with CBFs
  7. Reduction to Distributed QPs and Layered Control
  8. Experiments
  9. Setup and Controller Synthesis
  10. Hardware Experiments
  11. Comparison Analysis
  12. Conclusions

Key Result

Theorem 1

(CBF Condition DT-HOCBF): If $h^{i}$ is a continuous CBF, any control input $u^{i}(t)\in\mathcal{U}$ satisfying the CBF condition eq:CBF_condition will render the safety set given by $\mathcal{S}:=\{x^{i}:\,h^{i}(x^{i})\geq0\}$ forward invariant for agent $i\in\mathcal{V}$.

Figures (5)

  • Figure 1: Snapshot of the hardware experiment demonstrating the proposed ADMM-based CBF-DMPC framework, where two Unitree Go2 robots navigate a cluttered environment with rough terrain while maintaining safety-critical inter-agent and obstacle avoidance constraints.
  • Figure 2: Overview of the proposed layered control framework, consisting of a high-level ADMM-based CBF-DMPC for safety-critical trajectory planning, a mid-level NMPC layer enforcing the single rigid body (SRB) dynamics, and a low-level whole-body controller (WBC) enforcing full-order robot dynamics.
  • Figure 3: Hardware experiments of the proposed ADMM-based CBF-DMPC and layered control with two Unitree Go2 robots: (a) navigation among eight static obstacles (experiment 1), (b) disturbance rejection under external pushes (experiment 2), and (c) obstacle avoidance over rough terrain with ten obstacles (experiment 3). (d) Multi-agent simulation in RaiSim with four robots navigating among ten obstacles.
  • Figure 4: Plot of the optimal state trajectory $(x^{\star,i},y^{\star,i},\theta^{\star,i})$ generated by the high-level ADMM-based CBF-DMPC for agent 1, together with the corresponding reference trajectory toward its goal during experiment 2. The figure also depicts the optimal velocity commands $(v^{\star,i},\omega^{\star,i})$ and the minimum CBF values, representing obstacle-avoidance and inter-agent safety margins. The shaded regions indicate push intervals.
  • Figure 5: Comparison between the ADMM-based CBF-DMPC and centralized CBF-MPC for four agents navigating among obstacles in simulation. The resulting $xy$ trajectories demonstrate near-identical motion and safety behavior under both approaches.

Theorems & Definitions (2)

  • Definition 1: Discrete-Time CBF DT-HOCBF
  • Theorem 1