Multi-Agent Motion Planning on Industrial Magnetic Levitation Platforms: A Hybrid ADMM-HOCBF approach

Bavo Tistaert; Stan Servaes; Alejandro Gonzalez-Garcia; Ibrahim Ibrahim; Louis Callens; Jan Swevers; Wilm Decré

cs.ROMar 20, 2026

Multi-Agent Motion Planning on Industrial Magnetic Levitation Platforms: A Hybrid ADMM-HOCBF approach

Authors: Bavo Tistaert, Stan Servaes, Alejandro Gonzalez-Garcia, Ibrahim Ibrahim, Louis Callens, Jan Swevers, Wilm Decré

Abstract

This paper presents a novel hybrid motion planning method for holonomic multi-agent systems. The proposed decentralised model predictive control (MPC) framework tackles the intractability of classical centralised MPC for a growing number of agents while providing safety guarantees. This is achieved by combining a decentralised version of the alternating direction method of multipliers (ADMM) with a centralised high-order control barrier function (HOCBF) architecture. Simulation results show significant improvement in scalability over classical centralised MPC. We validate the efficacy and real-time capability of the proposed method by developing a highly efficient C++ implementation and deploying the resulting trajectories on a real industrial magnetic levitation platform.

Figures & tables

Fig. 1 : The Beckhoff XPlanar setup in the robotics lab. This industrial machine is used for the experimental validation of the motion planner.

Fig. 2 : To deal with nonconvex arenas, agents track a sequence of sub-targets before arriving at their main target. The sub-targets are located in the intersection of corridors, where agents can switch from one corridor to the next. The final sub-target is the destination of the agent.

Fig. 3 : Scalability plot of ADMM-HOCBF ( $m=1$ and $m=20$ ) and centralised MPC.

	ADMM-HOCBF		Centr. MPC
	$m=1$	$m=20$
transit time	$4.6$ s	$3.0$ s	$2.0$ s
avg. computation time	$115$ ms	$1244$ ms	$169$ ms
number of collisions	$0$	$0$	$0$
safety filter activity	$65.22\%$	$36.67\%$	$-$
avg. input correction	$6.75\;\text{m/s}^{2}$	$1.80\>\text{m/s}^{2}$	$-$

TABLE I : Performance and safety comparison between sequential ADMM-HOCBF and centralised MPC. Tests are performed in Python for five agents.

Panel of Figure 5 — Fig. 4 : Trajectories of 5 agents on the XPlanar system with ADMM-HOCBF (m=20).

	ADMM-HOCBF
	$m=1$	$m=20$
transit time	$4.5$ s	$3.6$ s
avg. computation time	$20$ ms	$204$ ms

TABLE II : Performance results of the parallel C++ implementation of ADMM-HOCBF.

Decentralized Multi-Agent Motion Planning

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Mar 19, 2026J/K move · Enter open · S save

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

Yicheng Zeng, Ruturaj S. Sambhus, Basit Muhammad Imran, Jeeseop Kim+2

Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA · The University of Texas at El Paso, El Paso, TX 79968, USA

Model Predictive Control Multi-Robot Motion Planning Multi-Robot Coordination Quadruped Locomotion

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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.

Abstract

Decentralized Multi-Agent Motion Planning

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