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

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.

Agent-based model predictive control (AMPC) has recently been proposed as a distributed scheme that collaborates with all agents to achieve optimal holistic performance. However, its optimality highly depends on the prediction accuracy that requires all agents or their contributions to be known, which is too idealistic for actual implementation. This research proposes a novel practical hybrid control scheme - learning agent-based MPC (LAMPC), combining the model-based AMPC approach and data-based learning methods to improve the holistic vehicle performance for multi-agent systems. The Gaussian process regression (GPR) enhanced by an online data management strategy serves as the learning core to predict unknown contributions. A novel multi-step prediction mechanism leverages the GPR learning potential along the horizon. The predicted mean, representing the learned unknown contributions, completes the system model in the MPC for more accurate control. Meanwhile, a stochastic framework is formulated to guarantee control safety and feasibility using soft chance constraints based on the prediction variance. Both simulations and experiments show that, with the learning capability, LAMPC outperforms the traditional AMPC. LAMPC can achieve higher tracking performance in well-learned scenarios and always guarantee constraint satisfaction even in less-learned scenarios. Moreover, the proposed hybrid control scheme is efficient for real-time implementation and is flexible to any control agent topology.

Safe multi-agent motion planning (MAMP) under task-induced constraints is a critical challenge in robotics. Many real-world scenarios require robots to navigate dynamic environments while adhering to manifold constraints imposed by tasks. For example, service robots must carry cups upright while avoiding collisions with humans or other robots. Despite recent advances in decentralized MAMP for high-dimensional systems, incorporating manifold constraints remains difficult. To address this, we propose a manifold-constrained Hamilton-Jacobi reachability (HJR) learning framework for decentralized MAMP. Our method solves HJR problems under manifold constraints to capture task-aware safety conditions, which are then integrated into a decentralized trajectory optimization planner. This enables robots to generate motion plans that are both safe and task-feasible without requiring assumptions about other agents' policies. Our approach generalizes across diverse manifold-constrained tasks and scales effectively to high-dimensional multi-agent manipulation problems. Experiments show that our method outperforms existing constrained motion planners and operates at speeds suitable for real-world applications. Video demonstrations are available at https://youtu.be/RYcEHMnPTH8 .