To deploy safe and agile robots in cluttered environments, there is a need to develop fully decentralized controllers that guarantee safety, respect actuation limits, prevent deadlocks, and scale to thousands of agents. Current approaches fall short of meeting all these goals: optimization-based methods ensure safety but lack scalability, while learning-based methods scale but do not guarantee safety. We propose a novel algorithm to achieve safe and scalable control for multiple agents under limited actuation. Specifically, our approach includes: ($i$) learning a decentralized neural Integral Control Barrier function (neural ICBF) for scalable, input-constrained control, (ii) embedding a lightweight decentralized Model Predictive Control-based Integral Control Barrier Function (MPC-ICBF) into the neural network policy to ensure safety while maintaining scalability, and (iii) introducing a novel method to minimize deadlocks based on gradient-based optimization techniques from machine learning to address local minima in deadlocks. Our numerical simulations show that this approach outperforms state-of-the-art multi-agent control algorithms in terms of safety, input constraint satisfaction, and minimizing deadlocks. Additionally, we demonstrate strong generalization across scenarios with varying agent counts, scaling up to 1000 agents. Videos andcode are available at https://maicbf.github.io/.

In this paper, we address the problem of reducing the computational burden of Model Predictive Control (MPC) for real-time robotic applications. We propose TransformerMPC, a method that enhances the computational efficiency of MPC algorithms by leveraging the attention mechanism in transformers for both online constraint removal and better warm start initialization. Specifically, TransformerMPC accelerates the computation of optimal control inputs by selecting only the active constraints to be included in the MPC problem, while simultaneously providing a warm start to the optimization process. This approach ensures that the original constraints are satisfied at optimality. TransformerMPC is designed to be seamlessly integrated with any solver, irrespective of its implementation. To guarantee constraint satisfaction after removing inactive constraints, we perform an offline verification to ensure that the optimal control inputs generated by the solver meet all constraints. The effectiveness of TransformerMPC is demonstrated through extensive numerical simulations on complex robotic systems, achieving up to$35 \times$improvement in runtime without any loss in performance.