Graph-of-Constraints Model Predictive Control for Reactive Multi-agent Task and Motion Planning

Sequences of interdependent geometric constraints are central to many multi-agent Task and Motion Planning (TAMP) problems. However, existing methods for handling such constraint sequences struggle with partially ordered tasks and dynamic agent assignments. They typically assume static assignments and cannot adapt when disturbances alter task allocations. To overcome these limitations, we introduce Graph-of-Constraints Model Predictive Control (GoC-MPC), a generalized sequence-of-constraints framework integrated with MPC. GoC-MPC naturally supports partially ordered tasks, dynamic agent coordination, and disturbance recovery. By defining constraints over tracked 3D keypoints, our method robustly solves diverse multi-agent manipulation tasks-coordinating agents and adapting online from visual observations alone, without relying on training data or environment models. Experiments demonstrate that GoC-MPC achieves higher success rates, significantly faster TAMP computation, and shorter overall paths compared to recent baselines, establishing it as an efficient and robust solution for multi-agent manipulation under real-world disturbances. Our supplementary video and code can be found at https://sites.google.com/view/goc-mpc/home .

Automaton Constrained Q-Learning

Real-world robotic tasks often require agents to achieve sequences of goals while respecting time-varying safety constraints. However, standard Reinforcement Learning (RL) paradigms are fundamentally limited in these settings. A natural approach to these problems is to combine RL with Linear-time Temporal Logic (LTL), a formal language for specifying complex, temporally extended tasks and safety constraints. Yet, existing RL methods for LTL objectives exhibit poor empirical performance in complex and continuous environments. As a result, no scalable methods support both temporally ordered goals and safety simultaneously, making them ill-suited for realistic robotics scenarios. We propose Automaton Constrained Q-Learning (ACQL), an algorithm that addresses this gap by combining goal-conditioned value learning with automaton-guided reinforcement. ACQL supports most LTL task specifications and leverages their automaton representation to explicitly encode stage-wise goal progression and both stationary and non-stationary safety constraints. We show that ACQL outperforms existing methods across a range of continuous control tasks, including cases where prior methods fail to satisfy either goal-reaching or safety constraints. We further validate its real-world applicability by deploying ACQL on a 6-DOF robotic arm performing a goal-reaching task in a cluttered, cabinet-like space with safety constraints. Our results demonstrate that ACQL is a robust and scalable solution for learning robotic behaviors according to rich temporal specifications.