Fully Distributed GNE Algorithms for Multi-Robot Placement without Consensus on Multipliers

Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.

Physical Agentic AI: An Architecture for Orchestrating a Robot Crew with LLMs

Agentic AI frameworks interpret open-ended task goals and decompose them into multi-step plans. Richer information about embodiment-specific capabilities, physical preconditions, and cross-robot coordination improves grounding, but does not eliminate infeasible, mistimed, or unsafe physical actions. Physical robot crews therefore require an explicit architectural interface between semantic planning and execution, where every planned action is verified against robot capabilities, system state, and workflow constraints before actuation. This paper introduces Physical Agentic AI, a framework for skill-grounded robot agent orchestration, in which each robot exposes a typed library of executable skills while a foundation model planner decomposes a task into phases and assigns each phase to a robot-skill pair. A Robot Orchestration layer exposes the skill library, robot state, named locations, and workflow contracts to a non-actuating Mission Planner, while a deterministic Robot Orchestrator validates and authorizes one skill at a time. We evaluate on a drone-UGV search-and-dispatch mission, where every mission in every condition is executed live in Gazebo, and on a humanoid-quadruped transportation task using hardware-equivalent skill interfaces plus two physical trials on a Unitree G1 and Go2. Varying planner knowledge and runtime enforcement independently, we find that retrieval raises skill grounding from 51% to 96% yet leaves informed planners dispatching 23-29% of faulted steps. Per-dispatch enforcement reduces false dispatch to 0% with no false blocks, and a held-plan ablation confirms that the gate, not plan variation, is responsible. Live execution makes the difference physical: without enforcement all eight injected faults crossed the orchestration boundary and six produced robot motion; with enforcement all eight were refused before motion.

Courteous Anticipation: Improving Long-Lived Task Planning in Persistent Shared Environments

We consider a task planning scenario in which robots sharing a persistent environment are assigned tasks one at a time from a held-out sequence. Standard task planners, lacking foresight of future tasks and inconsiderate of others' constraints, solve each task in isolation, leaving terminal states that increase future cost for all, side effects that compound over lengthy task sequences. To reduce cost over the sequence, a robot must anticipate how its actions now may impact performance on future tasks for all robots sharing the environment. Therefore, we present courteous anticipatory planning, wherein a model-based planner proposes candidate plans and selects the one that jointly minimizes immediate cost and aggregated expected future cost across all robots, estimated via independent per-robot learned estimators. This factored formulation avoids combinatorial joint rollouts and supports modular deployment: adding a robot requires only training its own estimator. We evaluate in two persistent PDDL domains, a home environment with robots that have similar capabilities but different responsibilities, and a restaurant environment where robots' distinct capabilities create states that other robots lack the capability to resolve. During lengthy task sequences, our planner reduces total cost by 10.43% versus myopic and 4.03% versus selfish anticipatory planning in a two-robot home environment and by 17.41% and 13.24%, respectively, in a three-robot restaurant.

Search-Based Spatiotemporal and Multi-Robot Motion Planning on Graphs of Space-Time Convex Sets

Spatiotemporal motion planning, especially in multi-robot settings, requires robots to reason about collision-free regions that change over time, which is challenging in continuous spaces when feasible regions are transient and geometrically constrained. We present an algorithmic framework based on graphs of space-time convex sets (ST-GCSs), where collision-free regions are represented as convex sets in space-time and trajectories correspond to paths on the graph together with continuous motions within the selected sets. We formulate time-optimal planning on ST-GCSs as a graph-search problem over path-indexed states and develop a best-first search solver that evaluates partial paths via continuous trajectory optimization, guided by admissible heuristics and dominance checks. We further present an Exact Convex Decomposition (ECD) scheme to reserve trajectory occupancies in space-time, enabling unified handling of dynamic obstacles and multi-robot interactions. For multi-robot motion planning, we integrate ST-GCS planning and ECD into prioritized planning methods and introduce a windowed coordination scheme to improve efficiency. Extensive experiments on single-robot and multi-robot problems demonstrate substantial speedups over various planners while maintaining high solution quality, particularly in environments with narrow and transient feasible regions. Large-scale demonstrations further show that the proposed multi-robot motion planner can solve instances with up to $100$ robots within only a few minutes. Project homepage: https://sites.google.com/view/stgcs