Online Multi-Robot Coordination and Cooperation with Task Precedence Relationships

The evolution of multi-robot systems has transitioned from simple task execution to complex coordination involving task dependencies, cooperation, and uncertainty management. Early approaches focused on static scheduling or simple heuristics, which struggled with scalability and adaptability. Recent advances introduced task graphs, coalition models, and dynamic algorithms, exemplified by works like Gage et al. (2014) on multi-robot task allocation, and Sahin et al. (2010) on cooperative control. Despite progress, existing methods often treat task relationships and cooperation separately, lacking a unified framework capable of handling complex precedence, large-scale coordination, and environmental uncertainties simultaneously. The challenge remains to develop algorithms that are both computationally efficient and robust enough for real-world deployment, especially in scenarios with dynamic changes and partial information.

The core challenge is designing a scalable, robust scheduling system that can handle complex task precedence, cooperative effects, and environmental uncertainties in large multi-robot teams. Traditional offline methods like mixed-integer programming (MINLP) are computationally expensive and lack adaptability. Static heuristics fail to respond to real-time failures or environmental changes, leading to suboptimal performance. The problem becomes more intricate when considering non-linear coalition effects, influence-based precedence, and the need for real-time re-optimization, which are crucial for practical applications such as autonomous construction, disaster response, and precision farming.

The paper introduces several key innovations: 1) a comprehensive task model integrating task graphs, coalition functions, and influence functions to capture complex relationships; 2) a nonlinear network flow formulation enabling efficient optimization; 3) an online iterative re-planning algorithm that dynamically reallocates resources based on real-time feedback; 4) a unified framework capable of scaling to large problem sizes (50+ tasks, 100+ robots). These innovations address the limitations of prior work by providing a flexible, expressive, and computationally feasible solution for complex multi-robot missions, bridging the gap between theoretical models and practical deployment.

• �� Construct a directed acyclic task graph (GT) representing task precedence and dependencies.
• �� Define coalition functions (ρj) to quantify robot team effectiveness per task.
• �� Model influence functions (δij) to describe how preceding task performance affects subsequent rewards.
• �� Use aggregation functions (αj) to combine multiple influence effects.
• �� Formulate the task reward as a product or sum of coalition and influence components.
• �� Convert the scheduling problem into a nonlinear network flow model, where nodes represent tasks and edges encode precedence and travel times.
• �� Develop offline algorithms solving the nonlinear flow for initial allocation.
• �� Design an online iterative algorithm that, during task execution, updates resource allocations based on observed outcomes, leveraging maximum flow and shortest path algorithms for rapid re-optimization.
• �� Validate the approach through extensive simulations with random task graphs, reward functions, and environmental uncertainties, comparing against MINLP and greedy heuristics.

The experiments utilize a custom simulation platform generating random task graphs with complex reward structures and precedence constraints. Baseline comparisons include MINLP solvers, greedy heuristics, and static offline algorithms. Metrics evaluated are total reward, computational time, and robustness under simulated task failures and model inaccuracies. The scenarios range from small (under 10 tasks) to large (over 25 tasks, 100 robots). The experiments incorporate realistic urban environment physics, with tasks like coverage, exploration, transportation, and collaborative carrying. Multiple runs ensure statistical significance, and ablation studies analyze the impact of online re-planning versus static allocation. Results consistently show the online method's superior reward and robustness, especially in large, uncertain scenarios.

The online algorithm achieves near-optimal rewards (within 20%) in small problems and outperforms greedy heuristics by over 30% in large-scale scenarios. It maintains high robustness, with less than 10% reward loss under simulated task failures. Computation times are significantly lower than MINLP, enabling real-time re-optimization. When tested with realistic physics models, the system successfully completes multi-task missions with reward errors below 15%, demonstrating high fidelity and practical applicability. These results confirm the effectiveness of the integrated modeling and online re-planning approach in complex, uncertain environments.

The framework is directly applicable to autonomous construction sites, where robots must coordinate complex sequences under uncertain conditions. It also benefits precision agriculture, enabling large-scale crop monitoring and resource distribution. Industrial automation can leverage this approach for dynamic manufacturing processes involving multiple robotic arms and mobile units. The method's scalability and robustness make it suitable for deployment in real-world scenarios requiring high reliability and adaptability, provided that task models and environmental feedback are accurately integrated.

The approach depends on predefined influence functions, which may not fully capture highly nonlinear or rapidly changing task dependencies in real environments. Computational complexity increases with task graph density and robot count, potentially limiting real-time performance in extremely large scenarios. The validation is primarily simulation-based; real-world deployment must address sensing errors, communication delays, and hardware constraints. Further research is needed to optimize algorithms for hardware acceleration and to develop adaptive influence models that learn from environment interactions.