Analytical Modeling of Task Allocation for Distributed Anthropomorphic Robots in Mission-Critical Environments

Efficient task allocation among mobile agents is critical in high-stakes scenarios such as disaster response, battlefield coordination, and emergency healthcare. This paper introduces a framework for task allocation across distributed anthropomorphic robots (androids) operating in dynamic, resource-constrained environments. The system leverages decentralized decision-making, context-aware prioritization, and adaptive communication protocols to maintain robust performance under intermittent connectivity, limited energy availability, and unpredictable task demands. We present an analytical model that formalizes the interplay between agent autonomy, resource limitations, and task urgency, enabling adaptive behavior in volatile conditions. Preliminary evaluation indicates the feasibility and effectiveness of the proposed approach, with notable gains in task distribution efficiency, reduced latency, and improved fault tolerance compared to centralized alternatives. In particular, the proposed leader-based allocation method that incorporates force, energy, and timing constraints achieves a success rate about <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2.0 \times$</tex> higher than existing approaches with 30 tasks and 100 androids and more than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3.5 \times$</tex> higher with 50 tasks and 300 androids. These results lay the foundation for resilient, scalable coordination mechanisms in mission-critical mobile networks.