This article develops a stochastic programming framework for multiagent systems, where task decomposition, assignment, and scheduling problems are simultaneously optimized. The framework can be applied to heterogeneous mobile robot teams with distributed subtasks. Examples include pandemic robotic service coordination, explore and rescue, and delivery systems with heterogeneous vehicles. Owing to their inherent flexibility and robustness, multiagent systems are applied in a growing range of real-world problems that involve heterogeneous tasks and uncertain information. Most previous works assume one fixed way to decompose a task into roles that can later be assigned to the agents. This assumption is not valid for a complex task where the roles can vary and multiple decomposition structures exist. Meanwhile, it is unclear how uncertainties in task requirements and agent capabilities can be systematically quantified and optimized under a multiagent system setting. A representation for complex tasks is proposed: agent capabilities are represented as a vector of random distributions, and task requirements are verified by a generalizable binary function. The conditional value at risk is chosen as a metric in the objective function to generate robust plans. An efficient algorithm is described to solve the model, and the whole framework is evaluated in two different practical test cases: capture-the-flag and robotic service coordination during a pandemic (e.g., COVID-19). Results demonstrate that the framework is generalizable, is scalable up to 140 agents and 40 tasks for the example test cases, and provides low-cost plans that ensure a high probability of success.

For robot swarms operating on complex missions in an uncertain environment, it is important that the decision-making algorithm considers both heterogeneity and uncertainty. This paper presents a stochastic programming framework for the vehicle routing problem with stochastic travel energy costs and heterogeneous vehicles and tasks. We represent the heterogeneity as linear constraints, estimate the uncertain energy cost through Gaussian process regression, formulate this stochasticity as chance constraints or stochastic recourse costs, and then solve the stochastic programs using branch and cut algorithms to minimize the expected energy cost. The performance and practicality are demonstrated through extensive computational experiments and a practical test case.