中文摘要：

建立系统的概率模型是描述和分析自组织多机器人系统的一条新思路。运用包括随机过程、矩阵论和线性代数等数学方法建立自组织多机器人系统的任务分配模型,克服了现存模型对任务类型数目无可扩展性的缺点。为了验证模型的一般性和有效性,以时间离散状态连续的马尔科夫链的极限分布作为任务分配的理论结果,优点是可以预测多机器人系统任务分配的长期稳定行为。任务分配的目的是保持执行任意一种任务的机器人数量占机器人总数的比例与该种任务所占总任务量的比例相等。仿真实验的结论也说明了任务分配模型可以达到理想的分配效果。

英文摘要：

The macroscopic probability modeling is a new way to describe and analyze the self-organizing multi-robot system.The mathematical method of stochastic process theory,matrix theory and linear algebra are used to model the task allocation of self-organizing multi-robot system and overcome the drawbacks of existing models,which has no scalability to the number of task types.The limit distribution of state -discrete time -continuous Markov chain is used as the theoretical result of task allocation,which takes advantage of predicting long-term behavior of robot system.The purpose of task allocation is to keep the proportion of the robots in arbitrary tasks to total robots being equal to that of performed tasks to total tasks.The simulation results show that the macroscopic probability model for multi-robot task allocation can complete the desired assignment of tasks.