Markov approach of adaptive task assignment for robotic system in non-stationary environments

Adaptive and decentralized task assignment in non-uniform and possibly even non-stationary conditions with the aim of ensuring stability is especially challenging knowledge requirements in order to negotiate within and interact with uncertain and dynamic environments such as robot malfunctions or error propagation. Task assignment addresses to the problem of coordination both in on autonomous and interacting robot. In the scenarios for task assignment robots are embedded in the environment, there are strict constraints on communication, and most importantly tasks that robots should execute are perceived by the robot itself during the mission execution, thus conflicts on the task assignment process might arise. The internal representation of timing constraints on interaction has many implications for the reliability, effectiveness, efficiency, validity, schedulability and robustness of the mobile robot. The task assignment processes and its control implying reasoning about objects and resources and their changing states are dominated by either discrete or stochastic-event dynamics or both. Stationarity is an unrealistic prior assumption for the multi-state components of complex systems. The numerical characteristics of the nonstationary random responses of complex structure are developed in the paper considering the uncertainty and volatility of process transitions states. The appropriate functional levels of multi-state systems components are placed between the two extremes: defect (0%) and the nominal (100%) state, allowing any intermediate state transiting from the range of perfect functionality to complete failure. Time analysis interval of a multi-state system is characterized by intermediate states (states of partial success). The paper proposes a stochastic model of assessing system probability of unidirectional or bidirectional transition states, applying the non-homogeneous (non-stationary) Markov chain. The capability of time-dependent method to describe a multi-state system is based on a case study, assessing the operatial situation of robotic system. The rationality and validity of the presented model are demonstrated via an example of quantitative assessment of states probabilities of an autonomous robot.