Adapted Metrics for Measuring Competency and Resilience for Autonomous Robot Systems in Discrete Time Markov Chains*

Autonomous robot systems are often designed to achieve specific goals. This paper restricts attention to a specific type of goal, namely reaching a desired state within a certain time bound. For such goals, a robot system’s competency and resilience can be defined as the probability of reaching the desired state as a function of the time bound under a nominal unperturbed condition and under known perturbation conditions, respectively. Two metrics taken from prior work for measuring competency and resilience, power and efficiency, are modified so that they do not require subjective parameters. This paper formalizes the adapted metrics for discrete time Markov chains. The adapted metrics are applied to a best-of-N case study that is solved by a graph-based approach and modeled as a discrete time Markov chain. The case study demonstrates that the modified metrics allow power-efficiency trade-offs to be more easily visualized than the cluttered visualizations produced by the original metrics.