Goodness of Fit in the Marginal Modeling of Round-Trip Times for Networked Robot Sensor Transmissions

When complex computations cannot be performed on board a mobile robot, sensory data must be transmitted to a remote station to be processed, and the resulting actions must be sent back to the robot to execute, forming a repeating cycle. This involves stochastic round-trip times in the case of non-deterministic network communications and/or non-hard real-time software. Since robots need to react within strict time constraints, modeling these round-trip times becomes essential for many tasks. Modern approaches for modeling sequences of data are mostly based on time-series forecasting techniques, which impose a computational cost that may be prohibitive for real-time operation, do not consider all the delay sources existing in the sw/hw system, or do not work fully online, i.e., within the time of the current round-trip. Marginal probabilistic models, on the other hand, often have a lower cost, since they discard temporal dependencies between successive measurements of round-trip times, a suitable approximation when regime changes are properly handled given the typically stationary nature of these round-trip times. In this paper we focus on the hypothesis tests needed for marginal modeling of the round-trip times in remotely operated robotic systems with the presence of abrupt changes in regimes. We analyze in depth three common models, namely Log-logistic, Log-normal, and Exponential, and propose some modifications of parameter estimators for them and new thresholds for well-known goodness-of-fit tests, which are aimed at the particularities of our setting. We then evaluate our proposal on a dataset gathered from a variety of networked robot scenarios, both real and simulated; through >2100 h of high-performance computer processing, we assess the statistical robustness and practical suitability of these methods for these kinds of robotic applications.