Non-probabilistic approach to cooperative position tracking in large swarm of simple mobile robots using triangular cross-observation

Many applications in mobile robotics require that the accurate position of the mobile robots to be known. Dead reckoning (DR) is the simplest and the most cost effective method of keeping track of mobile robots’ positions, but it is the most unreliable due to error accumulation problem. In multi-robot environment however, cooperative position tracking is a robust solution in the sense that the error in one robot will be compensated by the other group members. Unfortunately, many of the most popular approaches for cooperative localization in literature today are probabilistic, which are computationally complex and less tolerant to any deviation from their predetermined probabilistic motion and observation models. This research focuses on devising a computationally simpler non-probabilistic cooperative position tracking algorithm specifically for a large swarm of simple mobile robots with the purpose of reducing the error accumulation in the position estimates of an individual robot due to noise in odometric measurement. This algorithm, which is term triangular cross-observation (TCO), involves three mobile robots simultaneously in every update decision making process, which provides two observation data for every robot. These two observation data are tested using their signs before one of them with the highest probability of giving a positive update is selected to be used for position update. The update process is done using a fixed update gain calculated that will give the best performance for the proposed algorithm, which keeps the complexity of the algorithm to a minimum of 0(1) as compared to 0(N²) of an extended Kalman filter (EKF). In addition to that, this approach comes with the mechanism to validate the integrity of the observation data prior to the update process. The performance of the algorithm was validated and compared against that of the EKF through series of simulations using Stage multi-agent simulator. Simulation results have shown that despite the computational simplicity, the algorithm yields the percentage error of 0.033%, which is close to that of the EKF, which yields 0.028%, while the DR yields 0.125%. The simulation on the robot performance under the presence of outliers in position estimate among the group members yields an excellent result for the proposed approach with percentage error of 0.038% while the EKF has been badly affected with percentage error of 0.196%, higher than that of the dead reckoning, which is 0.131%. Similarly, corrupted measurement data introduced into the simulation have not affected the performance of the proposed approach as compared to that of the EKF. While the performance of the TCO was completely untouched with percentage error of 0.029% after 60 minutes of simulation, the performance of the EKF has been severely affected with percentage error of 0.115%, close to that of the DR with 0.122%. Overall, the theoretical analysis and simulations have shown that a computationally simpler non-probabilistic algorithm with a performance close to that of a probabilistic approach and robust against outliers can be devised by synthesizing information obtained from multiple simultaneous observations in cooperative position tracking.

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