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The growing trend of the use of robots in many areas of daily life makes it necessary to search for approaches to improve efficiency in tasks performed by robots. For that reason, we show, in this chapter, the application of the Kalman filter applied to the navigation of mobile robots, specifically the Time-to-contact (TTC) problem. We present a summary of approaches that have been taken to address the TTC problem. We use a monocular vision-based approach to detect potential obstacles and follow them over time through their apparent size change. Our approach collects information about obstacle data and models the behavior while the robot is approaching the obstacle, in order to predict collisions. We highlight some characteristics of the Kalman filter applied to our problem. Finally, we show of our results applied to sequences composed of 210 frames in different real scenarios. The results show a fast convergence of the model to the data and good fit even with noisy measures.

Predicting Collisions in Mobile Robot Navigation by Kalman Filter