Estimation des Cartes du Temps de Collision (TTC) Basée sur le Flot Otoptique en Vision Para-Catadioptrique

Estimation des Cartes du Temps de Collision (TTC) Basée sur le Flot Otoptique en Vision Para-Catadioptrique

Fatima Zahra Benamar Sanaa El Fkihi  Cédric Demonceaux  El Mustapha Mouaddib  Driss Aboutajdine 

LRIT, Unité associée au CNRST, URAC n◦29, Université Mohammed V-Agdal, Rabat, Maroc

RIITM, ENSIAS, Université Mohammed V Souissi, Rabat, Maroc

Le2i, UMR CNRS 6306, Université de bourgogne, Le Creusot, France

MIS, Université de Picardie Jules Verne (UPJV), Amiens, France

Page: 
197-219
|
DOI: 
https://doi.org/10.3166/TS.31.197-219
Received: 
27 September 2013
| |
Accepted: 
12 May 2014
| | Citation

OPEN ACCESS

Abstract: 

Thepresentpaperdealswithtimetocollision(TTC)foramobilerobotequippedwith a catadioptric camera. This type of cameras is very useful in robotics because it provides a panoramic view field. The time to collision has been extensively studied in the case of perspective cameras. Nevertheless, the methods used are not directly applicable due to strong distortions in the images produced by the omnidirectional camera and they, therefore, need to be adapted.

Extended Abstract

The time to contact or time to collision (TTC) is the time available to a robot before reaching an object. This is a crucial source of information for the robot in order to navigate freely in a place without risking a collision with an obstacle. In this paper, we propose to estimate this time using a catadioptric camera (Baker, Nayar, 1998) embedded on the robot. Indeed, whereas a lot of works have shown the utility of this kind of cameras in robotic applications (monitoring, localisation, motion,...), a few works deal with the problem of time to contact estimation on it. Thus, in this paper, we propose a new work which allows to define and to estimate the TTC on catadioptric camera. The theory of time to contact (TTC) was first introduced by Lee and Young (Lee, 1976). These authors conducted many studies on human beings and birds. The experiments clearly showed that TTC is a critical component used in the timing of motion and action. The first goal of time to contact for robot navigation is to estimate the free space around the robot and, thus, to decide if the robot has to turn or to stop when the collision is imminent. Numerous approaches have been developed in order to estimate the time to contact in perspective vision. These methods can be decomposed to three classes: Optical flow based time-to-contact (Subbarao,1990), (Meyer, 1994), (Lourakis, Orphanoudakis, 1999), (Camus, 1995), (McCarthy et al., 2007), Gradient-based time-to-contact (Horn et al., 2009), Time-to-contact from closed contours (Cipolla, Blake, 1997), (Marco et al., 2003). In this work, we propose to use the optical flow calculated on omnidirectional images to deduce the time to collision (TTC) between the robot and the obstacle. For this, we use para-catadioptric sensor. This is an optical system which combines a parabolic mirror and an orthographic camera. The image point is obtained thanks to a double projection. First, the 3D point is projected on the mirror and then on the camera plane. Nevertheless, due to this double projection, the classical formulation used on perspective vision becomes invalid. So, in this paper we introduce a new formulation of TTC adapted on paracatadioptric sensor. This formulation is based on the estimation of optical flow. The new model is validated using two different techniques of optical flow: Lucas-Kanade (Lucas, Kanade, 1981) and adapted Lucas-Kanade (Radgui et al., 2008). The results obtained on synthetic sequences show a good behavior of the model with respect tonoise, the change in the texture and geometric shape of the obstacles. In addition, we consider a real application to measure the robustness of our approach. This is an application on obstacle detection, is based on a simple binarization of TTC map. Consequently, the TTC model evaluated on real sequences for calculating the time to collision (TTC) give encouraging results. 

Finally, our work shows that the estimation of the TTC can be extended to catadioptric sensors. This is interesting because these sensors have many benefits in the context of robot navigation.

RÉSUMÉ

Cet article s’intéresse à l’estimation du temps de collision d’un robot mobile muni d’une caméra catadioptrique. Ce type de caméra est très utile en robotique car il permet d’obtenir un champ de vue panoramique à chaque instant. Le temps de collision a été largement étudié dans le cas des caméras perspectives. Cependant, ces méthodes ne sont pas directement applicables et nécessitent d’être adaptées, à cause des distorsions des images obtenues par les caméras omnidirectionnelles. Dans ce travail, nous proposons de tirer parti du flot optique calculé sur les images omnidirectionnelles pour en déduire le temps de collision (TTC) entre le robot et l’obstacle. Nous verrons que la double projection d’un point 3D sur le miroir puis sur le plan caméra aboutit à une nouvelle formulation du TTC pour les caméras catadioptriques. Cette formulation nous permet de connaître à chaque instant et sur chaque pixel de l’image le TTC à partir du flot optique en ce point. Notre approche est validée sur des données de synthèse et desexpérimentations réelles. Enfin, nous montrons que ce calcul permet de détecter les obstacles situés dans l’axe du mouvement du robot. 

Keywords: 

TTC, time to collision, omnidirectional vision, obstacle avoidance.

MOTS-CLÉS

TTC, temps de collision, vision omnidirectionnelle, évitement d’obstacles. 

1. Introduction
2. TTC et Caméras Perspectives
3. TTC et Caméras Para-catadioptriques
4. Flot Optique
5. Résultats
6. Conclusions
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