Team e-Motion

Overall Objectives
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities

Section: New Results

Localization and Mapping

Simultaneous Odometry and Extrinsic Camera Calibration

Participant : Agostino Martinelli.

This activity is the follow up of a collaboration with the ETHZ in Zurich in the frame-work of the European project BACS. In particular, during the last years, methods to perform on-line sensor calibration have been developed in the frame work of this collaboration [86] , [84] , [87] , [83] . Furthermore, always in the frame-work of this collaboration (in this case also with the help of the BlueBotics company in Lausanne), new methods to extract features from the environment have been introduced [91] [30] . During 2008, the problem of sensor self-calibration in mobile robotics by only using a single point feature (e.g. a vertical line) has been considered. In particular, the considered problem was the estimation of the extrinsic parameters of a vision sensor mounted on a mobile platform and simultaneously the estimation of the parameters describing the systematic error in the odometry system. In [22] special attention was devoted to investigate the dependence of the observability properties of these parameters on the chosen robot trajectory. The main contribution provided in [22] was the analytical derivation of the combinations of these parameters which are observable for a given robot trajectory. This derivation requires to perform a local decomposition of the system, based on the theory of distributions. Experiments have also been performed to validate the results.

Figure 10. One ofthe estimated parameters describing the extrinsic calibration of an omnidirectional camera mounted on a mobile platform.

Starting from the previous local decomposition, in [9] the observation function has been directly integrated and an analytical expression for this function has been derived. It has been shown that for special trajectories, this observation function is a periodic function whose characteristics (e.g. period, maxima, minima etc.) are simply related to the parameters that have to be estimated in order to perform the calibration. Since the evaluation of these characteristics can be easily done starting from the observation function, a very efficient and powerful approach to perform the calibration has been introduced. Experiments will be performed to validated the approach. Preliminary results are shown in figure 10 where one of the parameters describing the extrinsic calibration of an omnidirectional camera is plotted vs time. This work has been done in the scope of the BACS european project.

SLAM and Cooperative SLAM

Participant : Agostino Martinelli.

This activity is the follow up of the activity carried out since the beginning of 2006 about the problems of simultaneous localization and mapping [82] , [80] , [85] and cooperative localization [81] . While during 2007 the previous problems have been faced by using a filter approach, a distributed Maximum A Posteriori (MAP) estimator has been introduced in order to better deal with the system non linearities and also to deal with communication issues.

This activity was carried out in collaboration with prof. Stergios Roumeliotis from the Minnesota State University in Minneapolis. In particular, Dr. Agostino Martinelli has spent two months in his lab to acquire the necessary knowledge and to start this collaboration.

As opposed to centralized MAP-based Cooperative Localization, the proposed algorithm reduces memory requirements and computational complexity by distributing data and computations amongst the robots. Specifically, a distributed data-allocation scheme is presented that enables robots to simultaneously process and update their local data. Additionally, a distributed Conjugate Gradient algorithm is employed that reduces the cost of computing the MAP estimates while utilizing all available resources in the team, and increasing robustness to singlepoint failures. Finally, a computationally efficient distributed marginalization of past robot poses is introduced for limiting the size of the optimization problem. Extensive simulations studies validate the performance of the distributed MAP estimator and also compare its better accuracy to that of existing approaches. The main results have been submitted [28] . This work has been done in the scope of the BACS european project. It is also at the heart of our participation into the sFly european project.

2D/3D efficient environment reconstruction using point-based representation

Participants : Manuel Yguel, Olivier Aycard, Christian Laugier.

In 2007 we have started to explore a new mapping approach that uses a point-based representation that is able to compress the structure of the map. One of the objective was to give a theoretical framework to the point based map. This part is not yet published but already finished and a map reference vector is constituted by a couple formed by a point and a Mahalanobis matrix representing the local shape of the map. In 3D, for instance the map could be locally spherical and the Mahalanobis matrix is the identity for point based landmarks or can be locally planar and the Mahalanobis matrix is Im1 ${\#119847 \#119847 ^T}$ where Im2 $\#119847 $ is the normal to the plane or the map can be locally linear and the Mahalanobis matrix is Im3 ${I-\#119854 \#119854 ^T}$ where Im4 $\#119854 $ is a unit vector of the 3D line. The same framework is also valid in 2D, but only spherical and planar Mahalanobis matrices exist.

The other objective was to design a localization algorithm, this part was done and lead to two submitted publications: a conference paper to ICRA 2009 and a journal paper to PAMI in collaboration with the “Perception” EPI. Moreover a research report was published on the subject. The algorithm used is robust and can handle local geometry through the use of Mahalanobis matrices (see fig.  11 ).

A multi-scale compression framework and a multi-scale localization algorithm have been developped also and presented in the PhD thesis of Manuel Yguel (to be defended at the beginning of 2009). The next steps of this work are: to publish the theoretical framework developped, to develop the theory for hybrid maps based on this framework, to publish the multi-scale compression framework and the multi-scale localization algorithm developped for this map. This work is done is the scope of the BACS FP7 European project.

Figure 11. A point registration procedure, a H shape is observed and there is a H shape in the map, however some part of the map blue dots are not observed whereas some part of the observations, the small circles, are not part of the map. Even with those outliers, the pose registration is accurate.

One other aim of this work is to provide a data-structure that would be efficient to use with fast-slam algorithms where a lot of maps are drawn in a multiple hypothesis framework. This kind of SLAM algorithms, among the top efficient ones, were developped in  [89] .


Logo Inria