In a few recent works, we have formulated and investigated a novel problem called Mutual Localization with Anonymous Position Measures (MLAPM). This is an extension of Mutual Localization with Position Measures, with the additional assumption that the identities of the measured robots are not known. MLAPM is obviously of interest in applications when individual tagging (e.g., by appearance or color) of the robots is impractical, expensive or undesirable. An interesting consequence of the anonymity hypothesis is that, for certain configurations of the multi-robot system, it causes a combinatorial ambiguity in the inversion of the measure equation, resulting in the existence of multiple solutions.
Initially [1,2] we have developed a two-phase filter for solving the MLAPM problem. The first phase uses MultiReg, an innovative algorithm aimed at obtaining sets of geometrically feasible relative pose hypotheses. In the second phase, the output of MultiReg is processed by a data associator and a multiple EKF to rate and select the best hypothesis. We have studied the performance of the developed localization system using both simulations and real experiments.
In [3], we have investigated more in the detail the structure of the problem. We have found a necessary and sufficient condition for the uniqueness of the geometrical solution based on the notion of rotational symmetry in the physical plane. We have also derived the relationship between the number of robots and the number of possible solutions, and we have classified the solutions in a number of equivalence classes which is linear with the number of robots.
In the same paper, we have developed a control law that effectively breaks symmetric formations so as to guarantee the unique solvability of the problem. We have demonstrated the performance of this control law through simulations.
In [4] we have modified our localization system in a probabilistic sense, first by using particle filters (rather than EKFs) to compute the current belief on the robots' relative poses, and then by modifying MultiReg so that is can use this information as a feedback. This has several advantages, mainly (i) particle filters are intrinsically multi-modal and therefore do not require the use of heuristics for data association (ii) the new framework allows MultiReg to focus on solutions that are most likely according to the current belief, filtering out the effects of rotational symmetries that may arise in the system and avoiding the associated complexity increase. In practice, this results in a drastic reduction of the execution time whenever the task requires a rotational symmetric robot deployment (e.g., encirclement, escorting, etc). The proposed method is experimentally validated.
For an application of MLAPM in a multi-robot task execution, see also the encirclement page.
In [5] we have modified the system to solve the RML problem using anonymous bearing measurements, rather than full position (bearing plus distance) measurements. The new algorithm is then able to use measurements taken from non-depth sensors, such as video cameras, allowing the application of our method for mutual localization to a wider class of multi-agent systems.
In [6] we have extended the method proposed in [5] so as to solve the mutual localization problem in 3D environments using bearing-only measurements. Such extension is non-trivial, requiring not only a new multiple registration algorithm and a different filter, but also modifications to the system architecture and the use of a complementary filter to estimate the attitude based also on IMU data. The resulting localization system has been tested on a team of autonomous quadrotors, but in principle its field of application ranges from underwater vehicles to wheeled robots on 3D terrain.
[1] A. Franchi, G. Oriolo, and P. Stegagno, Mutual localization of a multi-robot team with anonymous relative position measures Department of Computer and System Sciences, Tech. Rep. 1, Jan. 2009. (download)
[2] A. Franchi, G. Oriolo, and P. Stegagno, Mutual localization in a multi-robot system with anonymous relative position measures. In 2009 IEEE/RSJ Int. Conf. on Intelligent Robot & Systems, St. Louis, MO, USA, pp. 3974-3980, Oct. 2009. (download)
[3] A. Franchi, G. Oriolo, and P. Stegagno, On the solvability of the mutual localization problem with anonymous position measures. In 2010 IEEE Int. Conf. on Robotics and Automation, Anchorage, AK, USA, pp. 3193-3199, May 2010. (download)
[4] A. Franchi, G. Oriolo, and P. Stegagno, Probabilistic mutual localization in multi-agent systems from anonymous position measures. In 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, pp. 6534-6540, Dec. 2010. (download)
[5] P. Stegagno, M. Cognetti, A. Franchi, and G. Oriolo, Mutual localization using anonymous bearing measurements. In 2011 IEEE/RSJ Int. Conf. on Intelligent Robot & Systems, San Francisco, CA, USA, pp. 469-474, Oct. 2011. (download)
[6] M. Cognetti, P. Stegagno, A. Franchi, G. Oriolo, and H. H. Bülthoff, 3D Mutual localization with anonymous bearing measurements. Submitted to 2012 IEEE Int. Conf. on Robotics and Automation, St. Paul, MN, USA, May 2012.
Mutual localization
experiments using the method in [1-2] (AVI
clip)
In this video, we show two mutual localization experiments performed on
a team of five Khepera III robots. A wireless card and a Hokuyo
URG-04LX laser range finder have been added to the standard equipment of
each robot. In both experiments, we show the robot arena and the
estimates computed by robot 4. The highly symmetric and ambiguous
starting configuration causes the initial estimates to be wrong.
However, when the robots start moving the symmetry is broken and the
right estimates are obtained in a few seconds. In the first experiment,
all five robots participate to the mutual localization process, while
the peculiarity of the second experiment is that two robots do not
participate, as they act as deceiving obstacles.
Anti-symmetry control
simulations using the control law in [3] (mp4
clip)
In this video, we show five simulations of anti-symmetry control. In
all simulations, the robots start in a rotational symmetric
configuration (hence ambiguous) and move under the action of the
proposed control law. On the left, we show the evolution of the
multi-robot system, while on the right we show the symmetry metric
function, a function used to quantify the "distance" from rotational
symmetry. We also show that the action of a random control law is much
less effective.
Anti-symmetry control experiments using the control law in [3] (mp4 clip)
Mutual localization experiments using the method in [4] (coming soon)
Mutual localizazion experiments and simulations using the method in [5] (bearing only)
(mp4 clip)
The first part of the video shows the proposed mutual localization system running on a team of 4 robots.
The second part shows the localization method in simulation with a 360° field of view. As expected,
the convergence is faster and the estimates are more precise than in the previous case.
Mutual localizazion experiments using the method in [6] (3D bearing only)
(mp4 clip)
The data for the experiment are collected in multiple sessions,
each session collecting the data from one robot. After,
the data are subsequently synchronized and the estimation is
conducted offline. The video shows the overlapped trajectories of the robots and the estimates gathered.