Mobile Robotics Laboratory Institute of Systems and Robotics ISR – Coimbra • Aim – Take advantage from intelligent cooperation between mobile robots, so as to build fast and accurate 3-D maps of unknown environments, through efficient information sharing based on information utility. • A multi-robot system may be more efficient , reliable and robust than a single robot solution. • The space and time distribution of multiple robots allow them to accomplish the mapping mission in less time. • If there is an overlap in individual robots capabilities (redundancy), the failure of any particular robot does not compromise the overall mission accomplishment. • It robots with different, complementary and specialized skills are used, they may overcome their individual limitations ( e.g. different sensors, locomotion, etc.) and increase the system’s robustness. • Background – Some authors have already addressed the problem, though there are important limitations that we intend to overcome: • Most approaches are restricted to 2-D indoor, flat maps and use a single robot; • There are some probabilistic approaches (e.g. occupancy grids), but do not minimize inter-robot communication when fusing the maps from different robots; • Very few authors used entropy to formulate the expected information gain of control actions – focused on coordination or not viable in real-time. • Studies about multi-robot communication focus mainly on the communication structure rather than on the communication contents. • They are tailored in indoor and flat environments; our approach is aimed at using a team of cooperating mobile robots to build 3-D coverage maps of environments not necessarily flat. – There is no a principled mechanism to assess information utility, which might be used to support efficient multi-robot communication. • Using efficiently communication resources is crucial to scale up MRS for teams of many robots. • Research issues – Grid-based probabilistic maps [3] • The occupancy of each cell – voxel – is modeled through a continuous random variable, ranging from empty cell to fully occupied voxel. • Compact representation: only two parameters are stored for each voxel. • Explicit representation of uncertainty through the entropy concept. • Straightforward update of the voxel’s coverage belief through a Bayes Filter. – Entropy gradient-based exploration [3] • Reformulation of frontier-based exploration: frontier voxels have maximum entropy gradient. – Distributed architecture model [1] • Each robot is capable of building a 3-D map, though it is altruistically committed to share useful measurements with its teammates, who also may provide it with useful data. – Entropy-based measure of information utility [1] • Used to support efficient information sharing. • Sensory data is as useful as it contributes to improve the robot’s map. – Coordinated exploration based on the minimization of mutual information [2] • Each robot avoids to sense regions that are already being sensed by other robots. • Minimize robots’ interference: partial occlusions and not reachable exploration viewpoints. • Selected publications [1] R. Rocha, J. Dias and A. Carvalho. Cooperative multi-robot systems: a study of vision-based 3-D mapping using information theory. In Proc. of Int. Conf. on Robotics and Automation (ICRA’2005), Barcelona, Spain, pages 386-391, Apr. 2005. [2] R. Rocha, J. Dias and A. Carvalho. Entropy gradient-based exploration with cooperative robots in 3-D mapping missions. In Proc. of ICRA’2005 Workshop on Cooperative Robotics, IEEE Int. Conf. on Robotics and Automation, Barcelona, Spain, Apr. 2005. [3] R. Rocha, J. Dias, and A. Carvalho. Exploring Information Theory for Vision-Based Volumetric Mapping. In Proc. of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS’2005), Edmonton, Canada, pages 2409-2414, 2-6 Aug. 2005. Cooperative Multi-Robot Systems Vision-based 3-D Mapping using Information Theory Contact Person: Rui Rocha Email: [email protected] Rui Rocha, M.Sc., Jorge Dias, Ph.D., Adriano Carvalho, Ph.D. t k =763 s H(C | M k )=91179 bits t k =1938 s H(C | M k )=70059 bits t k =9289 s H(C | M k )=28691 bits t {W} x y z Sensor Localization Actuator R obot’s platform W orld (.,.) U Measurements M em ory M ap U pdate 3-D M ap Survey C ontroller Communication ( ( ( ) ) ) Sep. 2005 uncoordinated coordinated 1/n 0 2500 5000 7500 10000 12500 15000 17500 20000 22500 1 2 3 4 5 6 7 8 9 10 0.00 0.20 0.40 0.60 0.80 1.00 1 2 3 4 5 6 7 8 9 10 uncoordinated coordinated 1/n