Distributed Control Algorithms for Networked Mobile Robots

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We wish to develop distributed algorithms for networked teams of robots that self-organize in response to the sensed environment. Such networks promise the ability to collect information over distributed, large-scale domains with minimum infrastructure maintenance. This technology will enable scientific studies on geological and ecological scales previously beyond reach, and provide tools for a host of security and surveillance applications.

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Approach

Thus far we have focused on the task of controlling the robots so that their configuration optimizes the sampling of a sensory function. We consider a group of robots that is dispatched over a bounded environment of interest. The group's task is to sample a sensory function over the environment. The sensory function is an unknown continuous scalar field that can be measured locally by the robots, such as light intensity, temperature, sound intensity, or chemical concentration. We have developed a decentralized control solution that can accomplish this task. Using sensory measurements and neighbor positions, the network self-organizes by positioning individual robots to optimize the measurement of the sensory function. This enables the network to record observations about the sensory environment with varying resolution, so that areas with larger sensory signals receive higher-density data observations than areas that are quiet. Our work builds on several important results in this area, notably [1].

Linear Function Approximation

We have developed a control algorithm by which robots are caused to move to the weighted centroid of their Voronoi regions, a position that has been shown to be optimal for sensing [2]. For each robot, the control algorithm is as follows:

1. Compute the local Voronoi region.

2. Measure the value and gradient of the sensory function and compute a linear estimate of the sensory function using these measurements.

3. Compute the centroid of the Voronoi region using the estimated sensory function as a density.

4. Move in the direction of the centroid.

5. Repeat.

In addition, techniques have been developed for the efficient computation of the above algorithm for implementation on platforms with limited computational resources. Stability and robustness of this algorithm is being investigated and the development of other algorithms is ongoing. The algorithm has been tested in numerical simulation. An example of the final state of a typical simulation run is shown in Figure 1. The red "x" denotes the center of a Gaussian sensory function, the circles represent robot positions, and the polygons show the Voronoi regions of the robots.

Figure 1. Results of a numerical simulation of the coverage algorithm.
File:PhiOffsetCollage.mpg

The algorithm has also been implemented and tested on a swarm of actual mobile robots. An example of the final state of a typical experiment is shown in Figure 2. The robots use light sensors to measure the light source at the right of the region.

Nonlinear Function Approximation

We have extended the main idea to the case of more complex sensory models. In [3] we designed a distributed adaptive controller for the case where the sensory function can be represented as a linear combination of nonlinear basis functions (or features). We proved convergence of the controller and showed its effectiveness in numerical simulations. Building upon that work, we considerable improved the performance of the adaptive controller in [4] by incorporating a consensus mechanism into the parameter adaptation algorithm of the controller. The consensus mechanism causes the sensor measurements for any one robot to be propagated around the network so that it can be used by all other robots. We proved that this addition speeds parameter convergence and guarantees that all robots' parameters approach a common parameter vector. Numerical simulations show orders-of-magnitude improvements in the rate of convergence robots to their final configuration and the parameters to their final values. The paper describing this work [4] was a finalist for the Best Conference Paper Award at the 2008 International Conference of Robotics and Automation (ICRA). Figures 3 and 4 show a simulation comparison of the performance of the adaptive controller with and without the parameter consensus mechanism. The results of [3] and [4] along with extension to various kinds of parameter adaptation laws and extended results on convergence are presented in [6].

File:AdaptiveBasicCoverageWithSensoryFunction.mpg File:ConsensusCoverageWithSensoryFunctions.mpg File:ACC Green LightSensor.mpg

The controller with parameter consensus was implemented on a swarm of robots, as documented in [7]. The results of an experiment run are shown in figure 5. The problem of providing sensory coverage environments that change in time was investigated in [8] in a collaboration with researchers at the GRASP lab at the University of Pennsylvania.

File:AdaptiveLadybugCoverageMovie.mpg

We also investigated combinations of exploration and coverage for situations in which the sensory environment has local areas of interest. In [5] we propose a new controller that pursues exploration as an objective that is orthogonal to coverage. We find that the behavior of the controller has similarities to the way ladybugs hunt for aphids. The performance of the controller with ladybug exploration is shown to be significantly improved over the one without. Intuitively this is because exploration give more informative trajectories for the robots allowing them to better learn the sensory function. This improvement is formalized our work [5]. We propose a metric to capture the notion of the "informativeness" of a trajectory. Figure 7 shows a numerical simulation of the adaptive coverage controller with ladybug exploration.

Optimal Camera Placement

Having considered the deployment of mobile agents living in the plane, we next turned our attention to developing coverage algorithms for hovering agents that move in three dimension, but monitor a two dimensional environment. In [9] we have focused on the specific scenario of flying or floating robots with downward-facing cameras. We address the question of how to deploy multiple robots so that together their cameras produce the most informative image of the environment. Surveillance and environmental monitoring applications are numerous for such an algorithm. We propose a cost function describing the aggregate information per pixel for the group of robots. Taking the gradient with respect to each robot's position yields a distributed controller for driving the robots to locally optimal positions. Figure 7 shows numerical simulations and robots experiments, respectively, for the algorithm.

File:ICRA09Cameras.mp4

References

[1]

J. Cortes, S. Martinez, T. Karatas, F. Bullo - Coverage Control for Mobile Sensing Networks
IEEE Transactions on Robotics and Automation 20(2):243-255, April 2004
Bibtex
Author : J. Cortes, S. Martinez, T. Karatas, F. Bullo
Title : Coverage Control for Mobile Sensing Networks
In : IEEE Transactions on Robotics and Automation -
Address :
Date : April 2004

[2]

Mac Schwager, James McLurkin, Daniela Rus - Distributed Coverage Control with Sensory Feedback for Networked Robots
Proceedings of Robotics: Science and Systems , Philadelphia, PA, August 2006
Pdf Bibtex
Author : Mac Schwager, James McLurkin, Daniela Rus
Title : Distributed Coverage Control with Sensory Feedback for Networked Robots
In : Proceedings of Robotics: Science and Systems -
Address : Philadelphia, PA
Date : August 2006
[3] Mac Schwager, Jean-Jacques Slotine, Daniela Rus - Decentralized, Adaptive Control for Coverage with Networked Robots
To Appear, Proc. International Conference on Robotics and Automation , Rome, April 2007
Pdf Bibtex
Author : Mac Schwager, Jean-Jacques Slotine, Daniela Rus
Title : Decentralized, Adaptive Control for Coverage with Networked Robots
In : To Appear, Proc. International Conference on Robotics and Automation -
Address : Rome
Date : April 2007
[4] Mac Schwager, Jean-Jacques E. Slotine, Daniela Rus - Consensus Learning for Distributed Coverage Control
Proceedings of International Conference on Robotics an Automation , Pasadena, CA, May 2008
Pdf Bibtex
Author : Mac Schwager, Jean-Jacques E. Slotine, Daniela Rus
Title : Consensus Learning for Distributed Coverage Control
In : Proceedings of International Conference on Robotics an Automation -
Address : Pasadena, CA
Date : May 2008
[5] Mac Schwager, Francesco Bullo, David Skelly, Daniela Rus - A Ladybug Exploration Strategy for Distributed Adaptive Coverage Control
Proceedings of International Conference on Robotics an Automation , Pasadena, CA, May 2008
Pdf Bibtex
Author : Mac Schwager, Francesco Bullo, David Skelly, Daniela Rus
Title : A Ladybug Exploration Strategy for Distributed Adaptive Coverage Control
In : Proceedings of International Conference on Robotics an Automation -
Address : Pasadena, CA
Date : May 2008
[6] Mac Schwager, Daniela Rus, Jean-Jacques E. Slotine - Decentralized, Adaptive Control for Coverage with Networked Robots
Submitted to International Journal of Robotics Research ,2008
Pdf Bibtex
Author : Mac Schwager, Daniela Rus, Jean-Jacques E. Slotine
Title : Decentralized, Adaptive Control for Coverage with Networked Robots
In : Submitted to International Journal of Robotics Research -
Address :
Date : 2008
[7] M. Schwager, J. McLurkin, J. J. E. Slotine, D. Rus - From Theory to Practice: Distributed Coverage Control Experiments with Groups of Robots
Proceedings of International Symposium on Experimental Robotics , Athens, Greece, July 2008
Pdf Bibtex
Author : M. Schwager, J. McLurkin, J. J. E. Slotine, D. Rus
Title : From Theory to Practice: Distributed Coverage Control Experiments with Groups of Robots
In : Proceedings of International Symposium on Experimental Robotics -
Address : Athens, Greece
Date : July 2008
[8] L. C. A. Pimenta, M. Schwager, Q. Lindsey, V. Kumar, D. Rus, R. C. Mesquita, G. A. S. Pereira - Simultaneous Coverage and Tracking (SCAT) of Moving Targets with Robot Networks
Proceedings of the Eighth International Workshop on the Algorithmic Foundations of Robotics (WAFR), Accepted , Guanajuato, Mexico, December 2008
Pdf Bibtex
Author : L. C. A. Pimenta, M. Schwager, Q. Lindsey, V. Kumar, D. Rus, R. C. Mesquita, G. A. S. Pereira
Title : Simultaneous Coverage and Tracking (SCAT) of Moving Targets with Robot Networks
In : Proceedings of the Eighth International Workshop on the Algorithmic Foundations of Robotics (WAFR), Accepted -
Address : Guanajuato, Mexico
Date : December 2008
[9] M. Schwager, B. Julian, D. Rus - Optimal Coverage for Multiple Hovering Robots with Downward-Facing Cameras
In the Proceedings of the International Conference on Robotics and Automation (ICRA 09), Accepted , Kobe, Japan, May 2009
Bibtex
Author : M. Schwager, B. Julian, D. Rus
Title : Optimal Coverage for Multiple Hovering Robots with Downward-Facing Cameras
In : In the Proceedings of the International Conference on Robotics and Automation (ICRA 09), Accepted -
Address : Kobe, Japan
Date : May 2009
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