MAS-net Distributed Control Research
MAS-net is a mobile robot platform for experimentation with mobile actuator networks and mobile sensor networks. Various topics in these areas can be addressed on the MAS-net platform. The platform employs a camera to generate a two dimensional map of the platform to give the mobile robots a pseudo-GPS location within the platform. This enables the robots to function on the basis of position control and to collaborate with other robots. This collaboration can be done through the base station or from robot to robot using wireless communication links based on each robot. The platform was developed to be a low cost experimental platform for experimentation of mobile sensor networks and cooperative control of multi agent systems.
Fig 1.1 The MAS-net platform with critical components diagramed.
Recently, the platform has been employed to achieve various decentralized cooperative control experiments. These experiments include multi-agent rendezvous, axial alignment and a v formation keeping motion. The experiments are validation of consensus seeking algorithms using local information for mobile robot formation control. The formal results of these experiments are contained in a manuscript submitted to IEEE Transactions on Control Systems Technology for Special Issue on Multi-vehicle Systems Cooperative Control, April, 2006. The videos from each of these experiments are shown below:
Autonomous Consensus Seeking Distributed Control
Autonomous robot rendezvous requires that each robot independently determines where the rendezvous point will be given information about the location of only a few of the other robots within the group. This achieved by algorithms that seek consensus among the various members of the group. For rendezvous, the following consensus algorithm is applied:
For axial alignment, the following extended consensus
algorithm is applied:
where δ has been chosen to guarantee that the robots align on a horizontal line with a separation distance of 40 cm along the x axis between two adjacent neighboring robots. For formation maneuvering, the following extended consensus algorithm is applied:
where αi > 0, rdg denotes
the desired trajectory of the formation, |Ji| denotes the
cardinality of set Ji, ` denotes the
index of the vehicle that has the knowledge of rdg (i.e, team leader), and δ i =
[δ ix; δ iy]T has
been chosen to ensure a separation distance of 40 cm between two adjacent neighboring
robots along both x axis and y axis.
Discrete time versions of these algorithms have been employed to achieve position control based algorithms for these experiments. The information received and transmitted from each robot is shown in diagrams with each video.
Rendezvous with well connected communication:
Fig 2.1 The communication exchange diagram for the initial Rendezvous experiments.
Early Experiments and Parameter Tuning
Given a good communication tree, accomplishing rendezvous simply required getting the robot hardware and MAS-net software in working order. This requires tuning the camera, robot low level control and debugging existing hardware issues. The Mika-z mas-motes were just built and the hardware still has some problems with the mote to robot interconnection this causes the robots to not receive information from the base station such as start commands or pseudo-GPS position updates. Without these key components, initially the experimentation ran through some iterative debug cycles.
Fig 2.2 Pictures of early test and debug experiments with rendezvous.
By tracing the red dotted paths, the overall trajectory of the robots in these initial test cases can be understood. In the first picture, due to improper tuning of the low level PID control, the robots rendezvous early with the nearest neighbor and then slowly converge to the real rendezvous location. The next picture demonstrates improper tuning of the camera. The lighting contrasts cause the robots near the top of the picture to receive inaccurate orientation information. This causes them to make wrong direction course corrections. The robots coming from the bottom of the picture are not affected as much by the lighting contrast and so are able to close on the top two robots and achieve rendezvous near the top of the platform.
The lower left picture is a demonstration of unintended axial alignment. The corner robots fail to respond to the start command to do a bad connection of the mote to the robot and so fail to move. The robots in the middle seek to center themselves in between the robots from which they are receiving position information. The end result of this is that the two middle robots achieve equal spacing between the four robots along the diagonal axis. Formal experiments with this type of result are shown later.
The bottom right picture demonstrates a better result with only minor camera orientation problems. Given this result, the formal experimental videos were begun.
Rendezvous Case Study
Case I
Fig 3.1 Case I video and communication tree diagram.
Case I is the formal rendezvous experiment given a good communication tree. The robots drive quickly to the rendezvous point with little deviation from the desired trajectory. This validates the consensus algorithms implementation and justifies further case studies with varying fixed communication topologies.
Fig 3.2 This is an example of case I type rendezvous with a triangular starting shape.
In order to demonstrate that the initial conditions of the system do not affect the overall rendezvous of the system, a triangular shape was employed with random starting orientations. The robots still achieved rendezvous with little difficulty. One problem shown here is the marker from the yellow robot was knocked off onto the blue robot. Although it cannot be easily seen, the actual yellow robot is in between the blue and orange robots at the end.
Case II
Fig 3.3 This shows the Case II rendezvous video and communication tree.
Case II involves a badly connected communication tree with prevents the rendezvous of the whole group. The group is able to achieve local rendezvous with a neighbor, but overall consensus on a rendezvous location could not be achieved. One interesting issue is shown in the rendezvous of the top two robots. The yellow robot received bad pseudo-GPS data for the first part of the experiment. This allowed the upper left robot to continue farther to the left than the original center of the two robots. This demonstrates the robustness of the consensus seeking algorithm in that the even in the presence of hardware or software failure of some member of the group, the group can adjust and still achieve the desired result in the least amount of time.
Case III
Fig 3.4 The video and communication tree for the Case III rendezvous experiment.
Case III is particularly interesting given the consensus algorithm employed here. Notice that three of the robots share information in only one direction around the communication tree. This causes robots 1, 2 and 3 to enter into a cyclic pursuit. The lack of dots in some parts of the traveling path symbolize points in which the camera vision lost sight of the robot and pseudo-GPS updates of that robots position cannot be obtained. Once again, due to the robust nature of the algorithm, the group is still able to achieve rendezvous in the presence of communication drop out or dynamic communication tree changes. This topic of switching communication topologies is addressed after the rendezvous case study with fixed topologies.
Case IV
Fig 3.5 Case IV is an example of cyclic pursuit communication topology with all agents following another agent in a circular pattern.
Cyclic pursuit strategies have received a lot of attention in various formation control related works. Case IV is a true demonstration of cyclic pursuit as the robots follow the robot in front of them. The circle is in the process of collapsing, but requires the robots to maintain a tight pattern in order to maintain a perfect cyclic pursuit. Here, due to vision dropout, the blue robot pulls out of the pursuit before complete rendezvous. The rest of the group is able to converge earlier than expected in this case. Even with the final breakdown, this is a good example of cyclic pursuit as it is applied by the consensus seeking algorithm.
Case V
Fig 3.56A leader follower type case rendezvous with the proper communication tree.
Here is a leader follower type formation where each robot sends information to
a robot behind them. The convergence of the robots to the lead robots
position is typical of a leader follower type motion. The yellow robot
does show some of the cyclic pursuit as it wraps around the orange robot while
trying to follow the orange robots trajectory. This shows the
relationship between these two types of communication topologies. In
fact, the only difference is the communication link from robot 1 to robot 2 is
broken in this case.
Case VI
Fig 3.7 A poorly defined communication tree where the two middle robots receive information from the two corner robots.
Finally, the case involving a poorly connected communication tree is explored where the two middle robots receive information from the two corner robots. This causes the corner robots not to move and the two middle robots to converge on the center of the two corner robots. Both middle robots go to the same location as they only have knowledge of the corner robots and not each other.
Switching Topology
In order to show the overall effect of communication delay and communication dropout on the rendezvous of the group, an experiment was done with a group of switching topologies. The union of the five different communication trees is a well connected communication tree. By cycling through the communication trees, the robots are able to converge finally to a position close to the fixed topology case given the fully connected communication tree.
Fig 4.1 These two videos show experiments comparing a switching topology with a connected union communication tree and a fixed communication tree given the union of the switching case.
The left video demonstrates the effect of a randomly switching communication tree. Notice the way the robots react to only receiving information from one of the other robots in the group. This causes the robots to stop and start or dramatically change direction to rendezvous with other robots at random times throughout the experiment. However, as the communication topologies are cycled through, the union of the trees eventually brings the whole group together in final position close to the fixed topology case. It does take longer to reach the rendezvous point, but the robust nature of the consensus algorithm compensates for the disjoint nature of the randomly switching topology.
This example is an important demonstration of what happens as communication delay and packet loss are introduced in a real world situation. Old information slows the rendezvous of the group and so would be disregarded in a receding horizon type control scheme. This shows how even in these situations, the system is still able to reach consensus and achieve the desired goal.
Axial Alignment
Axial alignment is a 2-D equivalent of a 3-D altitude alignment experiment with UAVS or submarine autonomous vehicles. The MAS-net platform is limited to the 2-D case so here we attempt to align along the y-axis and spread the robots equally spaced along that axis to avoid collisions. This is accomplished by the same consensus algorithm employed in the rendezvous case but the communication tree is poorly connected to achieve rendezvous and an offset is given to the end robots to ensure the equal spacing from robot to robot along the y-axis.
Fig 5.1 Axial alignment is achieved using a poorly connected communication tree based on nearest neighbor rules.
The communication tree is designed so robots can only communicate with robots immediately on their left or right. This is referred to as an example of nearest neighbor rule. This type of communication is used widely in limited range communication trees where spacing between robots is such that they can only just communicate with other robots close to them. Below are four videos of axial alignment experiments that achieve axial alignment on the MAS-net platform.
Fig 5.2 These are four axial alignment videos based on the communication tree in figure 5.1.
As can be seen in the videos, the platform is limited by the low level position controllers. These controllers have a 6 cm radius of convergence for their desired position. Once within 6 cm of the desired position, the robot considers itself at its desired position. This leads to somewhat diagonal alignments that are slanted by 6 cm from robot to robot. However, given that this is an intrinsic parameter of the platform, this is axial alignment achieved.
Another interesting tendency of the platform is the problem of robots going the wrong direction for certain periods of time. This is due to the vision software losing the orientation of the robot. The pseudo-GPS at this time is essentially telling the robot to turn and drive the wrong direction until the robot moves into a position on the platform that the vision software can correctly identify the robots orientation. Even with this error, the overall experiments still achieve the goal of axial alignment and further show the robust nature of the consensus algorithm.
V Formation Motion
This experiment is to achieve a formation motion example on the MAS-net platform. This is accomplished using the offset to the consensus algorithm scheme from the axial alignment experiment, but the front robot in the leader follower communication tree simply moves along the x-axis forcing the other robots to follow him in turn.
Fig 6.1 The video shows the result of a leader-follower type v-formation move along the x-axis.
This experiment also demonstrates the limitations of the MAS-net platform development at this point. Due to the limitation of the camera vision software, the robots have a tendency to turn the wrong direction when the camera vision software loses the correct orientation of the robots. In this experiment, the ambient lighting is insufficient and glare from overhead lighting creates a sloppy group motion. The overall motion of the group is in the correct direction and the end result is the correct formation at the correct place, but the transition does not exhibit perfect formation motion. This is not a reflection of the algorithm however, but more a reflection of the vision software limitations.
One problem inherent in the robots is a slow response time to dynamic changes in the robots around them. The error must be rather large for the group to react to changes in the lead robot. As an inherent part of the robots, this cannot be simply remedied without a redesign of the basic robot structures.
Developmental Videos
Now that the results are shown, an attempt will be made to show the developmental videos for the project. These videos demonstrate the limitations of the platform as it is applied to multi agent cooperative control research. The limitations of the vision software and the robots themselves will be further shown here.
The platform was not created to be a distributed network. Initially, MAS-net was to be a mobile sensor network based on a base station centralized control scheme. The base station was designed to compensate for any weak points inherent in the individual robot architectures. The robots themselves are simple mini-sumo robots that have been designed to incorporated mica-z wireless motes capable of wireless communication and low-level control using the microcontroller built into the mote. The encoders on the robots are simple incremental encoders with 128 point/rev. This gives reasonable position information in between pseudo-GPS updates. The robots are very dependent on the pseudo-GPS updates over any long distance and so the camera vision limitations have dramatic effect on the robots. The robots low-level control is run from the mote itself, but the periodic orientation and position updates come directly from the base station and overwrite the encoder based position information each time the pseudo-GPS position information is broadcast. The low-level control itself is done by a PID type controller tuned to each robot. The PID controller is the same for both motors but with different dead band offsets and different motor bias. This gives sufficient compensation, but not perfect control for the mas-mote robots.
The pseudo-GPS vision is another difficult component of the MAS-net platform. The robots depend on pseudo-GPS for x-y position and orientation periodic updates. The platform was developed to track a dynamically changing gas diffusion boundary using a mobile sensor network. This is done with color sensors mounted to the bottom of each robot and a fog machine projecting fog into a space under the robots. This requires the platform to be covered in transparent plexi-glass so the robots can detect the boundary of the fog with the color sensors. Given the overhead lighting, the glare developed on the plexi-glass creates difficulties for the image processing as the robots move in and out of varying levels of light reflection.
To track orientation and position, each robot has an individual identifying symbol on the top of the robot. Although the symbols have been selected out of a large number of symbols because of their ease of recognition, the lighting still confuses the image as the robots move around the platform. The room is surrounded in windows on two sides and so controlling the ambient lighting is difficult while conducting experiments. This is the chief cause of the failures in the experiments conducted here. Although the low-level control of the robots is not perfect, the pseudo-GPS updates causing the robots to turn the wrong direction had a decidedly more pronounced effect on the overall experiment outcome. Examples of these types of issues can be seen in the videos listed below.
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Experiment Type |
Video |
Description |
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Test |
This is a test with only three robots attempting to achieve rendezvous with out calibration of the vision software or tuning low-level control for the robots. |
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Case 1 Rendezvous |
Here is an example of rendezvous with the robots without proper tuning of the low-level control. |
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Case 1 Rendezvous |
This is a good rendezvous example. |
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Case 1 Rendezvous |
Another good rendezvous example. |
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Case 1 Rendezvous |
After this run, the formal case study was started. Everything ran perfectly here to achieve rendezvous and make appropriate videos. |
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Case 2 Rendezvous |
This shows the limitations of the pseudo-GPS vision. Notice the robot going the wrong direction part of the time. |
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Case 4 Rendezvous |
During experiments with case 4, the robots struggled because the robots were required to cover the entire platform for a relatively long time. This created a situation in which the camera vision problems could be much more noticeable. Particularly the blue robot orientation is hard to obtain from the camera vision. It breaks down first. |
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Case 4 Rendezvous |
Here the robots are put in an odd initial condition. It has the topology of case 4, but the initial relative positions of case 4 are not right. |
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Case 4 Rendezvous |
The Blue robots orientation is lost causing the group to converge early. |
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Case 4 Rendezvous |
The initial positions are changed to see the effect of the position with respect to the topology. A quick rendezvous. |
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Switching Topology |
This is a slightly different topology from the earlier switching topology case. Rendezvous is easily achieved to the center because one upper robot receives information about a bottom robot rather than the lower robots only knowing about the upper robots. |
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Switching Topology |
This is the fixed topology case of described by the video before this. |
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V Formation Motion |
A formation line move is attempted. The 6 cm error causes the robots not to respond quickly and the motion is more like a v formation move. The pseudo-GPS problems are highly apparent. |
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V Formation Motion |
Much like formation line 1 but the lead robot is moving much slower. Same result due to poor response time for the following robots and bad pseudo-GPS information. |
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V Formation Motion |
A v formation move where the pseudo-GPS information is all wrong. |
The Experiment Team
Wei Ren – Assistant Professor
at
Haiyang Chao – Research Assistant
CSOIS [Ph.D. Student at
William Bourgeous
– Research Assistant CSOIS [MSc Student at
Nathan Sorensen – Research
Assistant [MSc Student at
page by Nathan Sorensen