Team:ETH Zurich/integratedModel


We modelled the individual components to identify the critical parameters in each individual step during the design process of AROMA. Nevertheless, to evaluate the performance of AROMA in the scenario of the minefield, in a final step, we combined all the individual steps together.
Bringing the individual parts together
To reasonably model the overall behaviour of AROMA, the optimized path planning algorithm is then brought together with the other parts into the integrated model. This is done in the following way. At each point, we calculate the concentration of our target molecule in air via our diffusion model. Next, the bubbling model determines how much of the molecule dissolves in our medium. Then we simulate how our bacteria react to this new concentration with the help of our chemotaxis model which outputs the adaptation time of the bacteria. We chose to use the chemotaxis model for the modelling of the overall system as the biological pathway actually reacts faster and since experimental data on this approach was available already early on. In practice, when flushing the new media into the microfluidic chip, it takes approximately 10 seconds until the flow stops, therefore we know that we can only sense an in- or decrease in concentration if the bacterial response lasts longer than those 10 seconds. Finally the information about the in- or decrease of the concentration is passed into our path planning algorithm which then processes this information, determines the next step to take and leads the robot to the source. As 2,4 DNT is a compound that is less present in the environment than Aspartate we assume that 2,4 DNT will activate the pathway at lower concentrations. This is demonstrated by the sensitivity of transcription factors for 2,4 DNT. As a result we shifted the concentration range of the chemotaxis model into the order of nM.
Optimizing Parameters
The only parameter of the path planning algorithm is the initial stepsize. This parameter is important to optimize as it influences the success rate of finding the source. Below, the plots illustrate on the one hand the rate of success (i.e. finding the source) and the mean number of steps needed to achieve this, given a single landmine only and a bubbling time of 60s
Step size 10m, bubbling of 60s
Step size 20m, bubbling of 60s
Step size 50m, bubbling of 60s
Fraction of succesful completions for different step sizes
Therefore, a higher initial stepsize of for instance 50m is absolutely necessary if one starts more than 40 meters away from the source. Nevertheless, the plots still illustrate that when starting too far away from the source our optimized path planning algorithm does not always find it. In the scenario of clearing a minefield this is a major problem. Therefore, we adapted our search algorithm to first use an algorithm that scams through the field until a measurable concentration of DNT is detected before actually activating the local path planning algorithm which fastly and efficiently locates the source.
Furthermore we wanted to analyse whether an increased bubbling time of 3 minutes actually increases our detection range.
The figure below shows the success rate for a bubbling time of 3 minutes at an initial stepsize of 20m. When comparing this plot to the one shown above one realizes that the rate of completions only slightly increases. Therefore for the application of AROMA this additional 2 minutes of bubbling does not make sense. Hence, we decided to go with a bubbling time of 60s and an initial stepsize of 20 meters
Fraction of successful completions for a step size of 20m and 180 seconds of bubbling.
In a last step, we integrated the uncertainty of the readout of our microscopy system and the corresponding image processing algorithm into our model. Our own measurement data showed, that the standard deviation of the adaptation time scales linear with the mean. Furthermore, it takes us about 10 seconds to stop the flow, so basically 10 seconds of the response time of the bacteria are lost. Our image readout algorithm can detect on average 5 bacteria per frame and if 2 react, then we decide that the concentration indeed increased. Including those statistics into our model leads to the following rate of success as shown in the figure below. Therefore our algorithm is very robust against this form of uncertainty measurement as the performance is still comparable to the situation without any noise. This is due to the fact that in almost all of the cases, the adaptation time of the bacteria is significantly higher than the 10 seconds in which it is not possible to sense.
Figure showing performance under measurement uncertanty
Finally, we simulated the behaviour of the robot in a field with multiple sources. Therefore, the path planning algorithm to find the source is now run multiple times in the same field. After having identified a source, the next starting position is chosen to be the current position plus a random direction times the step length.
The figures show how AROMA consecutively explores the field and finds one source after the other.
The figures show how AROMA consecutively explores the field and finds one source after the other. This also underlines the fact that the previously made assumptions of only having to find one source is valid as when once being close to a source the influence of all the others is negligible. Furthermore, adding a GPS signal to AROMA would allow to keep track of the previously explored places and would also ensure to not miss exploring a certain area.
On the whole, the overall integrated model showed the feasibility of AROMA and helped to refine the path planning algorithm. AROMA is capable of efficiently finding the sources of DNT, even in case of having multiple sources.
  1. Bacterium-inspired Robots for Environmental Monitoring, by Amit Dhariwal et al. Proceedings of the 2004 IEEE
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