This paper describes flow-relative and flow-aided navigation of a biomimetic underwater vehicle using an artificial lateral line for flow sensing. Most of the aquatic animals have flow sensing organs, but there are no man-made analogues to those sensors currently in use on underwater vehicles. Here, we show that artificial lateral line sensing can be used for detecting hydrodynamic regimens and for controlling the robot’s motion with respect to the flow. We implement station holding of an underwater vehicle in a steady stream and in the wake of a bluff object. We show that lateral line sensing can provide a speed estimate of an underwater robot thus functioning as a short-term odometry for robot navigation. We also demonstrate navigation with respect to the flow in periodic turbulence and show that controlling the position of the robot in the reduced flow zone in the wake of an object reduces a vehicle’s energy consumption.
All fishes have developed a lateral line organ for detecting and processing hydrodynamic events . Also, some crustaceans  and aquatic mammals have flow-sensitive organs . At the same time, man-made underwater vehicles mostly rely on ultrasonic sensing and vision for getting feedback from the environment [4,5]. The standard method for flow detection of underwater vehicles is using an acoustic Doppler current profiler (ADCP). ADCPs measure the global flow speed and its readings are incorporated into the vehicle’s navigational system to compensate for the drift [6,7]. As opposed to the highly distributed lateral line organ of fish, ADCP does not measure local flow. Also, ADCPs are expensive, bulky devices consuming lots of energy and are therefore not suitable for small vehicles.
At the same time, many possible application scenarios require miniature, efficient and manoeuverable autonomous underwater vehicles. For example, pipeline inspection, shipwreck penetration and harbour monitoring are such kinds of tasks.
Small vehicles become more dependent on the environment as currents and eddies can easily deviate them away from their desired path. This is especially relevant to riverine technology where flow is often rapid, turbulent and obstructed by objects.
Rheotropism is a tendency of fish to react to mechanical stimuli of the flow . For example, it is shown that fish can detect the direction of flow and face towards the oncoming current , known as the rheotaxis behaviour. This helps migrating upstream or holding a position in a favourable place in the stream to detect odours and food carried with the flow. In the study of Chagnaud et al. , it is also discussed that fish are able to detect the velocity of the flow and keep their position without drifting down- or upstream.
One of the most interesting expressions of rheotropism for both biologists and engineers is the fish’ behaviour behind a bluff object in flow . An object in the flow generates a repeating pattern of swirling vortices, known as the Kármán vortex street (KVS). The KVS is a well-studied hydrodynamic effect that can be realized in laboratory conditions with high repeatability . In rivers such vortex streets can be generated by rocks or other objects. Some fish, for example, rainbow trout Oncorhynchus mykiss, are shown to use KVS to reduce their energy consumption  by taking advantage of the reduced flow speeds behind the object or adapting a specific locomotion pattern (called Kármán gaiting) when interacting with the vortices [14–16].
Such behaviours demonstrate high sensitivity, discrimination ability and redundancy of the biological lateral line and have inspired researchers to mimic its working principles and functionality.
The biological lateral line is a dual system consisting of superficial neuromasts, which are sensitive to flow speed and canal neuromasts responding to pressure changes . Several types of artificial superficial MEMS-based neuromasts have been developed [18,19] and demonstrated to be capable of detecting hydrodynamic events, such as a dipole source . Pressure sensors  or optical flow sensors placed in artificial canals  have been also used, and it is demonstrated that the presence of KVS can be detected and the position of the cylinder generating the street can be estimated from those sensor readings .
Although several artificial lateral line systems have been developed, to the best of our knowledge, they have never been mounted on an underwater robot and used for controlling the robot in the flow.
In this paper, we demonstrate flow-relative control of an underwater robot (figure 1). We use on-board pressure sensors for local flow sensing for
— identification and discrimination of flow regimens (uniform flow and periodic turbulence);
— detecting the orientation of the robot with respect to the flow direction in a steady stream;
— measuring the flow speed; and
— estimating the position of the robot in a wake of an object.
With the feedback from the lateral line sensors, we control the robot to hold its position with respect to the flow by first identifying the flow regimen and then compensating for its downstream drift and the lateral displacement in the wake.
The robotic platform used in this study is a biomimetic underwater robot FILOSE (Robotic FIsh LOcomotion and SEnsing) developed to study fish and flow interaction and to extract bioinspired design principles using a reductionist approach. As opposed to the traditional mechanical design of using serial chain kinematics for generating undulating motion [23,24], the FILOSE robot uses a compliant tail driven by a single motor. Thrust is generated using vibrations at a resonance frequency mimicking the kinematics of a trout at cruising speeds [25,26].
We have also applied the principle of minimal complexity to the sensor and controller design. Though fish lateral line is generally very elaborate, its morphology varies from species to species in design and complexity . For example, some species, such as Ruffe have been observed to have short lateral line canals consisting of only three neuromasts (S. Van Netten 2012, private communication). In our previous work, we have shown that rheotaxis behaviour (facing upstream) can be achieved using only two pressure sensors on the sides of the robot and a simple Braitenberg 2b controller . Here, we use standard linear control methods to investigate to what extent the seemingly complex behaviours of flow-based control can be achieved with the low-complexity artificial lateral line configuration and control. The artificial lateral line here consists of pressure sensors, but as they record absolute pressure values translated to the flow speeds their functionality is rather analogous to the superficial neuromasts.
2. Experimental set-up
(a) The robot
The 50 cm long FILOSE robot mimics the geometry and swimming mode of a rainbow trout (Oncorhynchus mykiss). Rainbow trout is a subcarangiform swimmer. It generates thrust by undulating three-fifths of its posterior body . Similarly, the FILOSE robot has a 30 cm long compliant posterior body where the motion is generated using only a single actuator. The servo-motor creates vibrations in the tail through steel cables. The tail actuation can be expressed by sinusoidal motion. 2.1where φ is the motor angle, A the actuation amplitude, f the frequency and φ0 the motor angle offset. As the system is, in principle, a non-homogeneous cantilever beam with a decreasing cross section, the amplitude of oscillations increase towards the end of the tail. Varying the amplitude and the frequency of the oscillations changes the swimming speed of the robot, whereas adding an offset to the actuation signal will make the robot turn left or right. Modelling of the tail and the selection of geometry and compliant materials is described in more detail in .
The fish robot is equipped with piezoresistive silicon absolute pressure sensors. These sensors form an artificial lateral line. The sensors are mounted inside the rigid plastic head of the robot and are connected to the 1 mm pressure taps on the surface of the head. There are all together five pressure taps: one at the tip of the nose, two on the sides of the head 50 mm from the nose and two on the sides of the head 100 mm from the nose (figure 2).
We use Intersema MS5407-AM miniature low-noise, high-sensitivity, high-linearity sensors. The signals are digitized by using a 22-bit differential analog–digital converter mounted directly on the printed circuit board (PCB) under the sensor to minimize noise. The range of the sensors is 7 bar and the sensitivity is 0.1 Pa. As the pressure sensors are sensitive to temperature changes, a temperature sensor was attached on the PCB of every sensor, and the pressure is compensated for temperature drifts.
The sensors are connected to a 400 MHz miniature ARM computer mounted inside the FILOSE fish head. The ARM processor also controls a high-torque brushless servo motor used for tail actuation. The on-board computer communicates with the external computer over a serial interface through a cable connected to the robot. The cable is relatively thin to minimize its effect on the robot’s motion. All the higher level control and processing is implemented in LabView on board the external computer for runtime debugging, monitoring and analysis.
(b) Test tank
The experiments with the robotic fish were conducted in a flow tunnel with a closed working section 0.5 m wide and high and 1.5 m long. The ceiling of the tunnel is transparent. Flow speed calibration using digital particle image velocimetry (DPIV) system confirmed that up to 50 cm s−1 uniform flow can be created with our set-up. As the maximum speed of the fish robot is 19 cm s−1, the maximum flow speed in the experiments was also limited to 19 cm s−1.
For the control experiments, the robot was mounted on a slender polystyrene bar that gave it a positive buoyancy of 0.2 N (figure 3). The robot with the bar was placed in the tunnel so that the bar was supported against the upper glass wall of the flow tunnel with two sharp-ended plastic tips. The depth of the robot was thus fixed and it only moved in the horizontal plane. This type of set-up simplifies the experiments as the robot does not need to have active buoyancy control. The effect of the bar on the swimming dynamics is small because of the much smaller size of the bar compared with the fish robot and minor friction against the glass. This set-up also permits trajectory tracking and motion analysis of the robot with the help of two LEDs mounted on the polystyrene bar detectable with an overview camera through the transparent ceiling.
(c) Kármán vortex street
KVS is a repeating pattern of vortices in the wake of an object. We used two types of objects to create the KVS. First, we experimented with the vertical half-cylinder, which is a classic, well-repeatable approach described thoroughly in the literature . We used a half-cylinder with a diameter of 10 cm and a flow speed of 0.15 cm s−1. DPIV was used to characterize the flow behind the cylinder. The DPIV data were analysed using a custom-made toolbox described in . In figure 4, an instant vorticity (below) and the mean downstream velocity (above) are shown. Table 1 indicates the parameters required for our study. Figure 4c illustrates that the cylinder generates well-developed vortices. Figure 4a shows that the velocity behind the cylinder is considerably slower (blue colour) than the velocity next to the cylinder outside the vortex street (red colour). When moving closer than 13.7 cm to the cylinder (the suction point), the downstream flow becomes negative. This is an important distance to consider in the controller design because an object placed into the suction zone will be sucked against the cylinder. Downstream from the suction zone is the area of reduced flow. This is the most favourable place for the fish robot station holding because of the decreased drag.
To test our artificial lateral line robot control also in less perfect and thus more natural conditions, we replaced a cylinder with a cuboid. The height of the cuboid was 155 mm and the width and length were 100 mm. The centre of the cuboid was placed at the same height as the robot’s centre plane. Figure 4d demonstrates that no well-developed vortex street exists behind the cuboid. From the velocity image in figure 4b, it can be seen that the suction zone is shorter than behind the cylinder. Also the flow speed in the area of reduced flow is narrower and not as stable as behind the cylinder.
3. Station holding in steady flow
(a) Flow speed detection
From our previous studies with a fixed robotic fish with pressure sensors, we know that the flow speed can be estimated by the pressure drop on the sides of the robot or by the pressure difference between the tip of the nose and on the sides . Here, we study if the same relations hold for the freely swimming robot and if they can be used to design a controller for station holding.
If the robot is facing directly towards the flow, the pressure sensor at the tip of the nose measures the stagnation pressure p0. It is equal to the sum of the free-stream static pressure pfs and the free-stream dynamic pressure: p0=pfs+1/2ρV 2, where ρ is the density of water and V the free-stream velocity. From that we can find the flow speed 3.1where pfs can be measured at the point on the robot’s head, where the flow speed is equal to the free flow speed. None of our sensors is mounted at this point, meaning that pressure difference (p0−pfs) cannot be directly measured. We measure the difference between the nose sensor and the average pressure of the side sensors (p0−pa) instead. Within the velocity range of our robot, we have found that the difference of these two values can be approximated by a constant multiplier Cs, giving (p0−pfs)=Cs(p0−pa).
To experimentally validate the relation (3.1), we fixed the robot in the flow tunnel and recorded the pressure sensor signals at different flow rates. The results are shown in figure 5. With a correction coefficient Cs=0.45, the theoretical relation (3.1) fitted the experimental data with a goodness of fit R2=0.975.
We also estimate the speed using only the average pressure on the sides of the robot. The relationship between the average pressure drop ΔPa and the flow speed is also plotted in figure 5. We can see that it can be well fitted (R2=0.993) with an equation 3.2The sensors also measure the environmental pressure, which changes at different velocities because of the motor that is generating flow. Therefore, equation (3.2) is not proportional to the square root of pressure drop as derived from Bernoulli’s law, but includes also another component describing the change in environmental pressure.
A validation experiment was conducted with a freely swimming robot. The robot fish was placed in the flow tunnel and its downstream position was kept constant using a proportional, integral, derivative (PID) controller with the feedback from the overhead camera, while the speed of the flow was gradually changed. The controller changed the amplitude of the tail to match the velocity of the robot with that of the flow. The pressure data were recorded and the estimated flow speed was calculated using equations (3.1) and (3.2). The results are shown in figure 6. It can be seen that by using the estimation (3.2) (the average pressure on the sides) the water flow can be estimated with a rather high precision, whereas the estimation from (3.1) is noisy and deemed not to provide high enough precision to be used for downstream position control.
Another set of experiments was conducted to establish the relationship between the flow speed estimation and the orientation angle of the robot. This is important to see whether the estimation also holds when the robot is not directly aligned with the flow. The robot was fixed to the motor using a stiff rod, while the angle of the motor was changed by the control software. The experiments were carried out with a constant flow speed of 15 cm s−1. The maximum orientation angle with respect to the flow direction was ±45°. The pressure readings were recorded and the flow speed estimations were calculated. The results are presented in figure 7, where figure 7a shows the speed estimation and figure 7b shows the corresponding robot’s orientation. As we can see, equation (3.2) estimates the flow speed with a high precision even if the robot is not oriented towards the flow. There is only a slight increase in error when the angle gets larger. We can also see that equation (3.1) cannot accurately estimate the flow speed unless the robot is facing directly upstream.
The high noise of the estimation (3.1) with a moving robot and the high angle dependability comes from the fact that the stagnation point moves away from the robots nose when it turns or when its head oscillates. The usage of this relation for robot control is therefore limited to a static robot facing the flow or could be applied with highly distributed lateral line that is able to detect the moving stagnation point. Otherwise the method is very versatile as it does not depend on the depth of the robot or other parameters affecting the environmental pressure.
The estimation (3.2), on the other hand, depends on the environmental pressure and has to be calibrated for every specific environment. However, it is much less orientation-dependent as the pressure drop on the one side of the robot is compensated by the increase in the other side. Also the signal-to-noise ratio of that method is better as the average value of four sensors can be used.
(b) Flow direction detection
When the robot is not directly heading against the flow, the pressure on the side turned towards the flow will be higher. To find the relation between the pressure readings and the robot’s orientation, we placed the robot in a steady flow, changed the angle of the robot and recorded the pressure data. The experiment was repeated with three different flow speeds. The anterior sensor pair (S2 and S4) and the posterior sensor pair (S1 and S5) were analysed separately. The correlations are shown in figure 8. We can see that there is a linear relationship between the pressure difference and the robot’s orientation. The slope of the trend increases with the increasing flow speed and is larger for the anterior sensor pair.
Using these relations, we can measure the angle of the robot for the given flow speed and robot geometry. For every different situation, the relation has to be recalibrated. However, if the aim is to orient the robot towards the flow, the exact relation is not necessary as the controller can work only by equalizing the pressure on both sides.
(c) Actuation characterization
The robotic fish was characterized by measuring the swimming velocity at different actuation parameters. The velocity can be varied by changing the amplitude or the frequency of the robot’s tail. We have identified that our fish robot is most efficient at the tail-beat frequency of 2 Hz, therefore we fixed the frequency and only found the relation between the robot’s forward speed and the actuation amplitude. We placed the robot into the flow tunnel and actuated it with the 2 Hz frequency, while the flow speed was changed and the amplitude was controlled by a PID controller using the position feedback from the camera to keep the robot’s downstream position constant. This gave us the amplitude required to make the robot swim at the desired flow speed and actuation frequency. The results show a linear relationship (R2=0.9885) between the swimming velocity and the actuation amplitude, making it a reliable control output. The relationship between the velocity and amplitude are described by 3.3
We implemented a controller for station holding in a steady flow consisting of two parts: the speed controller and the orientation controller (figure 1).
(i) Speed control
The speed controller matches the velocity of the robot to the velocity of the flow U=V . This can be achieved by substituting the estimated velocity V from equation (3.2) into equation (3.3) and finding the actuation amplitude A 3.4To test the performance of our method for station holding, the freely swimming robot was controlled in flow while the flow speed was gradually changed. The initial flow speed was 11 cm s−1 and it was increased after every 30 s by 1 up to 19 cm s−1. The results are shown in figure 9. From the graph, we can see that when the flow was started, the robot overestimated the flow speed and started quickly drifting forward. However, shortly after that the position of the robot became very stable. When the flow was increased further, the robot started slowly drifting backwards owing to small underestimation of the flow speed. This is characteristic to the odometry-based robot localization where the error is integrated over time. In general, the downstream position was very stable. The maximum error over 270 s was about 400 mm (four of five body lengths) and the downstream drift in the end of the experiment was 100 mm (one of five body lengths).
The aim of the orientation control is to control the heading of the robot with respect to the flow. The flow direction estimations presented in §3b can be used as an input to the controller. The output will be the offset of the tail’s motor. To test the principle and the robustness of the method, we used a simple proportional control 3.5where θs is the desired orientation angle; θe the estimated orientation angle and Kp the proportional gain. We experimentally identified the controller gain for 15 cm s−1 flow and tested the controller in the flow tunnel with a desired orientation angle of 0°. Using different angles is problematic in our set-up as the robot would swim quickly against the wall of the tunnel. The controller’s performance is demonstrated in figure 10. The graph shows a comparison between the controlled and the uncontrolled orientation angle. When the angle was not controlled, the robot started to oscillate between the walls of the flow tunnel. With a simple pressure-feedback sensor, however, the robot’s angle was very stable. The standard deviation of the angle of the uncontrolled robot was 11.3° while adding the simple controller reduced the standard deviation to 2.9°. The lateral deviation was reduced from 146.3 to 59.2 mm. The excursion from the set angle in the beginning of the dataset is caused by the disturbance when the flow was started. We can see that the controller was able to quickly recover from the disturbance and stabilize the angle.
4. Station holding in the Kármán street
(a) Kármán vortex street detection
From the previous experiments with static pressure sensor arrays, two approaches have been proposed for the KVS detection: frequency spectrum analysis and turbulence intensity analysis . We conducted an experiment with a swimming fish robot in the KVS behind the cylinder to study the feasibility of those approaches for real-time control. The distance from the cylinder was 30 cm and the translational movement was restricted by fixing the floater with a magnet. The robot was actuated and the pressure data were logged. A comparative experiment was conducted in steady flow.
A fast Fourier transform of the recorded data was computed to see whether it is possible to detect dominant frequencies from the frequency spectrum. It was discovered that peak frequencies are present in pressure sensor readings at 2 Hz (actuation frequency) and at 0.4 Hz (vortex shedding frequency), but the minimum time window of the fast Fourier transform was about 30–50 s. This window is obviously too long and not suitable for real-time control.
Another method for KVS detection in  analysed the turbulence intensity using the standard deviation of the pressure readings. We compared the standard deviation over different timeframes and detected a 10 per cent average increase in the standard deviation when the robot was in KVS. However, to get a stable difference, a long timeframe (more than 30 s) was needed. When the deviation was calculated from shorter time series, the KVS detection was not reliable enough.
As the proposed methods for KVS detection did not meet the requirements of a real-time application, we developed an alternative approach to KVS detection by measuring the absolute pressure and identifying the reduced flow area behind the object. To test the usability of such an approach, we conducted an experiment, where the tail’s offset was controlled manually inside and outside KVS. The tail-beat amplitude was controlled automatically using a camera-feedback control to keep the distance from the cylinder constant at 50 cm. The results of the experiment are shown in figure 11. Figure 11a shows the lateral position of the robot with respect to the KVS midline while figure 11b presents the corresponding pressure at the tip of the nose. The red line on the lateral position graph is the outer limit (6.8 cm from the midline) of the KVS identified from the DPIV data. It can be seen that the pressure data correlates very well with the presence of the vortex street. We manually determined a pressure threshold for KVS identification. From figure 11c, it can be seen that the estimation matches with the actual presence of the KVS.
(b) Downstream distance estimation
To implement the station-holding controller in the KVS, the robot needs to have an estimate of its distance from the cylinder. To find the correlation between the pressure on the head of the robot and the distance, the robot was placed in KVS at the incoming flow speed 15 cm s−1. The robots downstream position was varied by manipulating it with a magnet through the upper glass wall of the flow tunnel and the pressure data were recorded at various distances. From the results (figure 12), we see that when approaching the cylinder, the average pressure on the sides of the robot is slightly decreasing owing to the lower flow speed behind the cylinder. Another trend is the pressure drop at the tip of the nose when going closer to the cylinder, which is also an expected result because the static pressure behind the cylinder is lower compared with the areas outside the KVS. By combining these two trends, we get a good estimation about the distance from the cylinder: 4.1where Dxe is estimated distance from the cylinder; P3 pressure at the nose and Pavg average pressure on the sides. The constant C takes into account the reduced dynamic pressure at the nose resulting from the lateral oscillation of the head. It was identified by actuating the robot in still water and comparing the sensor signals with a steady robot and the actuated robot.
(c) Lateral position estimation
Another input for the controller is the estimation of the lateral position of the robot with respect to the cylinder or in other words the sideways deviation from the midline of the KVS. As it may be predicted, the sideways movement will cause the asymmetry in the pressure on the left- and on the right-hand sides of the robot owing to the reduced pressure behind the cylinder and increased flow speed when deviating from the midline. To identify this asymmetry, the robot was moved laterally in the KVS at the distance of 200 mm from the cylinder while the pressure data were recorded. The relationship between the lateral position and the pressure difference is presented in figure 13 and is described by the equation 4.2where Dye is the deviation from the midline of the KVS; Pl the average pressure on the left-hand side of the robot and Pr the average pressure on the right-hand side of the robot.
The station-holding controller for the KVS again consists of two parts: the downstream position control and the lateral control (figure 1).
(i) Downstream position control
The downstream position controller keeps the robot in the KVS at the desired distance from the cylinder, which is somewhere between the suction zone and the end of the street, by changing the actuation amplitude of the motor and therefore the forward velocity V of the robot. When the robot is aligned along the midline of the KVS, then there is an actuation amplitude A for every distance D from the cylinder that gives the robot’s velocity V equal to the water flow speed U at this point. This stable amplitude is dependent on two components: the water flow speed outside the KVS and the distance from the cylinder. The water flow speed defines the maximum amplitude required to make the robot hold station. When getting closer to the cylinder, the required amplitude gets smaller because of reduced flow behind the cylinder. It is implemented in the controller design by adding another component A2 to the tail-beat amplitude A1.
To find A2, we characterized two points in the KVS. The distance D1 was chosen at the border of the suction zone. This is the distance, where theoretically no actuation is needed to hold the robot at the same location (figure 4). The second point is the minimum distance D2 where the effect of KVS is becoming insignificant. When increasing the distance beyond this point, the stable amplitude is equal to the free-stream amplitude A1. We assumed the decrease in amplitude between these points to be linear giving the component A2 a form of 4.3where Dx is the distance from the cylinder. In the controller, Dx is equal to the distance estimation Dxe described by equation (4.1). Distances D1 and D2 were determined from DPIV images.
The third component of the actuation signal A3 is introduced to compensate for the up- or downstream drift of the robot. It consists of a proportional and an integral part. 4.4where Dxs is the setpoint; Kp and Ki are experimentally determined controller gains.
The final control law is therefore a combination of all the three described components: 4.5
(ii) Lateral control
The task of the lateral position controller is to keep the fish robot aligned along the midline of the cylinder. We use lateral position estimation described by equation (4.2) as a controller input and turn the robot towards the midline using a proportional control algorithm 4.6where φ is the tail actuation offset for turning the robot; Dys the set point for lateral position and Kp the experimentally determined proportional gain.
(e) Controller testing
(iii) Station holding behind a cylinder
A typical trajectory of a robotic fish holding station in the KVS can be seen in figure 14. We can see that the robot is holding its position during the whole 270 s long experiment. The standard deviation of the downstream position is 40.5 mm and that of the lateral position is 12.7 mm.
(iv) Station holding behind a cuboid
To test the robustness of our control, we repeated the experiment with a cuboid in the flow. The cuboid was placed in uniform flow as described in figure 4. Owing to its non-streamlined shape, it creates a less perfect KVS—the dominant frequency varies and the turbulence is less predictable.
We tested the control with the same controller parameters as behind the cylinder, but the robot was not able to keep a stable position. This is mainly because the area of the reduced flow behind the cuboid is different and more turbulent flow increases the drag. Therefore, we again characterized the environment by identifying D1 and D2. All the other controller parameters were kept the same.
The trajectory of the robot behind the cuboid is presented in figure 15. It can be seen that the robot is able to keep its position for the whole length of the test trial, 270 s. The standard deviation of the downstream position was 21.2 mm and that of the lateral position was 13.3 mm.
(f) Energy consumption in Kármán vortex street
During the experiments, we also monitored the total energy consumption by recording the current consumption of the motor. We compared the energy consumption in the steady flow and in KVS behind the cylinder and behind the cuboid (figure 16). The results show 7 per cent reduced energy consumption in the reduced flow region behind the cylinder and 17 per cent behind the cuboid. We assume that the better performance behind the cuboid is mainly caused by the well-defined suction zone behind the cylinder. The steeper pressure drop in the cylinder’s shadow made it too difficult to approach the suction zone without been sucked in.
The experiments described in this paper test the feasibility of flow-related control using an artificial lateral line. We designed simple proportional controllers and conducted a series of experiments.
The flow speed detection experiments showed that two different methods can be used for speed estimation. The first approach is finding the difference between the stagnation pressure and the static pressure. The second approach would be measuring only the average pressure drop on the sides of the robot. The first approach is applicable in every environment without the need for calibration. However, it gives reasonable results only with a static robot facing directly the flow. To use it in a more general situation, the measurements have to be combined with data about the fish orientation in flow. The second method needs to be calibrated for the specific environment, but is less angle-dependent. For a more general situation, the usage of these two estimations could be combined together with other sensors of the robot, for example, the inertial measurement unit.
For the moving platform, the pressure measurements provide the odometry reading estimating the robot’s relative position with respect to the flow with the accuracy less than one body length of the robot over a duration of 270 s with varying flow speeds. The downstream drift in the end of the experiment was one-fifth of the robot’s body length. It suggests that the method can provide an accurate enough odometry estimate to be used in case of the absent global reference. As such, it may propose a low cost alternative for the Doppler effect-based odometry [6,7] and for small underwater vehicles for which ADCP devices are too bulky.
We showed that the orientation with respect to the flow can be estimated using the pressure difference on the left- and the right-hand sides. To test if this estimate can be used for orientation control, a set of experiments has to be conducted at varying flow speeds and angle setpoints. The width limits of our test tank do not allow us to experiment with different desired orientation angles. Therefore, we tested the controller only with a robot oriented directly towards the flow, where the robot was able to keep a desired orientation. A variation of this experiment was previously reported in , where a simple Braitenberg controller was used to keep the robot facing upstream.
Furthermore, we implemented a controller for station holding in KVS as well as a method for discriminating KVS from uniform flow. Our results showed that periodic turbulence (KVS) can be detected by simply monitoring the pressure readings in the nose of the robot. As opposed to the spectral and turbulence analyses proposed in , this method works in real time owing to the very fast response and the very distinctive change in pressure readings at the nose when entering the KVS. If the change is caused solely by the changing speed of the uniform flow, then there will also be difference in the pressure on the sides of the robot, making the identification of those two different events possible. The negative side of our proposed method is that the robot has to be aware of the initial flow properties. It can only detect when the environment changes from one flow regimen to another, because we have manually adjusted the discrimination threshold. The threshold value is valid only for the specific object geometry and flow speed, but the method gives instantaneous feedback about the change of flow regimen. It could be combined with more advanced methods for identification and classification of flow regimens using, e.g. supervised learning or state vector machines. For example, visual data or obstacle detection sensor data could be used to adapt the threshold value for a specific situation.
When the robot has detected the presence of the KVS in the flow, it can switch controlling its position behind an object. The distance from the object as well as the deviation from the KVS midline can be estimated using pressure sensors. The robustness of the controller was tested by repeating the experiment under less perfect, and more natural, environmental conditions, in turbulence generated by a rectangular object. The performance of the robot was stable. However, this conclusion holds only when the properties of the specific KVS are known and the controller parameters are identified based on the specific flow conditions. In our case, we used DPIV imaging to detect the important parameters of the vortex street, but in reality the size of the object generating vortices, its shape and the flow speed can vary. More advanced control methods can be based upon those test results for detecting the parameters of the KVS and fine tuning, e.g. an adaptive controller.
In this paper, we demonstrated a flow-based control of an underwater vehicle using artificial lateral line pressure sensors. Various technological solutions have been proposed for implementing artificial lateral lines and their ability to detect hydrodynamic events have been tested, but their application for robot control has not been studied so far. We show that flow regimen identification and flow-related control can be achieved with a simple control architecture using the pressure distribution around the body of a moving robot. This approach for flow-based navigation could be used on any underwater vehicle but is especially valuable for small-scale underwater vehicles in turbulent flows.
We have shown that flow-related control can be achieved in various flow regimens using a simple linear control. Increased signal-to-noise ratio of the sensors and more sophisticated control would improve the performance and make it applicable in a greater variety of hydrodynamic environments. The main limitation of the present approach is the need of calibration for specific conditions. In different situation, the calibration is not valid, however in principle the relations will hold. This allows the use of pressure sensors without exact calibration, for example, when orienting towards the flow or aligning itself behind the object. Our lateral line could be combined with other sensing mechanisms to create adaptive control based on learning algorithms. The biomimetic approach could also be used here as fish have also no awareness of absolute pressures and exact relations.
Our experiments in KVS also showed that station holding behind the object resulted in the reduced energy consumption of the robot. This is consistent with the biological evidence of fish flow refuging , where fish are observed to exploit regions of reduced flow to save energy. In real world applications, the artificial lateral line can be used for detecting reduced flow and holding station in the hydrodynamic shadow similar to the fish refuging behaviour to reduce energy consumption of underwater vehicles. This would lead to increased autonomy and longer missions of the robots.
This work was supported in part by European Commission 7th Framework program under FP7-ICT-2007-3 STREP project FILOSE (Robotic FIsh LOcomotion and SEnsing) and Estonian Information Technology Foundation under Tiger University program.
- Received November 9, 2012.
- Accepted February 7, 2013.
- © 2013 The Author(s) Published by the Royal Society. All rights reserved.