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Project Objective
Identify the aerial disturbances and gather data
Build model of the disturbances
Integrate the model in the FMA simulator
Feedforward model in the controller
Validate the model and the proposed strategies
3. ||
Thrust Efficiency (e.g. Ground Effect)
Drag-like Forces (e.g. Vertical Flight)
External Forces (e.g. Disturbance from Wake)
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Overview - General Disturbance Model
Control Strategy: Feedforward the identified model into thrust calculation
Objective of Control Strategy: Improve tracking performance
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Vertical Flight Drag Model
Vz (m/s)
CommandedThrust(m/s^2)
Vertical Flight Model
Dynamic Equation:Vz
ascentdescent
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Vertical Flight Compensator Results
Implement the compensator with random
trajectories
Improvement in tracking accuracy when Vz>0 ,
but not when Vz <0
Enters vortex ring state/turbulence wake state
when 2Vi<Vz<0 -- unable to model
Vi : induced downwash velocity at hoverVz (m/s)
Zerror(m)
2Vi< Vz < 0
Vz>0
ascentdescent
9. ||
Size of region influenced by wake of a
quadrocopter
Force and moment induced on a
quadrocopter inside wake region
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The Wake of a Quadrocopter
?
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Quadrocopter Wake Measurement
Distancebelowaquadrocopter(m)
Measured Thrust Required to Hover (m/s^2)
Distance away from a quadrocopter (m)
4m
2m
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Quadrocopter Wake Downwash
Downwash Velocity vi Calculated (m/s)
Distancebelowaquadrocopter(m)
Measured Thrust Required to Hover (m/s^2)
Distance away from a quadrocopter (m)
Use Vertical
Ascent Model
Distancebelowaquadrocopter(m)
Distance away from a quadrocopter (m)
!
Theoretical
Value
vi =4m/s
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Quadrocopter Wake Downwash Model
Downwash Velocity vi Model
(m/s)Downwash Velocity vi Calculated (m/s)
Distancebelowaquadrocopter(m)
Distance away from a quadrocopter (m)
Distancebelowaquadrocopter(m)
Distance away from a quadrocopter (m)
Divided into
3 sections
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Quadrocopter Wake Downwash Model
Downwash Core (0m- 0.2m) – Strong radius mixing, uniform velocity distribution in radius
Downwash Decay Layer (0.2m-0.5m) – energy dissipates into vertices, velocity decays linearly with radius
1 2 3
1
2
3 Wake Turbulence Region (0m -1m) – vertices energy dissipates, flow is turbulent with no clear direction
Downwash Velocity vi Model
(m/s)
Distancebelowaquadrocopter(m)
Distance away from a quadrocopter (m)
Proposed Physical
Explanation
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Quadrocopter Wake Model in Simulator
Initialize new
wake element
1/2
• pos, att same as parent vehicle
• downwash vi T
• H = vi * t
• pos moves vi*t
• vi decays exponentially with time
• if vi<vi_min, element deleted
• H= vi*t
Wake dynamics
Impact on other
vehicles
•if vehicle inside
•force on vehicle from vertical
ascent model using vi
• apply a random moment
every t sec
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Ground effect model - improves tracking
performance without integral control near
ground
Vertical ascent model - improves the
position tracking performance
Wake model - simulates the influence on a
vehicle by other vehicles in the vicinity
Angle of attack/attitude as parameter
Disturbance on each propeller separately
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Summary Future Work
20. ||
Ground effect measurement from multi-vehicle
Translation Flight Drag Coefficient
Wake model Turbulence
Wake model Dynamic Flight validation
Wake model raw data 2D
Wake Simulation Validation
Propeller Downwash Velocity
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Back up slides
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Ground Effect Measurement from three vehicles
Distance from vehicle bottom to ground surface (m)
Thrustrequiredtohover(N)
Hello everybody, welcome to my presentation, my name is Autumn, I’m working on my master thesis here with Federico. Today I’d like to present some interesting results of aerial disturbances on our beloved quadrocopter.
I started the project by identifying the situations where aerial disturbances is present and do experiments to gather data. With the data and some background physical knowledge, I try to come up with a model of the effect. Then I implement the model in the simulator as well as feed forward it to the controller, in order to improve the tracking performance in random trajectories.
From literature, the disturbances on quadrocopter can be grouped into three categories: disturbance by changing thrust efficiency, disturbance from drag-like forces induced by airspeed, and disturbance from external environment.
Then the standard equation of motion is modified by the presence of the disturbance. In this presentation, I will talk about one example in each category: i.e. the ground effect, the vertical flight and the disturbance from wake.
Once the disturbance model is identified, the corresponding control strategy would be feedforwarding the information of the model into the calculation of thrust to command. Since the control strategy is very simple here, I won’t talk much about it, but focus more on the disturbance models.
So first lets look at ground effect. As shown in the graph, the presence of the ground will alter the course of the downwash, and changethe pressure field on the prop, and therefore cause the thrust efficiency increase.
In literature, the ground effect on helicopters is usually modelled by the cheeseman’s theory, where, T is the thrust would be produced in ground effect , and T inf is the thrust would be produced far from ground. The magnitude of the effect depends on the radius of the propeller and the distance from ground, and the effect decays quadratically when moving away from ground.
To identify how ground affects our quadrocopter, I commanded the vehicle to hover at various height. Since the vehicle is hovering, the actual mass normalize thrust should be 9.8m/s2. However, as we can clearly observe, the commanded thrust decreases when getting closer to the ground, down to 7.5m/s2 when touching down.
So if we divide 9.8 by the commanded thrust, we will end up with the thrust efficiiency. Which are shown in red circles and agrees with Cheeseman’s theory.
I fit the experiment data into a rational function which Cheeseman’s equation can be also cast into the same form. Then this equation will describe the model of ground effect for our vehicles.
Then by feeding this model into the controller, the desired commanded thrust can be calculated as the required thrust divided by thrust efficiency. As a result, the tracking performance in z direction near ground is improved, it’s possible to do smooth touch down without integral controller.
Now let’s look at the vertical flight, where I conducted a set of the experiments where the vehicle flying up and down with constant velocities and recorded the commanded thrust as shown in the figure. There is a clear corelation between the thrust and vertical velocity. Then I build a piece wise linear model from the data.
Then we integrate the model information into the controller as a compensator. We test this compensator by flying a vehicle along random trajectories. The result z position error from the standard controller and the compensator are plotted against the vertical velocity. As we can observe, with the compensator, the tracking error is reduced when the vehicle is going up, but no improvement is observed during descending. So why is that? From literature, helicopters enter a state with lots of reverse flow and turbulence when it’s descending slowly. So slow? Slower than 2 times the induced downwash velocity at hover, which is the air velocity right below the propeller when the vehicle hovering. In our case, it is about 4m/s. With these unsteady flow, we are unable to model the real behavior of the vehicle in the descending case. However, we will make use of the vertical ascent model to derive the wake model.
So what is the wake/downwash of a quadrocopter? I define it as a spatial region below a flying quadrocopter, where the air velocity is altered as the result of the thrust producing mechanism. I think most of you already have a very good idea that roughly, the wake consists of a downward flow along with turbulence. In FMA, we fly multiple vehicles within a relatively constrained space, the vehicles will influence each other’s path through the wakes. In order to quantity this phenomena, I want build a model of the wake, and identify the size of the region, and how much force and moment will be induced on a quadrocopter.
So again, we start with a simple experiment. I have one vehicle hovering at 5m height, and another vehicle hover at different locations below that vehicle. And I recorded the commanded thrust on the lower vehicle as shown in this contour plot. As we can observe, there is a clear influence at this spatial region.
Then I made an assumption that the influence on the vehicle is through a downward flow in the wake.
As in, there is air flowing downward that hitting on the vehicle, which is the same as the vehicle flying up in still air.
Thus, I used the previously derived vertical ascent model to calculate the downwash velocity in the wake.
Which is about 4m/s right below the parent vehicle and decays to almost zero 4m below. Notice that this number agrees with our previously calculated theoretical value for induce velocity.
By observing the data, I decided to divide the area into 3 sections and fit a piece wise linear model to represent the downwash velocity profile in the wake.
Here I want to propose some possible physical explanations to the 3 sections.
The downwash velocity vi stays constant in the radius direction in the inner core, which is about 20cm in radius. I think it is due to the fact we have four props, and there are four streams of downwash coming down in counter acting spirals, and this results in very fast momentum exchange, so the downward velocity remains almost constant in the radius direction.
If we move outward, it’s a layer which I call the downwash decay layer, about 30cm thick. the downward velocity decays linearly with radius. This is because air in this layer is decelerated by the ambient still air, The downward velocity is reduced due to this friction, and the energy is converted to vortices and turbulence gradually.
And outside this layer, there is another layer I call the wake turbulence region, where is the vortices generate from decay layer, drifts and dissipates in space .
Now let’s see how the model is implemented into the FMA simulator. The wake is discretized into wake elements. Each wake elements is a cylinder with three layers, and it is defined by states such as position, attitude, height and downwash velocity vi. As we can see here, this pattern of wake elements represents a typical wake evolution in time and in space when the vehicle is flying.
Every t seconds, every flying vehicle will generates a new wake element. The position and attitude of the element is initialized the same as the parent vehicle. vi is proportional to the square root of the parent vehicle thrust. The height of the cynlinder is the vi times t.
Then all the existing wakes will be updated by the wake dynamics, where the wake element moves in space by vi times t, the vi decays exponentially with time, if vi is smaller than a certain threshold, the wake element is deleted.
And then for every wake element, we check if there is a vehicle inside it. If so, a force is apply onto the vehicle by the vertical ascent model and a random moment is also applied to simulate the random turbulence.
To validate our model, I fly three vehicles very close to each other with some random trajectories.
The x,y, z position, as well as the z position deviation from the desire value are shown in this figure.
We can see there are sometimes dips in the z position deviation. These are caused by the wake, for example, if we look into the situation in the light blue box, the red and blue vehicles are quite close in x and y position and red one is about 2m above the blue one, thus we can imagine the blue vehicle is pushed down by the red vehicle’s downwash. Thus this downwards deviation.
I run this test in the FMA ,in the standard simulator and in the wake simulator. The resulting z position deviations from all three cases are shown in the three figures. The z deviation from standard simulation doesn’t match the result from reality in turns of wake effect, but the wake simulation successfully predict the dips in the z deviation.
Simulator error are from other source,
To see it more clearly, Here we compare the z deviations from the real flight in black, and from the standard simulator in green and the wake simulator in red on the same figure for each vehicle.
As we can see, both the trend and magnitude from the wake simulator and the real flight matches quite well.
With that I would like to conclude my presentation with a short summary. We discussed three aerial disturbance models. The ground effect model and the vertical ascent model, which are used to improve tracking performance. And the wake model, which predicts the influence of multi-vehicles on each other.
Some suggested future work will be including the angle of attach as a parameter in disturbance modeling, and maybe consider the effects on each propeller separately.
Thank you all for coming. And I will be answering your questions now.
Computational time… think about that dt, number of vehicles quadratically
With the model implemented in the simulator, I’m able to validate it by conducting the previous experiment in simulation. The result thrust contour from the model simulation and from the flight test are compared in these two figures.
To remove
