The D-day is tomorrow, the day to defend my report, September 18th 2008 on 8 am.

Wish me luck …

Stanford computer scientists have developed an artificial intelligence system that enables robotic helicopters to teach themselves to fly difficult stunts by watching other helicopters perform the same maneuvers.

The result is an autonomous helicopter than can perform a complete airshow of complex tricks on its own.

The stunts are “by far the most difficult aerobatic maneuvers flown by any computer controlled helicopter,” said Andrew Ng, the professor directing the research of graduate students Pieter Abbeel, Adam Coates, Timothy Hunter and Morgan Quigley.

The dazzling airshow is an important demonstration of “apprenticeship learning,” in which robots learn by observing an expert, rather than by having software engineers peck away at their keyboards in an attempt to write instructions from scratch.

Stanford’s artificial intelligence system learned how to fly by “watching” the four-foot-long helicopters flown by expert radio control pilot Garett Oku. “Garett can pick up any helicopter, even ones he’s never seen, and go fly amazing aerobatics. So the question for us is always, why can’t computers do things like this?” Coates said.

Computers can, it turns out. On a recent morning in an empty field at the edge of campus, Abbeel and Coates sent up one of their helicopters to demonstrate autonomous flight. The aircraft, brightly painted Stanford red, is an off-the-shelf radio control helicopter, with instrumentation added by the researchers.

For five minutes, the chopper, on its own, ran through a dizzying series of stunts beyond the capabilities of a full-scale piloted helicopter and other autonomous remote control helicopters. The artificial-intelligence helicopter performed a smorgasbord of difficult maneuvers: traveling flips, rolls, loops with pirouettes, stall-turns with pirouettes, a knife-edge, an Immelmann, a slapper, an inverted tail slide and a hurricane, described as a “fast backward funnel.”

The pièce de résistance may have been the “tic toc,” in which the helicopter, while pointed straight up, hovers with a side-to-side motion as if it were the pendulum of an upside down clock.

“I think the range of maneuvers they can do is by far the largest” in the autonomous helicopter field, said Eric Feron, a Georgia Tech aeronautics and astronautics professor who worked on autonomous helicopters while at MIT. “But what’s more impressive is the technology that underlies this work. In a way, the machine teaches itself how to do this by watching an expert pilot fly. This is amazing.”

Writing software for robotic helicopters is a daunting task, in part because the craft itself, unlike an airplane, is inherently unstable. “The helicopter doesn’t want to fly. It always wants to just tip over and crash,” said Oku, the pilot.

To scientists, a helicopter in flight is an “unstable system” that comes unglued without constant input. Abbeel compares flying a helicopter to balancing a long pole in the palm of your hand: “If you don’t provide feedback, it will crash.”

Early on in their research, Abbeel and Coates attempted to write computer code that would specify the commands for the desired trajectory of a helicopter flying a specific maneuver. While this hand-coded approach succeeded with novice-level flips and rolls, it flopped with the complex tic-toc.”

It might seem that an autonomous helicopter could fly stunts by simply replaying the exact finger movements of an expert pilot using the joy sticks on the helicopter’s remote controller. That approach, however, is doomed to failure because of uncontrollable variables such as gusting winds.

When the Stanford researchers decided their autonomous helicopter should be capable of flying airshow stunts, they realized that even defining their goal was difficult. What’s the formal specification for “flying well?” The answer, it turned out, was that “flying well” is whatever an expert radio control pilot does at an airshow.

So the researchers had Oku and other pilots fly entire airshow routines while every movement of the helicopter was recorded. As Oku repeated a maneuver several times, the trajectory of the helicopter inevitably varied slightly with each flight. But the learning algorithms created by Ng’s team were able to discern the ideal trajectory the pilot was seeking. Thus the autonomous helicopter learned to fly the routine better—and more consistently—than Oku himself.

During a flight, some of the necessary instrumentation is mounted on the helicopter, some on the ground. Together, they continuously monitor the position, direction, orientation, velocity, acceleration and spin of the helicopter in several dimensions. A ground-based computer crunches the data, makes quick calculations and beams new flight directions to the helicopter via radio 20 times per second.

The helicopter carries accelerometers, gyroscopes and magnetometers, the latter of which use the Earth’s magnetic field to figure out which way the helicopter is pointed. The exact location of the craft is tracked either by a GPS receiver on the helicopter or by cameras on the ground. (With a larger helicopter, the entire navigation package could be airborne.)

There is interest in using autonomous helicopters to search for land mines in war-torn areas or to map out the hot spots of California wildfires in real time, allowing firefighters to quickly move toward or away from them. Firefighters now must often act on information that is several hours old, Abbeel said.

“In order for us to trust helicopters in these sort of mission-critical applications, it’s important that we have very robust, very reliable helicopter controllers that can fly maybe as well as the best human pilots in the world can,” Ng said. Stanford’s autonomous helicopters have taken a large step in that direction, he said.

By: Dan Strober, Stanford News

Traditional flight simulators try to emulate the real-world performance of an aircraft by using lookup tables to determine things such as lift or drag. These simulators do a good job of simulating the flight characteristics of the aircraft they were designed to simulate, but are not useful in design work, and do not predict the performance of aircraft when the actual figures are not available. X-Plane reads in the geometric shape of any aircraft and then figures out how that aircraft will fly. It does this by an engineering process called blade element theory, which involves breaking the aircraft down into many small elements and then finding the forces on each little element many times per second. These forces are then converted into accelerations which are then integrated to velocities and positions. A wing, for example, may be made up of many sections (1 to 4 is typical), and each section is further divided into as many as 10 separate sections, then the lift and drag of each section is calculated, and the resulting effect is applied to the whole aircraft. When this process is applied to each component, the simulated aircraft will fly virtually like its real counterpart does. This approach allows users to design aircraft on their computer quickly and easily, as the simulator engine will show immediately how an aircraft with a particular design might perform in the real world.

X-Plane goes through the following steps to propagate the flight:

1: Element Break-Down

Done only once during initialization, X-Plane breaks the wing(s), horizontal stabilizer, vertical stabilizer(s), and propeller(s) (if equipped) down into a finite number of elements. The number of elements is decided by the user in Plane-Maker. Ten elements per side per wing or stabilizer is the maximum, and studies have shown that this provides roll rates and accelerations that are very close to the values that would be found with a much larger number of elements.

2: Velocity Determination
This is done twice per cycle. The aircraft linear and angular velocities, along with the longitudinal, lateral, and vertical arms of each element are considered to find the velocity vector of each element. Downwash, propwash, and induced angle of attack from lift-augmentation devices are all considered when finding the velocity vector of each element.
Propwash is found by looking at the area of each propeller disk, and the thrust of each propeller. Using local air density, X-Plane determines the propwash required for momentum to be conserved.
Downwash is found by looking at the aspect ratio, taper ratio, and sweep of the wing, and the horizontal and vertical distance of the “washed surface” (normally the horizontal stabilizer) from the “washing surface” (normally the wing), and then going to an empirical look-up table to get the degrees of downwash generated per coefficient of lift.

3: Coefficient Determination
The airfoil data entered in Part-Maker is 2-dimensional, so X-Plane applies finite wing lift-slope reduction, finite-wing CLmax reduction, finite-wing induced drag, and finite-wing moment reduction appropriate to the aspect ratio, taper ratio, and sweep of the wing, horizontal stabilizer, vertical stabilizer, or propeller blade in question. Compressible flow effects are considered using Prandtl-Glauert, but transonic effects are not simulated other than an empirical mach-divergent drag increase. In supersonic flight, the airfoil is considered to be a diamond shape with the appropriate thickness ratio. Pressures behind the shock waves are found on each of the plates in the diamond-shaped airfoil and summed to give the total pressures on the foil element.

4: Force Build-Up
Using the coefficients just determined in step 3, areas determined during step 1, and dynamic pressures (determined separately for each element based on aircraft speed, altitude, temperature, propwash and wing sweep), the forces are found and summed for the entire aircraft. Forces are then divided by the aircraft mass for linear accelerations, and moments of inertia for angular accelerations.

5: Get Back to Work
Go back to step 2 and do the whole thing over again at least 15 times per second.

Blade element theory does have its shortcomings, as it can sometimes be difficult to design an aircraft that performs precisely like the real-world aircraft. However, as the flight model is refined, the simulator can better resemble real-world performance (as well as the aircraft’s quirks and design flaws.)

X-Plane is capable of modeling fairly complex aircraft designs, including helicopters, rockets, rotor craft and tilt-rotor craft. Famous real world aircraft modeled in X-Plane include the V-22 Osprey, the Harrier Jump Jet, the NASA Space Shuttle, and Scaled Composites SpaceShipOne.

Through the plugin interface, users can create external modules that extend the X-Plane interface, flight model, or create new features. One such feature is the Xsquawkbox plugin, which allows X-Plane users to fly on a worldwide shared simulation network. Other work has been done in the area of improving X-Plane’s flight model and even replacing entire facets of X-Plane’s operation. X-Plane is also capable of communicating with other applications via UDP. Through a relatively simple interface, third party developers can control the simulator and extract data regarding the simulation state.

The maps and scenery are also fully editable. While no tool is provided to edit the 3D mesh objects, there are tutorials for using the third party 3D modeler AC3D. Once built, editing landscape elevation and 3D object placement is easily accomplished with the scenery editor. In fact, much of the world’s detail, including detail in airports, such as ramps, buildings, and taxiways, is provided by the end-users.

Map imagery and aircraft paint can be created and modified with any paint program capable of manipulating PNG images. Additionally, Laminar Research has released a 7 DVD “Global Scenery Package” containing imagery of a much higher quality than the default information. This package covers close to 85% of the Earth’s surface. The release of X-Plane 9, in January 2008, has introduced much improved areas of high ground relief (in particular, mountains) and a plethora of other improvements.

Taken and edited from: X-Plane and Wikipedia

First, I tried to send a constant number (double type) from computer to AVR. Inside the microcontroller (uC), there is a program that will multiply the input with a gain (in this case the gain is 5). After being multiplied, the result is being send back to the computer. It worked, both of the results were same.

Then I added a transfer function block (in this case, 1/(s² + 2s + 1) ) and a step signal for the reference input. This experiment also worked, the direct simulation and HIL simulation showed same result. The problem occured when I added a negative feedback to the system. The results between HIL simulation and direct simulation were not same. Picture below is the result. The output signal using HIL simulation (yellow) doesn’t match with using direct simulation (red).

I tried to post this problem on Avrfreaks Forum and someone named ‘buffi‘ gives me advices about his problem. Below is some of his advices:

The following happens: During the short period when e > 0.5, simulink sends 1 to the controller. This shows up in the terminal as 1′s being sent from the beginning of the step input to about 0.6 seconds after the rise. After that, the error is < 0.5 and zeros are sent to the controller. Negative errors are sent as zero. The plant will (in your case) now receive zeros from the controller: 0 * 5 = 0. The plant output goes down to zero, but when it crosses the 0.5 line, the error is greater than 0.5 again, so the controller receives a 1 and outputs 5 to the plant again. This causes your plant output to oscillate. You can do several things now. First, rescale the output from simulink to your controller by k and from the controller to simulink by 1/k, k > 0 to get a higher resolution than just 0 and 1. Second, use 32-bit float in “To Instrument” and figure out how to store it for your C code.

Thanks for the advices. Trying to implemented them now.

We should learn and discipline ourself to finish something that we started. If the situation is getting harder, it means that we are on the right track on forming our “S-curve”. It should be harder and it will be harder than ever. What we need is to keep struggling in a such way that we may be victorious. At the end, we will stand still, facing the world and say that we have give our best to finish it.

Struggling to finish this project. Aiming for October, here we go.

Begeistert!

Aiming for June …

• the flight data : don’t detrend (cruise data —detrend—> hover data ) it, use the proper data for each flight condition, use data in its trim condition
• coupled effect of the model structure
• the model’s initial value list given

Assignment:

• Identification using the uncoupled model and the model proposed by Mettler’s
• Identification in cruise and hover condition
• Try to identify using Shim’s procedure

Deadline: Monday, January 7th 2008

ps: CENTRUM = Center for Unmanned System Studies

The state space structure of this project is given bellow. This model is proposed by Budiyono in his paper.

The ARX model is the simplest model incorporating the stimulus signal. The estimation of the ARX model is the most efficient of the polynomial estimation methods because it is the result of solving linear regression equations in analytic form. Moreover, the solution is unique. In other words, the solution always satisfies the global minimum of the loss function. The ARX model therefore is preferable, especially when the model order is high.

The disadvantage of the ARX model is that disturbances are part of the system dynamics. The transfer function of the deterministic part G(q–1, è) of the system and the transfer function of the stochastic part H(q–1, è) of the system have the same set of poles. This coupling can be unrealistic. The system dynamics and stochastic dynamics of the system do not share the same set of poles all the time. However, you can reduce this disadvantage if you have a good signal-to-noise ratio.

When the disturbance e(n) of the system is not white noise, the coupling between the deterministic and stochastic dynamics can bias the estimation of the ARX model. Set the model order higher than the actual model order to minimize the equation error, especially when the signal-to-noise ratio is low. However, increasing the model order can change some dynamic characteristics of the model, such as the stability of the model.

The ARMAX model structure includes disturbance dynamics. ARMAX models are useful when you have dominating disturbances that enter early in the process, such as at the input. For example, a wind gust affecting an aircraft is a dominating disturbance early in the process. The ARMAX model has more flexibility in the handling of disturbance modeling than the ARX model.

The Box-Jenkins (BJ) structure provides a complete model with disturbance properties modeled separately from system dynamics.The Box-Jenkins model is useful when you have disturbances that enter late in the process. For example, measurement noise on the output is a disturbance late in the process.

The previous classical parametric system identification methods minimize a performance function which is based on the sum of squared errors. These methods work well in many cases. However, for complex systems characterized by being of high order i.e. having many parameters, with several inputs and outputs, and having a large number of measurements, the classical methods can suffer from several problems. They can experience many local minima in the performance function and thereby a lack of convergence to global minima. The user will need to specify complicated parameterization of system orders and delays. They also may suffer potential problems with numerical instability and excessive computation time to execute the iterative numerical minimization methods needed. In addition, modern control methods require a state-space model of the system. For cases such as these the State-Space (SS) identification method is the appropriate model structure.n general, the state-space model provides a more complete representation of the system, especially for MIMO systems, than polynomial models because state-space models are similar to first principle models. The identification procedure does not involve nonlinear optimization so the estimation reaches a solution regardless of the initial guess. Moreover, the parameter settings for the state-space model are simpler. You need to select only the order, or the number of states, of the model. The order can come from prior knowledge of the system. You also can determine the order by analyzing the singular values of the information matrix.

When the model order is high, use an ARX model because the algorithm involved in ARX model estimation is fast and efficient when the number of data points is very large. The state-space model estimation with a large number of data points is slow and requires a large amount of memory. If you must use a state-space model, for example in modern control methods, reduce the sampling rate of the signal in case the sampling rate is unnecessarily high.

The other polynomial models, including the ARMAX, output-error, Box-Jenkins, and general-linear models, involve iterative, nonlinear optimization in the identification procedure. They require excessive computation time, and the minimization can get stuck at a false local minimum, especially when the order is high and the signal-to-noise ratio is low. However, you can use these models when the stochastic dynamics are important because they provide more flexibility for the stochastic dynamics.