See the September report for the previous update.
Rotors have been designed for the 150g vehicle. The design process utilized the experimentally tested Wes-Technik 10" diameter prop as an initial starting point. Based on a geometry survey of the Wes-Technik propeller, a NACA 7402 is used for the new rotor. This is not the exact camberline of the test article but matches the maximum camber and maximum thickness distributions. The diameter was fixed at 10" since the Wes-Technik prop exhibited sufficient thrust at this diameter. The final planform is displayed below.
The design process for this rotor was modified in several ways from previous work. The operating range of the very low Re airfoils used in smaller rotors had been constrained to low lift coefficients and an approximately linear range of operation in terms of lift curve slope. The design code used this linear assumption in determining the angle of attack and thereby the incidence of an individual blade element. While these smaller rotors operated almost exclusively below Re 6000, the 10" rotor operates predominantly in the Re 20,000 to Re 30,000 range at lift coefficients approaching 1.0. Under these conditions, the non-linearity of the lift curve slope introduces a significant error in the final incidence distribution across the blade when the linear assumption is used. This has been remedied by adding angle of attack information to the 2-D airfoil performance interpolation.
The motor performance values used in the optimization process have been constant voltage curves of output power vs. RPM. Manufacturer's data is often limited to operation at only one or two different voltage levels and experimental determination across a wide range of voltages is costly in terms of time. A single voltage was selected to be close to the expected design point, but for a given rotor, varying RPM is equivalent to varying motor voltage. This model is only truly correct at the one point where the RPM vs. voltage curve crosses the rated motor voltage. For a given rotor, this has the effect of under predicting the power available at higher voltages and over predicting the power available at lower voltages. For this design, motor performance over a wider range of voltages was approximated by correlating results of the rotor analysis code with experimental results for the Wes-Technik propeller and the Firefly motor. This power curve is also not really generalizable since it is a function of the specific rotor, but it correctly captures the trends in power available vs. RPM for a fixed rotor geometry. For designs not radically different from the Wes-Technik this represents a reasonable engineering approximation.
The predicted thrust for the resulting design is provided below. The thrust performance is seen to be close to, but slightly inferior to the experimental results for the Wes-Technik rotor. The design method de-rates the maximum sectional lift coefficient to provide some margin for error in the models and manufacturing. With this restriction, the optimal design comes up slightly short of the Wes-Technik product in thrust produced, but there may be an advantage in power required due to higher sectional lift to drag ratios.
Initial results from the OVERFLOW-D analysis of the 4-blade, 2.5 cm diameter rotor indicate the presence of unsteady separated flow over the inboard 30% to 40% of each blade. This is clearly visible in the pressure colormap shown below, red representing the locations of highest pressure and blue the lowest. The outer half of the blade appears well behaved, but the current computational results can only be taken as qualitatively correct. The analysis assumed a steady-state flow field in the rotor frame of reference; the presence of substantial unsteady separation violates this and prevented the convergence of the analysis. Several causes for this interior separation are being explored. The design may simply be incorrect, either due to shortcomings in the model resulting in over predicted inflow in the interior, or due to inaccuracies in the determination of the blade incidence. The second issue can be addressed by implementing the modified analysis code incorporating airfoil angle of attack data. It is also possible that the problem lies with the starting method of the computational analysis. The incidences of the inboard stations are in the range of 20 to 25 degrees. These large angles assume an established inflow velocity field. Computationally ?starting? the rotor in still air may stall these sections to such an extent that the necessary inflow conditions are never attained. Currently, we are examining the data sets from this initial calculation to determine at least qualitatively the nature of the inflow distribution and, at the outer extents of the blades, if the 2-D viscous solutions are representative of the 3D sectional behavior.
More efforts were made this month to fabricate aluminum rotors in an effort to reduce deformations. Gluing the first machined surface to the mold was proved to be unsatisfactory. A better approach is to make the mold as a vacuum chuck. The rotor can be held tightly and completely by vacuum. The mold making process became more complicated. A plateau was first machined from the backside of the mold, sealed carefully, and connected to a vacuum pump. On the top surface of the mold, holes and grooves were distributed evenly over the blades to ensure the sufficient vacuum. The rotors were manufactured successfully through this vacuum approach. The lift test was performed and the aluminum rotor was sent out for laser scanning to verify the geometry.
From the laser scanning results, similar analyses of incidence distributions along radial direction were conducted and compared with epoxy rotors in the following plots. The incidences of each blade and the designed model are illustrated in the same plot.
The deviation from the designed incidence is much smaller in the aluminum rotor than in the epoxy rotor. Apparently, the aluminum rotor is stiffer to retain the geometry than the epoxy rotor is. Since the aluminum rotor is closer to the designed geometry, we expected to obtain better performance if the geometry variation influenced the performance significantly. However, the lift test results of aluminum rotor shown in the following table demonstrate little improvements in lift, frequency, and input power.
| Voltage (V) | Current (A) | RPM | Lift (g) | Input Power (W) | |
| Aluminum Rotor | 6.0 | 0.12 | 24000 | 0.831 | 0.720 |
| 7.0 | 0.14 | 28000 | 1.147 | 0.980 | |
| 8.0 | 0.16 | 32000 | 1.620 | 1.280 | |
| 9.0 | 0.19 | 34000 | 1.994 | 1.710 | |
| 10.0 | 0.21 | 40000 | 2.492 | 2.100 | |
| 11.0 | 0.23 | 44000 | 3.007 | 2.530 | |
| 12.1 | 0.25 | 48000 | 3.489 | 3.025 | |
| 13.1 | 0.28 | 50000 | 4.071 | 3.668 | |
| 14.0 | 0.30 | 52000 | 4.486 | 4.200 | |
| Epoxy Rotor | 6.1 | 0.12 | 25500 | 0.864 | 0.732 |
| 7.1 | 0.14 | 29625 | 1.235 | 0.994 | |
| 7.6 | 0.15 | 31875 | 1.440 | 1.140 | |
| 8.8 | 0.17 | 35625 | 1.975 | 1.496 | |
| 9.8 | 0.19 | 38250 | 2.387 | 1.862 | |
| 10.6 | 0.21 | 39750 | 2.716 | 2.226 | |
| 11.6 | 0.23 | 41700 | 3.127 | 2.668 | |
| 12.7 | 0.25 | 44250 | 3.539 | 3.175 |
A prototype circuit, consisting of a gyro, filters and PIC microcontroller, was successfully implemented. The microcontroller periodically sampled the filtered gyro signal and converted it into digital value. The digital value was then periodically sent to one of the output ports of the microcontroller. LED connected to the output port helped visualize the gyro signal. This proved the concept of the gyro measurement and the circuit will be integrated into existing mesicopter electronics.
Continuing efforts were made to design a control law for the mesicopter. For a first cut, it was assumed that only the angular rate is available to feedback using off-the-shelf MEMS rate gyros. Feedback gains were chosen using an LQR design, and an integrator was added to estimate the orientation. This controller was only applied to one axis. The assumption has been made that for small deviations, the pitch and roll axis can be decoupled. Evidence of this was shown last month using the three-dimensional simulation. Thus far, the control laws have only been tested in the two dimensional simulation environment.
The effect of adding the control law can be seen in the plots below. The first plot is that of the previous two dimensional simulation with an initial offset in the orientation angle. The rotational speed of the rotors was fixed during these simulations. Compare this with the resulting closed loop response shown in the next plot. The mesicopter is now well damped, and the angular rate is monotonically driven to zero.
Simulated 2D response with Constant Rotor Speed.
Simulated 2D response with Angular Rate Feedback to Rotor Speed.
The dynamics exhibited by the model with angular rate feedback appear to be slow enough that a human could now control the vehicle. It should be noted that the simulation currently assumes perfect knowledge of the system in a noise free environment with no disturbances. The next step is to apply this feedback algorithm to the pitch and roll axes of the three dimensional model individually. Once this is accomplished, the behavior of the mesicopter under simulated noise, disturbance, and model irregularities can be examined.
As of September (see the previous report), we could track LEDs using a ControlShell vision repository adapted from the Yale XVision package. The repository provided simple tracking components which could easily be used on our Linux platform. Earlier this month we integrated some of the repository's software components to reenable the one-degree of freedom mesicopter demo which we had previously ran in June. At that time, we used outdated vision hardware as the tracking mechanism for the demonstration.
In August, we had proposed a new vision system made up of modular Controlshell components. In an attempt to meet the specification of the vision format we had proposed, the first version of vision repository was created which included the inheritable base class and implementations of acquisition, processing, state, network, and display components. We modeled some of our internal code after the XVision repository.
The new vision repository will be available to other research groups. Groups that have already expressed interest include the Aerospace Robotics Lab at Stanford, the Underwater Robotics group at Santa Clara University, and various groups at NASA Ames. We will provide our software to these groups in hope that we can improve the reliability of the package and so the stock of vision tracking and processing components will grow.
We are designing a multi-point tracking component for our new vision repository that will give the location of multiple LEDs. With this component in place, we will track two LEDs on the wire-restricted mesicopter and calculate both height and yaw information. We will then incorporate a new MIMO controller based on the dynamics we had modeled this summer for the restricted mesicopter. The wire based mesicopter demonstration will be fully autonomous with these components in place.
Ilan will present work on mesicopter control ideas and future concepts at two conferences in December, one on cooperative control in Florida, and one on Biologically-Inspired Engineering of Exploration Systems at JPL. We continue to discuss potential applications with NASA Ames, Langley, and JPL.