wiki/ rockettracks

Rocket Tracks

(formerly Trackmaster 3000)

Project Goals

The goal of this project proposal is to design and build a motorized antenna tracking device. The tracking device will be outfitted with telemetry antennas, video cameras, and still camera equipment.

  1. Rocket Tracks
    1. Project Goals
    2. Summary:
    3. Background:
    4. Design Requirements
      1. Features
      2. Tracking performance
      3. Trackmaster Motion
      4. Power Requirements
    5. Design Concepts
      1. Concept 1
      2. Concept 2
    6. Fabrication
      1. Base
      2. Vertical Axis
      3. Lateral Axis
    7. Control System
      1. Feedback Sensors
      2. Electronic Hardware
      3. Control Algorithm
    8. Demo
      1. Video of the tracker moving:

Summary:

Portland State Aerospace Society (PSAS) has been launching high power rockets for over a decade. As rocket systems become more sophisticated, tracking the rocket with telemetry antennas and high definition camera equipment is critical. As flight altitudes increase past 5000 meters, the high gain telemetry antennas are difficult to accurately point toward the rocket. Further, because the parachutes open at maximum altitude, no one has ever filmed the parachutes as they deploy.

Background:

Since our return to active flight in 2009, much emphasis has been placed on the importance of still photos, onboard video and ground based video of PSAS rockets. It’s one thing to say we have a great rocket program, but the media created over the last 3 years has placed PSAS on the map among the rocketry community.

For this reason, it seems that improved data and media collection capabilities will improve the image of PSAS and PSU as engineering education leaders.

Design Requirements

Features

Tracking performance

Trackmaster Motion

The following graph shows the required acceleration of the antenna tracking machine at various distances between the antenna and the launch pad; all for a 14g rocket acceleration.

Power Requirements

To spec the motor correctly we need to know the max torque we'll need to supply at the motor. To obtain that, we draw a free body diagram of the rocket tracks antenna pointer and identify forces.

Add Scan...

We see from the FBD that the only forces acting on the rocket tracks are gravity, the torque applied by our motor, and friction countering our motor. Say that the sum of the torques applied to the rocket tracks is equal to the moment of inertia multiplied by the angular acceleration. Assuming that friction is independent of speed and acceleration:

torquelatex.png

The following equation describes the relationship between torque, mass moment of inertia, and angular acceleration:

 \sum \tau = I_{xx} \alpha

Solving for the torque required to attain a desired acceleration:

Consider a mass moment of inertia of 2.25 kgm2. To simplify the math, assume that max rotational acceleration occurs at θ = 0, the torque required is:

\overset{\centerdot \centerdot}\theta (rad/sec2) \tau (N*m)
0.27440066499855 0.61740149624673
0.13720033249927 0.30870074812337
0.091472706097023 0.2058135887183
0.054873151682702 0.12346459128608
0.027436575841351 0.061732295643039
0.013718287920675 0.03086614782152
0.006859143960338 0.01543307391076

Add concept 2 mass / torque calcs

Design Concepts

Concept 1

First design consists of 3 main 'weldments':

Concept 2

This concept is not as mechanically 'efficient' as the concept 1, meaning that an equivalent strength and stiffness of design could be made lighter with concept 1. The difference, however, is that concept 2 is much easier to manufacture. This comes because the bearings, spindles and hubs are mostly commercial off the shelf (COTS) parts.

The second design consists of the following:

Concept two is the design chosen for construction.

Fabrication

Base

Deployed
Stowed

Vertical Axis

The vertical axis consists of a trailer spindle and hub assembly welded to the vertical tube on the base.

The vertical axis position is sensed using a potentiometer in a sensor housing.

The potentiometer is connected to a shaft:

Which is attached to the spindle and supported by the housing:

Lateral Axis

The lateral axis requires a few machined parts to hold the bearings and position sensor.

The assembled lateral axis:

Complete Mechanical Hardware:

Control System

Feedback Sensors

The vertical and horizontal axis position is sensed using a high quality "servo mount" potentiometer from Bourns, P/N 6539S-1-102; Mouser 652-6539S-1-102.

Electronic Hardware

Control system hardware for the Rocket Tracks antenna and camera pointing system consists of a Generic Front End (GFE) and a Generic Motor Driver (GMD).

Generic Motor Drivers:
Motion Control Console:

Control Algorithm

The basic control philosophy offers two control modes: 1) Position tracking 2) Velocity tracking. In the position tracking mode, the vertical and lateral axes follow the respective positions of the vertical and lateral control levers by means of a PID control loop. This allows absolute positioning of the antenna, but can be a little shaky because any hand movements that are not completely smooth will be transferred to antenna motion that is equally not smooth.

In the velocity mode the control keeps internal "position targets" that are tracked by the vertical and lateral PID loops. The vertical and lateral position targets are increased or decreased by rotating the control levers away from the centered "neutral" position. In this way, the control provides a position target that is changing at some "velocity" based on the lever position. Further, if the velocity is decreased to zero, the control will continue to follow the internal position target. This means that the antenna will remain in position even if some external disturbance is applied to the antenna such as wind, or a significant change in mass.

Automatic tracking

There are presently other PSAS systems which give the location of the rocket relative to the antenna in an Azimuth-Elevation format. This is similar to the standard aerospace coordinate frame transformation sequence, giving rotations about the Z, Y, and then X axes; through angles of \psi, \phi, and \theta. Because our antenna tracker is designed to avoid gimbal lock in a vertical position, the axes are changed and the axis sequence is Y, Z, and then X (\phi, \psi, \theta). For this reason, a coordinate frame transformation is needed to change from ZYX to YZX rotations.

In the following equations, the following substitutions will be made:

C_x = cos(x)

S_y = sin(y)

The coordinate frame transformation for ZYX rotation sequences is as follows:


\overset{-} T_{ZYX} =
\left [ \begin{matrix}
C_\psi C_\phi    &    -S_\psi C_\theta + C_\psi S_\phi S_\theta    &    S_\psi S_\theta + C_\psi S_\phi S_\theta \\
S_\psi C_\phi    &     C_\psi C_\theta + S_\psi S_\phi S_\theta    &   -C_\psi S_\theta + S_\psi S_\phi C_\theta \\
-S_\phi          &     C_\phi S_\theta                             &    C_\phi C_\theta
\end{matrix} \right ]

To determine the X, Y, and Z unit vector toward an object we wish to track, we need to multiply the above matrix (substituting in the respective azimuth and elevation angles) by a unit vector in the positive X axis:


\overset{-} r_{o->rocket} =
\left [ \begin{matrix}
C_\psi C_\phi    &    -S_\psi C_\theta + C_\psi S_\phi S_\theta    &    S_\psi S_\theta + C_\psi S_\phi S_\theta \\
S_\psi C_\phi    &     C_\psi C_\theta + S_\psi S_\phi S_\theta    &   -C_\psi S_\theta + S_\psi S_\phi C_\theta \\
-S_\phi          &     C_\phi S_\theta                             &    C_\phi C_\theta
\end{matrix} \right ]
\left [ \begin{matrix}
1 \\
0 \\
0
\end{matrix} \right ]

Which simplifies to:


\overset{-} r_{o->rocket} =
\left [ \begin{matrix}
C_\psi C_\phi \\
S_\psi C_\phi \\
-S_\phi
\end{matrix} \right ] =
\left [ \begin{matrix}
r_x \\
r_y \\
r_z
\end{matrix} \right ]

Next, we convert the unit vector r to our YZX rotation sequence. Since we need only the vertical and lateral axis rotations, we get them from the unit vector r in terms of the rotation derived above:


ROT_{vert} =
arctan(r_{z} / r_{x})


ROT_{vert} =
arctan(-S_\phi / C_\psi C_\phi)


ROT_{lateral} =
arctan(r_{y} / r'_{x}) =
arctan(r_{y} / C_{vert})


ROT_{lateral} =
arctan((r_{y} / r_{x}) * C (arctan(-S_\phi/C_\psi C_\phi)))


ROT_{lateral} =
arctan((S_\psi C_\phi / C_\psi C_\phi) * C (arctan(-S_\phi/C_\psi C_\phi)))

An easier derivation of the lateral angle, knowing that we started with a unit vector:


ROT_{lateral} =
arcsin(r_y / 1)


ROT_{lateral} =
arcsin(S_\psi C_\phi)

Demo

Video of the tracker moving:

During the first half we have the nobs in velocity control -- moving either the vertical or lateral lever will change the target rotation speed of the tracker. In the second half it is switched to position control which is 1:1 with nob position and tracker position. Note the aggressive motor control.

Same idea, but with the video camera strapped to the tracker

Camera being attached: