Converting GPS coordinates to a local X, Y Coordinate Frame
It's typical practice for a robot in its Home position to be located at the Origin (0, 0) of its World coordinate frame, with its own Local coordinate frame initially superimposed thereon.
This is ideally suited to robots that use wheel odometry to reckon their location. (Our robot doesn't need to do that. It uses GPS for its location.)
Until the robot leaves its Home, it is poised to go forward in the X direction with a theta-Z value = 0.
The robot's initial Pose is (X, Y, theta-Z) = (0, 0, 0).
However, in the case of this robot it isn't neccesary that the robot's Home position must be located in any particular place, but it is important that the IMU yaw = ZERO when the robot is facing in the X-direction.
It is important for the robot to have an IMU that gives reliable values for its Theta-Z orientation without drift
Transforming from Lat/Lon --> Easting/Northing --> X/Y Reference Frame
GPS technology is wonderful for allowing our robot to figure out where it is, but we have to do a couple of transformations to get our desired X, Y coordinates in meters.
First we declare the Latitude / Longitude of our chosen Home postion to be our reference coordinates. All other Lat/Lon coordinates are considered to be relative to the coordinates of our Home positon.
With the Home position as the origin, we can come up with a 2D frame which looks like a normal map, with East-West direction along the horizontal axis and North-South direction along the vertical direction.
A Northing value (meters) is calculated from the latitude of any other location.
Measuring the Earth's circumference C in a longitudinal direction allows us to come up with a pretty simple relationship between latitude and Northing distance that holds true everywhere.
An Easting value (meters) is calculated from the longitude of any other location.
This isn't as simple. It also depends on your latitude. At the equator, you would have to travel a great distance East or West to go 360 degrees and get back to where you started, but if you are near one of the poles, you only have to travel a much shorter distance to get back to your starting point. So you have to know your latitude in order to know the distance around the world in the E/W direction.
Finally, set the X/Y coordinate frame at the desired rotation. Zero rotation would align the X-axis to the East (Y-axis to the North). If it is desired to have the X-axis square to the face of the garage as shown above, the Easting/Northing map would need to rotate 148 degrees CCW about the origin.
Test drive CCW around circle
The picture below shows the locations of waypoints numbered 1 through 9.
At power-up, robot orientation must be aligned along the desired X-axis (square to the face of the garage)
After power-up, the onboard led flash's quickly, until the start button is pressed.
Once the start button is pressed, the robot then waits until the GPS module is providing good 3D fixes
Once valid GPS values are produced:
a relay closes, allowing solar power to the motor
robot steers toward the first waypoint
upon arrival at the waypoint, the current waypoint is set to next in list.
upon arrival at the final waypoint, relay cuts power to the motor and program exits.
