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On of the other engineers on our team developed a simulation based on a tracked robot with differential steering. He modeled the motors to include accelleration lag and to account for the different outputs in forward/reverse for the drill motors.
Its set up to simulate the robot in near real-time, accounting for the fact that the RC samples at only 40Hz and the gyro output is nominally 50Hz. The sample uses a PID control loop to drive in an arc, but it could be extended to do anything the real robot could do.
The competition could be something along the lines of simulating the robot following a path and seeing how closely it matches the real thing. You can be given the path the morning of the competition, use your simulator to work out the command set points, then see how close you can get. The only space requirement would be a small area and a few cones to mark the path.
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