Motion Profiling

[Jared]

The lookup table method was the best way for our team, as all of our autonomous action is based on distance triggers. We would generate the desired motion profile on the roboRIO, generate a .csv file from the data, copy it to the laptop, and open it in excel. This let us sit in front of graphs and data and decide when and where each action in autonomous would happen. It takes some amount of time for our elevator and container swatter to move, so knowing how fast the robot was going at each point was very helpful to determine where we should set the distance trigger for starting elevator or swatter movement.

The table method is also super easy to explain. The polynomial method would require separate polynomials for acceleration ramp up, constant positive acceleration, acceleration ramp down, constant velocity, deceleration ramp, constant deceleration, and final deceleration ramp. That seems harder to keep track of.

The table calculation method also gave me an easy way to work in motor equations. You get more torque, and therefore more acceleration, from your motor at lower speeds. If your profiling takes this into account, you can go much faster. Without taking this into account, you must limit your max acceleration to less than the robot can actually achieve so that as it accelerates, it can still achieve the same acceleration.

The solution to the dc motor equations for a pulley driven lift is

v = (r * w_n * (a_g * r * m - T_s)/T_s) * (1 - e^(-(t * T_s)/(r^2 * w_n * m))))

where v is velocity, r is pulley radius, w_n is no load speed (rad/sec), a_g is acceleration of gravity, m is mass carried, T_s is stall torque, and t is time.

If you have lots of time, you could integrate this again and find the position equation, and use that to determine your motion profile.

However, that's difficult, and you can come up with a simpler equation, v * a = k, where k is some constant specific to your setup. This means you either get a large acceleration or a large velocity, but not both at the same time. This equation is only valid when a is less than the acceleration achieved by stall torque and v is less than the no load speed. This is really easy to add into your calculations for the constant acceleration portion with

a = k/v_prev

If you have a large velocity, you can't accelerate as fast.

This would let you achieve the most aggressive and fastest profile possible for when speed really matters.