[Paul Copioli]

Tom,

I am sitting in the HK airport so I have some time to kill. I will try to go through a simple double linear filter motion profile scheme. This is the fastest way, computationally, to do real time motion profiling. However, for FRC autonomous mode applications, the real time filtering really isn't required.

Some definitiions:

itp = iteration time (loop time)
T1 = Time, in ms for the first filter
T2 = Time, in ms for the second filter
FL1 = Filter 1's length, unitless. Must be an integer. FL1=RoundUp(T1/itp)
FL2 = Filter 1's length, unitless. Must be an integer. FL2=RoundUp(T2/itp)

Vprog = Desired Max Speed, ft/sec (can be any units you desire, just be consistent)

Dist = Desired travel distance, ft (can be any units ...)

T4 = Time, in ms, to get to destination if always at Vprog. T4 = Dist / Vprog
N = Total number of inputs to the filter, Integer. N = RoundUp (T4/itp)

That is really all you need to do the filtering so here is an example with numbers:

Vprog = 10 ft/sec
Dist = 4 ft
itp = 50ms (doing this to make the math short and easy)
T1 = 200 ms
T2 = 100 ms (this makes it an even trapezoid, as this number increases, it becomes a more traingular accel profile)

T4 = 4/10 *1000 = 400
FL1 = 200/50 = 4
FL2 = 100/50 = 2
N = 400/50 = 8

Ok, now time to fill the filters. How this works is simple. FIlter 1 has FL1 number of boxes, Filter 2 has FL2 # of boxes, and your inputs are N # of 1s until all filters are cleared.

Step # Time Input FL1 FL2 Output (Vel)
1 0 0 0 0 0 0 0 0 0 * Vprog
2 .05 1 1 0 0 0 0 0 1/6 * Vprog
3 .10 1 1 1 0 0 0 0 1/3 * Vprog
4 .15 1 1 1 1 0 0 0 1/2 * Vprog
5 .20 1 1 1 1 1 0 0 2/3 * Vprog
6 .25 1 1 1 1 1 1 0 5/6 * Vprog
7 .30 1 1 1 1 1 1 1 1 * Vprog
8 .35 1 1 1 1 1 1 1 1 * Vprog
9 .40 1 1 1 1 1 1 1 1 * Vprog
10 .45 0 0 1 1 1 1 1 5/6 * Vprog
11 .50 0 0 0 1 1 1 1 2/3 * Vprog
12 .55 0 0 0 0 1 1 1 1/2 * Vprog
13 .60 0 0 0 0 0 1 1 1/3 * Vprog
14 .65 0 0 0 0 0 0 1 1/6 * Vprog
15 .70 0 0 0 0 0 0 0 0 * Vprog

This is now your velocity command. Some interesting statistics:

Total time to end point = (N + FL1 + FL2)*itp
Total time to Max Speed = (FL1 + FL2)*itp
Theoretical time to end point = N*itp. This now corresponds to the time when decel starts.

In theory, if your itp time is short enough, then you can simply do a velocity PI routine on each of these commands in the Jag and get great position control. In addition, you can manipulate the ratio between T1 and T2 to get different Velocity trajectories based on your robot's capabilities. At FANUC, the T1 = 2 * T2 was pretty much a golden rule, but I violated it once or twice on specific painting robot models.


Let me know if you have any questions.

Paul