Iterative learning control

The tracking error repeats almost exactly from run to run. Iterative learning control (ILC) uses the error of one run to correct the commands of the next run:

cmd[k+1](/mycobot-280-lab/results/ilc/t/) = cmd[k](/mycobot-280-lab/results/ilc/t/) + gain · w(t) · Q[ref − measured](t + lead_j)

Term	Value	Purpose
gain	0.5	Corrects half of the error per run. A low gain is stable.
Q	forward-backward moving average, 80 ms	Learns only the slow, repeatable part. No phase shift.
lead_j	the joint’s lag (DEFAULT_LAG)	The command at t shows in the measurement near t + lead_j.
w(t)	1 inside, 0 within 0.3 s of the ends	The plan still starts and ends at rest.

ILC does not model the servos. It learns a correction for one trajectory. A new trajectory starts from zero again.

On a model plant with delay, lag and sticking (the test suite), the error goes down in every iteration and halves in five.

Results on the circle

Run	Laptop, ~300 Hz (RMS / max)	ATOM, 500 Hz (RMS / max)
Lag compensation only	5.0 mm / 12.4 mm	5.0 mm / 12.5 mm
ILC iteration 1	2.5 mm / 6.5 mm	2.6 mm / 6.8 mm
ILC iteration 2	1.3 mm / 4.0 mm	1.5 mm / 4.0 mm
ILC iteration 3	0.8 mm / 2.2 mm	1.0 mm / 3.4 mm

The error halves in each iteration, including the peaks where J2 and J3 stick. The largest correction in a step was 0.9°.

With our gains (firmware 4.0, 2026-10-04)

The table above used the servos’ stored gains (32/8/0). With our gains (integral action on J1–J3), ILC with gain 0.5 improved once (2.6 → 1.4 mm) and then got worse. With gain 0.3 it converges again. ATOM, 500 Hz, 50 Hz cubic plans:

Run	Error RMS / max	IMU acceleration RMS
Lag compensation only	2.8 mm / 8.0 mm	159 mg
ILC 1	2.4 mm / 8.2 mm	170 mg
ILC 2	1.8 mm / 7.4 mm	155 mg
ILC 3	1.7 mm / 7.2 mm	148 mg
ILC 4	1.5 mm / 6.1 mm	145 mg
ILC 5	1.2 mm / 4.4 mm	136 mg
ILC 6	1.4 mm / 6.2 mm	142 mg
ILC 7	1.4 mm / 3.9 mm	154 mg
ILC 8	1.1 mm / 2.8 mm	145 mg

• The RMS error levels off at ~1.1–1.4 mm, about the same as with the stored gains (1.0 mm). The maximum keeps falling, to 2.8 mm.
• The integral action makes the servos slower to settle, so a lower ILC gain is needed. Use scripts/ilc_step.jl ... --gain=0.3 with our gains.
• What is left (~1 mm) changes from run to run (sticking after reversals), so ILC cannot learn it.

Run it

julia --project=. scripts/ilc_step.jl tools/python/plans/circle.csv tools/python/recordings/<last recording>.csv
julia --project=. scripts/play_plan.jl tools/python/plans/circle_ilc1.csv [--atom=<ip>]

Keep separate plan names for the laptop series and the ATOM series. The ATOM series uses circle_atom.csv → circle_atom_ilc1.csv …