Validating Robot Friction Compensation Effects: An AI-Automated Experiment Case Study

We applied two compensation techniques to the Neuromeka Indy7 collaborative robot:

1. Friction Compensation: Compensates for mechanical friction in joints
2. Acceleration Feedforward (FF): Pre-compensates for inertial forces during acceleration

A question arose: "How much does each technique actually contribute? Is one sufficient, or are both necessary?"

To answer this question, we conducted 160 runs of 2x2 experiments. After tuning friction coefficients with an AI agent (ralph-loop), we performed validation experiments using automated scripts.

The Problem: Before Compensation

Before applying compensation techniques, severe position tracking errors were observed, especially in J1 (shoulder joint). J1 is the joint with the highest friction due to its large reducer and the structure that supports the entire arm load.

J1 position tracking before compensation. Clear delay and error between command (cmd) and actual position

J1 torque before compensation. Large torque fluctuations due to friction are observed

To address these friction problems, we applied friction compensation techniques. This experiment quantitatively validates their effectiveness.

Conclusions First

Condition	Position RMSE	Improvement	p-value	Cohen's d
B0 (baseline)	1.526 mrad	-	-	-
B1 (friction only)	0.974 mrad	36.1%	p<0.01	1.49
B2 (FF only)	1.450 mrad	5.0%	p<0.05	0.80
B3 (both)	0.932 mrad	38.9%	p<0.01	1.44

Friction compensation alone achieved 93% of total improvement. Acceleration FF contributed only 5%.

Experimental Design

We combined 4 conditions to analyze the independent effects and interactions of each technique:

Condition	Friction Comp.	Acceleration FF	Description
B0	OFF	OFF	Baseline
B1	ON	OFF	Friction only
B2	OFF	ON	FF only
B3	ON	ON	Both

Test Trajectories

• 5 joints: J0-J4 (J5 excluded due to minimal friction Fc=1Nm)
• 2 speeds: SLOW (vel=0.1), FAST (vel=0.3)
• 10 total trajectories: 4 repetitions each (2 each for directional balance)
• Total experiment runs: 4 conditions x 10 trajectories x 4 repetitions = 160 runs

Friction Coefficients (Fc)

Joint	Fc (Nm)	Characteristics
J1 (shoulder)	35.0	Maximum friction - supports entire arm load
J2 (elbow)	10.0	Medium friction - gravity load
J0 (base)	5.0	Vertical axis - less friction in gravity direction
J3, J4 (wrist)	2.0	Low friction - small joints
J5 (end)	1.0	Minimum friction

AI-Automated Experiment Pipeline

Tools Used

Tool	Role
Claude Code	AI agent - code modification, build, execution, analysis
ralph-loop	Iterative execution plugin - auto-repeat until complete
run_experiment.py	Single experiment automation script
motion_analyzer.py	Result analysis and metric extraction

Two-Stage Workflow

Stage 1: Friction Coefficient Tuning (using ralph-loop)

AI judgment required: Error analysis -> Adjustment direction -> Code modification -> Repeat

Stage 2: 160 Validation Experiments (script repetition)

B0 (40 runs) -> B1 (40 runs) -> B2 (40 runs) -> B3 (40 runs)
Condition changes were done manually

Key Results

Effect Decomposition

Comparison	Improvement	Ratio
Total (B0->B3)	0.594 mrad	100%
Friction only (B0->B1)	0.551 mrad	93%
FF only (B0->B2)	0.076 mrad	13%

Friction compensation is the key factor.

Speed-wise Analysis

Improvement comparison between SLOW (vel=0.1) and FAST (vel=0.3)

Condition	SLOW Improvement	FAST Improvement	Difference	Theory Validation
B1 (friction)	42.3%	31.3%	+11.0%	Confirmed
B2 (FF)	4.7%	5.1%	+0.4%	Rejected
B3 (both)	42.9%	35.8%	+7.1%	-

Theory Validation Results:

• Friction compensation is more effective at low speeds (where static friction is prominent)
• The expectation that FF would be more effective at high speeds was rejected

Joint-wise Analysis: Correlation Between Friction Coefficient and Improvement

Correlation between Coulomb friction coefficient (Fc) and B1 improvement. J0 is an outlier due to its vertical axis

Joint	Fc (Nm)	Axis Direction	B1 Improvement
J1	35.0	Horizontal	73.5%
J2	10.0	Horizontal	46.7%
J0	5.0	Vertical	10.1% (outlier)
J3	2.0	-	39.5%
J4	2.0	-	39.0%

J0 is a vertical axis, so it has less friction load in the gravity direction. Despite having higher Fc than J3/J4, its improvement rate is lower.

Unexpected Finding: j3_fast Anomaly

B2 (FF only) actually degraded performance in the j3_fast trajectory

Phenomenon: B2 (FF only) condition showed 13.8% degradation compared to baseline in j3_fast

Statistic	Value
B2 > B0 in all 4 runs	Consistent degradation
t-test	t=20.7, p=0.0002
Verdict	Systematic phenomenon, not random

J4 with the same Fc=2Nm behaved normally - This is a J3-specific phenomenon

Implications: Applying FF alone without friction compensation can degrade performance under certain conditions. B3 (both) performed normally.

Friction Model Implementation

Chattering Prevention: tanh vs sign

The existing sign() function causes abrupt torque changes near zero velocity:

Velocity (rad/s)	sign() Output	Torque Change
+0.001	+1	+35 Nm
-0.001	-1	-35 Nm
Difference	-	70 Nm jump

Using the continuous tanh() function for smooth transition:

constexpr double kTransitionVelocity = 0.05;  // rad/s (~3 deg/s)
tau_compensation = Fc * tanh(velocity / kTransitionVelocity)

Velocity (rad/s)	tanh() Output	Torque Change
+0.001	+0.02	+0.7 Nm
-0.001	-0.02	-0.7 Nm
Difference	-	1.4 Nm (continuous)

Meaning of kTransitionVelocity

kTransitionVelocity defines "how quickly to determine friction direction near zero velocity":

Value	Characteristic	Trade-off
Smaller	Closer to sign() (sharp transition)	Accurate but chattering risk
Larger	Smooth S-curve	Stable but inaccurate at low speeds

Empirical meaning of 0.05 rad/s (approximately 3 deg/s):

• Below this speed: Friction direction is considered "uncertain"
• Above this speed: tanh is approximately equal to +/-1, nearly identical to the original Coulomb model

note

This value requires tuning based on system noise, velocity measurement resolution, and drive system characteristics.

Torque Usage Changes

Condition	Torque RMSE	vs B0	Torque MAX	vs B0
B0	1.94 Nm	-	22.2 Nm	-
B1	2.04 Nm	+5.1%	23.2 Nm	+4.5%
B2	2.10 Nm	+7.9%	27.5 Nm	+23.7%
B3	2.08 Nm	+7.2%	28.4 Nm	+27.6%

Friction compensation (B1) has minimal torque increase, but FF (B2) increases maximum torque by 24%.

Operational Recommendations

Scenario	Recommended Setting	Reason
General operation	B1 (friction only)	Core effect only, simplicity, stability
Maximum precision needed	B3 (both)	Additional 3% improvement
High-speed tasks	B1 (friction only)	Minimal FF effect, noise risk
FF alone	Caution	j3_fast degradation observed

Why FF Effect Was Limited

1. Limitations of simple numerical differentiation: Uses only 2 samples, amplifies noise
2. Indirect compensation by PD gains: Existing PD controller partially compensates for inertia
3. Unnecessary for low-inertia joints: J3, J4 have minimal inertia
4. Asymmetric effects without friction compensation: Acceleration/deceleration torque imbalance

Experimental Limitations

1. Fixed condition order (B0->B1->B2->B3): Temperature/time drift possible
2. Paired t-test used: Used instead of 2-way ANOVA, interaction significance not tested
3. No multiple comparison correction: B2 significance questionable after Bonferroni correction
4. Sample structure: 160 runs summarized as averages of 10 trajectories (df=9)

Key Takeaways

1. Friction compensation is the key factor. 36.1% improvement (p<0.01, Cohen's d=1.49) accounts for 93% of total improvement.
2. Acceleration FF effect is limited. Only 5.0% improvement, and the expectation of greater effectiveness at high speeds was rejected.
3. The two effects are largely independent. Interaction effect is approximately 0.033 mrad, negligible.
4. Maximum effect in joints with high friction coefficients (J1). 73.5% improvement in J1 (Fc=35Nm).
5. Caution required for FF-only application. 13.8% degradation observed in j3_fast.