Differentiable Iterative Learning Control for Black-Box Position-Commanded Manipulators

Mohammed Al-Ghaili; Yakoop Qasim; Hassan Almubarak

cs.ROOct 31, 2026

Differentiable Iterative Learning Control for Black-Box Position-Commanded Manipulators

Authors: Mohammed Al-Ghaili, Yakoop Qasim, Hassan Almubarak

Organizations: Control & Instrumentation Engineering Department, KFUPM, Dhahran, Saudi Arabia.

Abstract

High-accuracy repetitive tracking is challenging for position-commanded manipulators whose low-level controllers are inaccessible, while constrained model-based iterative learning control (ILC) can require substantial manual parameter tuning. We present Differentiable Iterative Learning Control (Diff-ILC), an online bilevel framework that adapts the parameters of a constrained ILC update between physical robot executions. A closed-loop differential model is identified once from paired smooth perturbations and subsequently kept fixed. At each trial, a constrained quadratic program computes a feasible command correction, while a real-anchored next-trial prediction defines a task-level objective. Hypergradients are obtained by implicitly differentiating the locally active KKT system, enabling multiple computational parameter updates without additional robot executions. Experiments on a 6-DoF DOBOT CR3 across unseen planar and three-dimensional trajectories show substantially faster physical-trial convergence than fixed-parameter model-based ILC. Across the four primary trajectories, after only two trial-to-trial updates, Diff-ILC achieves 78.8% and 76.4% lower mean joint-vector and Cartesian RMSE, respectively, than fixed-parameter model-based ILC.

Figures & tables

Fig. 1: Diff-ILC combines constrained model-based ILC with implicit differentiation through the locally active KKT system to adapt ILC parameters between physical robot executions. This online adaptation accelerates tracking-error reduction over the first few repetitions on the DOBOT CR3.

Fig. 2: Computational graph of Diff-ILC at physical trial $j$ . The measured trajectory anchors the constrained ILC update and real-anchored next-trial prediction, while hypergradients through the locally active KKT system update the ILC parameters over multiple computational epochs. After the final outer update, the inner QP is re-solved using $\phi_{j+1}$ , and only the resulting updated command is executed on the robot at trial $j+1$ .

Fig. 3: Joint and Cartesian tracking convergence over the first five physical trials for the four

0.1~\mathrm{Hz}

evaluation trajectories using fixed-parameter model-based ILC and Diff-ILC with five and ten outer optimization epochs between physical executions.

Trajectory	Method	T1 (nominal)	T3	T5	$T_{\mathrm{MB}}/T_{\mathrm{Diff}}$ (5%)	$\Delta_{\mathrm{T3}}$ J/C (%)
Circle	Fixed MB-ILC	5.47/15.12	1.48/4.05	0.49/1.26	–	–
	Diff-ILC (5 epochs)	5.52/15.18	0.53/1.30	0.26/0.68	T5/T3	64.2/67.9
	Diff-ILC (10 epochs)	5.46/15.09	0.28/0.73	0.26/0.67	T7/T3	81.1/82.0
Fast circle	Fixed MB-ILC	9.06/22.60	2.40/6.02	0.84/2.06	–	–
	Diff-ILC (5 epochs)	9.11/22.73	2.10/4.62	0.55/1.30	T4/T3	12.5/23.3
	Diff-ILC (10 epochs)	9.06/22.59	0.60/1.45	0.53/1.26	T8/T3	75.0/75.9

TABLE I: Joint-vector and Cartesian tracking performance at selected physical trials. Entries report the mean joint-vector RMS ( ∘ )/Cartesian position RMS (mm) over three repeated experiments. The penultimate column reports the trial pair

T_{\mathrm{MB}}/T_{\mathrm{Diff}}

at which fixed MB-ILC reaches the 5% criterion relative to Diff-ILC for both joint and Cartesian RMS errors; the final column gives the Trial 3 reduction relative to fixed-parameter model-based ILC.

Fig. 4: Joint-wise tracking errors for the star trajectory at Trial 3 using fixed-parameter model-based ILC and Diff-ILC with ten outer optimization epochs.

Fig. 5: Cartesian position-error magnitude along the four primary evaluation trajectories at Trial 3 for fixed-parameter model-based ILC and Diff-ILC with ten outer optimization epochs.

Fig. 6: Online evolution of the learned Diff-ILC (10) parameters for the star trajectory (a) correction penalties

\lambda_{i}

, (b) first-difference penalties

\rho_{i}

, (c) second-difference penalties

\eta_{i}

, and (d) shared correction bound

\delta

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Reinforced Iterative Learning Control for elastic joint arms: Guaranteed cross-trajectory generalization under model uncertainties

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Robot Trajectory Tracking Iterative Learning Control Compliant Robot Control RL Control

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Trajectory tracking for compliant robots is challenging due to nonlinear dynamics and modeling uncertainties, often requiring learning-based methods to avoid explicit parameter identification. Iterative Learning Control (ILC) ensures theoretically high precision and preserves the passive compliance of the robot. However, traditional ILC requires a separate learning phase for each new trajectory. Conversely, Reinforcement Learning (RL) generalizes to new trajectories, but practically suffers from high sample complexity and limited tracking precision. This work proposes Reinforced Iterative Learning Control (RILC) that combines the strengths of both approaches to achieve fast adaptation and guaranteed tracking convergence across diverse trajectories. By establishing a concurrent coupling between the two controllers, RILC overcomes the high initial errors and slow adaptation of traditional ILC, enabling high-performance tracking from the very first trials. In this architecture, ILC provides high-quality samples, while RL contributes as a generalizing best-effort policy across iterations. Additionally, a theoretical proof is presented to show that the RL component preserves ILC stability and, under specific conditions, can also reduce the error bound asymptotically. The efficacy of this framework is demonstrated through simulation and experiments on an underactuated 4-degree-of-freedom serial elastic robot using different trajectories and modeling mismatches.

Abstract

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