Design and Modeling of a HASEL Actuator-Based Micro Parallel Robot

Agustin Feregrino (UMLP; Alexis Lef\`evre (UMLP; ENSMM; FEMTO-ST); Nelson Cisneros (UMLP; Yann Le Gorrec (UMLP; Yongxin Wu (UMLP

arxiv: 2604.25337 · v1 · submitted 2026-04-28 · 🧮 math.OC

Design and Modeling of a HASEL Actuator-Based Micro Parallel Robot

Agustin Feregrino (UMLP , ENSMM , FEMTO-ST) , Nelson Cisneros (UMLP , Alexis Lef\`evre (UMLP , Yongxin Wu (UMLP , Yann Le Gorrec (UMLP This is my paper

Pith reviewed 2026-05-07 15:51 UTC · model grok-4.3

classification 🧮 math.OC

keywords HASEL actuatormicro parallel robotport-Hamiltonian modelnonlinear dynamicsgrey-box estimationsoft roboticskinematics3PS topology

0 comments

The pith

A port-Hamiltonian model with forward and inverse kinematics captures the nonlinear dynamics of a HASEL-actuated 3-DOF micro parallel robot.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper designs and prototypes a three-degree-of-freedom micro parallel robot driven by three HASEL soft actuators arranged in a 3PS topology, with a compliant interface serving as a spherical joint. It develops a port-Hamiltonian model that incorporates the mechanism's forward kinematics to represent the nonlinear dynamic behavior and applies inverse kinematics to determine the actuator displacements required for target platform motions. Parameters in this model are identified from experimental data using nonlinear grey-box estimation, producing a compact representation intended for controller design. This modeling step matters because HASEL actuators introduce compliance and electrostatic actuation that standard rigid-body models cannot handle directly.

Core claim

The authors fabricate a prototype with three base-integrated HASEL actuators and track platform motion via an XY laser system. They formulate a port-Hamiltonian model augmented by forward kinematics to describe the system's nonlinear dynamics and employ inverse kinematics to map desired platform poses to actuator lengths. Nonlinear grey-box estimation then tunes the model parameters against measured trajectories, delivering a control-oriented dynamic description of the soft-actuated parallel mechanism.

What carries the argument

The port-Hamiltonian model integrated with the robot's forward kinematics and inverse kinematics, with parameters fitted by nonlinear grey-box estimation to match observed behavior.

If this is right

The identified model supplies the actuator displacements needed to achieve commanded platform motions via inverse kinematics.
The compact port-Hamiltonian representation supports the design of nonlinear controllers for the robot.
Experimental validation on the laser-tracked prototype confirms that the model reproduces the observed dynamic response.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same port-Hamiltonian-plus-kinematics structure may transfer to other parallel robots that use compliant or soft actuators.
Improved dynamic models of this type could enable higher-precision trajectory tracking in micro-manipulation applications.
The approach suggests that electrostatic soft actuators can be incorporated into existing port-Hamiltonian control frameworks without requiring entirely new formalisms.

Load-bearing premise

The compliant interface behaves exactly like a spherical joint and the port-Hamiltonian model with kinematics contains no major unmodeled effects that would invalidate its use for control.

What would settle it

A direct comparison in which simulated platform trajectories from the model deviate substantially from laser-tracked experimental positions under identical actuator inputs would falsify the claim that the model accurately captures the nonlinear dynamics.

Figures

Figures reproduced from arXiv: 2604.25337 by Agustin Feregrino (UMLP, Alexis Lef\`evre (UMLP, ENSMM, FEMTO-ST), Nelson Cisneros (UMLP, Yann Le Gorrec (UMLP, Yongxin Wu (UMLP.

**Figure 1.** Figure 1: a) Top view HASEL actuator schematic design view at source ↗

**Figure 2.** Figure 2: 3PS prototype showing the integrated antenna view at source ↗

**Figure 3.** Figure 3: Left: Forward kinematics; Right: Inverse kinematics view at source ↗

**Figure 4.** Figure 4: Overall experimental setup 4.2 Nonlinear Grey-Box Identification The dynamics of each HASEL actuator were represented using a nonlinear ordinary differential equation (ODE) model, as described by (5). The adopted grey-box model included nine parameters: (i) electrical parameters (R0, R1, R2) representing equivalent resistances and C1 denoting the effective capacitance; (ii) mechanical parameters K, Kb an… view at source ↗

**Figure 5.** Figure 5: Parameter identification results. (a–c) Experimen view at source ↗

**Figure 6.** Figure 6: Validation results under ω = 11 rad/s. (a–c) Experimental vs. simulated vertical displacements hi(t); (d) Reconstructed tip trajectory obtained via FKM. apply the framework to biomedical and microscale robotic systems. REFERENCES Acome, E., Mitchell, S., Morrissey, T., Emmett, M., Benjamin, C., King, M., Radakovitz, M., and Keplinger, C. (2018). Hydraulically amplified self-healing electrostatic actuator… view at source ↗

read the original abstract

This paper presents the mechatronic design, dynamic modeling, and experimental validation of a three-degree-of-freedom (3-DOF) micro parallel robot featuring a prismatic-spherical (3PS) topology actuated by three Hydraulically Amplified Self-Healing Electrostatic (HASEL) actuators. Each soft actuator provides the prismatic motion of an individual limb, while a compliant interface to the moving platform functions as a spherical joint. A prototype incorporating three base-integrated HASEL actuators was fabricated, and the platform motion was measured using an XY laser-tracking system. For control purposes, a port-Hamiltonian (PH) model, combined with the mechanism's forward kinematics (FKM), is developed to capture the robot's nonlinear dynamic behavior, whereas the inverse kinematics (IKM) is employed to estimate the required actuator displacements. Model parameters were identified using nonlinear grey-box (NLGB) estimation, yielding a compact and control-oriented representation suitable for subsequent controller design.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A working 3-DOF HASEL micro parallel robot prototype with port-Hamiltonian modeling and NLGB parameter fitting, but the validation evidence is too thin to judge model quality.

read the letter

This paper builds and models a small 3-DOF parallel robot that uses three HASEL actuators in a 3PS layout. The platform sits on a compliant interface treated as a spherical joint, the base holds the actuators, and motion is tracked with an XY laser system. They write the dynamics in port-Hamiltonian form plus forward kinematics, use inverse kinematics for actuator commands, and identify the parameters with nonlinear grey-box estimation to produce a compact model meant for control design. That specific hardware-plus-modeling combination is new for HASEL actuators in this topology. The prototype fabrication and the choice of an energy-based modeling framework are the parts that actually work. They close the loop from design to an identified model using real sensor data, which is more than many modeling papers manage. The soft spot is the validation. The abstract claims experimental validation and NLGB fitting, yet supplies no fit errors, residual plots, hold-out predictions, or checks against unmodeled effects such as actuator hysteresis or joint compliance deviations. If the identification ran on the full set of trajectories without separate test motions, the fitted model could look good while still missing dynamics that matter for control. The stress-test note on missing cross-validation is therefore on target unless the full manuscript adds those checks. This is for researchers who already work on soft actuators or parallel mechanisms and want a concrete example they can adapt. A reader focused on control-oriented modeling of compliant systems will find the PH-plus-kinematics setup and the identification steps useful as a template. It is worth sending to peer review. The hardware exists and the modeling route is reasonable, so referees can assess the actual data and decide whether the model is ready for controller work.

Referee Report

2 major / 1 minor

Summary. The manuscript presents the mechatronic design of a 3-DOF micro parallel robot with 3PS topology driven by three base-integrated HASEL actuators and a compliant interface acting as a spherical joint. It develops a port-Hamiltonian (PH) dynamic model combined with forward kinematics (FKM) to capture nonlinear behavior, employs inverse kinematics (IKM) to compute actuator displacements, and identifies parameters via nonlinear grey-box (NLGB) estimation from XY laser-tracking experiments on a fabricated prototype, yielding a compact model intended for controller design.

Significance. If the fitted PH model is shown to generalize, the work supplies a control-oriented energy-based representation for soft-actuator parallel mechanisms at micro scale, which is useful for subsequent passivity-based or energy-shaping control designs. The combination of standard PH formulation with mechanism kinematics is a reasonable approach for obtaining a low-dimensional model suitable for real-time control.

major comments (2)

[Abstract / Parameter Identification] Abstract and modeling section: the NLGB estimation is presented as yielding a validated dynamic model, yet no quantitative metrics (RMSE, R², or residual plots), dataset description (number of trajectories, excitation signals), or cross-validation procedure (hold-out sets or out-of-sample prediction on independent motions) are reported. Without these, it is impossible to verify that the identified parameters capture the claimed nonlinear dynamics rather than fitting artifacts, directly undermining the central claim that the model is suitable for controller design.
[Kinematics / Dynamic Modeling] Kinematics and modeling sections: the assumption that the compliant interface behaves as an ideal spherical joint is used to close the kinematic and dynamic models, but no experimental quantification of deviations (e.g., compliance-induced rotation errors or hysteresis) or sensitivity analysis is provided. If these effects are non-negligible, they would propagate into both FKM and IKM and invalidate the PH model accuracy.

minor comments (1)

[Abstract] The abstract states that experimental validation occurred but provides no numerical results or figure references; adding a brief statement of achieved tracking accuracy or model fit quality would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our results. We address each major comment below and will revise the manuscript to incorporate the suggested improvements where feasible.

read point-by-point responses

Referee: [Abstract / Parameter Identification] Abstract and modeling section: the NLGB estimation is presented as yielding a validated dynamic model, yet no quantitative metrics (RMSE, R², or residual plots), dataset description (number of trajectories, excitation signals), or cross-validation procedure (hold-out sets or out-of-sample prediction on independent motions) are reported. Without these, it is impossible to verify that the identified parameters capture the claimed nonlinear dynamics rather than fitting artifacts, directly undermining the central claim that the model is suitable for controller design.

Authors: We agree that explicit quantitative metrics and dataset details are necessary to substantiate the validity of the identified model. The manuscript describes the use of nonlinear grey-box estimation on data from the XY laser-tracking experiments but does not report RMSE, R², residual analysis, the number of trajectories, excitation signal characteristics, or cross-validation procedures. In the revised version, we will add these elements to the modeling section and abstract to demonstrate that the parameters capture the nonlinear dynamics and support the claim of suitability for controller design. revision: yes
Referee: [Kinematics / Dynamic Modeling] Kinematics and modeling sections: the assumption that the compliant interface behaves as an ideal spherical joint is used to close the kinematic and dynamic models, but no experimental quantification of deviations (e.g., compliance-induced rotation errors or hysteresis) or sensitivity analysis is provided. If these effects are non-negligible, they would propagate into both FKM and IKM and invalidate the PH model accuracy.

Authors: The ideal spherical joint assumption is adopted as a standard modeling simplification for the 3PS topology to obtain closed-form forward and inverse kinematics that integrate with the port-Hamiltonian dynamics. The laser-tracked platform trajectories provide overall validation through the parameter identification process. We acknowledge that direct experimental quantification of compliance-induced errors is not included. In the revision, we will add a sensitivity analysis examining the effects of deviations from the ideal joint assumption on the FKM, IKM, and PH model predictions. revision: partial

Circularity Check

0 steps flagged

No significant circularity; standard PH modeling, kinematics, and NLGB identification

full rationale

The derivation chain consists of applying the established port-Hamiltonian formalism to the 3PS mechanism, combining it with standard forward and inverse kinematics, then performing nonlinear grey-box parameter estimation on experimental laser-tracking data. None of the load-bearing steps reduce by construction to fitted quantities or self-citations; the PH structure and kinematic relations are independent of the identification dataset, and the final claim of a control-oriented representation follows directly from the modeling choices without tautological redefinition or renaming of known results. This is a conventional modeling-plus-identification workflow with no evidence of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated beyond standard assumptions of port-Hamiltonian modeling and spherical-joint approximation.

pith-pipeline@v0.9.0 · 5502 in / 1236 out tokens · 48660 ms · 2026-05-07T15:51:22.242627+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 8 canonical work pages

[1]

Acome, E., Mitchell, S., Morrissey, T., Emmett, M., Benjamin, C., King, M., Radakovitz, M., and Keplinger, C. (2018). Hydraulically amplified self-healing electrostatic actuators with muscle-like performance. Science, 359, 61--65

2018
[2]

Cisneros, N., Wu, Y., Rabenorosoa, K., and Le Gorrec , Y. (2025). Dynamic modeling of a curling HASEL actuator using the port H amiltonian framework with experimental validation. Mechatronics, 109, 103342. doi:10.1016/j.mechatronics.2025.103342

work page doi:10.1016/j.mechatronics.2025.103342 2025
[3]

Cisneros, N. (2025). PhD Thesis: Modeling and control of HASEL actuators for micro-robotics applications . Ph.D. thesis, École Nationale Supérieure de Mécanique et des Microtechniques, Besançon, France. Defended on January 29, 2025

2025
[4]

Cisneros, N., Wu, Y., Rabenorosoa, K., and Le Gorrec, Y. (2024). Port- H amiltonian modeling and control of a curling HASEL actuator. In IFAC/IEEE CSS Workshop on Control of Systems Governed by Partial Differential Equations CPDE and XI Workshop Control of Distributed Parameter Systems, volume 58, 143--148. Elsevier / IFAC PapersOnLine. doi:10.1016/j.ifac...

work page doi:10.1016/j.ifacol.2024.08.271 2024
[5]

Ehrlich, J., Löscke, P., Ziegler, J., Lacroix, M., and Böse, H. (2025). High performance HASEL actuators as self-healing trigger devices for biomedical diagnostics. Proceedings of SPIE, 13431, 1343109. doi:10.1117/12.3050100

work page doi:10.1117/12.3050100 2025
[6]

El-Atab, N., Mishra, R.B., Al-Modaf, F., Joharji, L., Alsharif, A.A., Alamoudi, H., Diaz, M., Qaiser, N., and Hussain, M.M. (2020). Soft actuators for soft robotic applications: A review. Advanced Intelligent Systems, 2(10), 2000128

2020
[7]

Hainsworth, T., Schmidt, I., Sundaram, V., Whiting, G.L., Keplinger, C., and MacCurdy, R. (2022). Simulating electrohydraulic soft actuator assemblies via reduced order modeling. In Proceedings of the IEEE International Conference on Soft Robotics (RoboSoft), 21--28. IEEE, Edinburgh, UK

2022
[8]

Kim, S., Laschi, C., and Trimmer, B. (2013). Soft robotics: A bioinspired evolution in robotics. Trends in Biotechnology, 31, 287--294

2013
[9]

Lyko, B., Katzschmann, R.K., M \"u ller, B., et al. (2024). In vitro testing of an artificial muscle for the treatment of incontinence. In Electroactive Polymer Actuators and Devices (EAPAD) XXVI, volume 12945, 34--43. SPIE

2024
[10]

Mitchell, S.K., Wang, X., Acome, E., Martin, T., Ly, K., Kellaris, N., Venkata, V.G., and Keplinger, C. (2019). An easy-to-implement toolkit to create versatile and high-performance HASEL actuators for untethered soft robots. Advanced Science, 6, 1900178

2019
[11]

Ortega, R., van der Schaft , A., Maschke, B., and Escobar, G. (2001). Interconnection and damping assignment passivity-based control of port-controlled H amiltonian systems. Automatica, 38(4), 585--596. doi:10.1016/S0005-1098(01)00278-3

work page doi:10.1016/s0005-1098(01)00278-3 2001
[12]

Perera, O., Liyanapathirana, R., Gargiulo, G., and Gunawardana, U. (2024). A review of soft robotic actuators and their applications in biomedical engineering. Frontiers in Robotics and AI, 11, 524. doi:10.3389/frobt.2024.000524

work page doi:10.3389/frobt.2024.000524 2024
[13]

Rothemund, P., Kellaris, N., Mitchell, S., Acome, E., and Keplinger, C. (2020). HASEL artificial muscles for a new generation of lifelike robots—recent progress and future opportunities. Advanced Materials, 33(19), 2003375. doi:10.1002/adma.202003375

work page doi:10.1002/adma.202003375 2020
[14]

and Maschke, B

van der Schaft , A. and Maschke, B. (2002). H amiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics, 42(1-2), 166--194. doi:10.1016/S0393-0440(01)00077-3

work page doi:10.1016/s0393-0440(01)00077-3 2002
[15]

Volchko, A., Mitchell, S., Morrissey, T., and Humbert, J. (2024). Model-based data-driven system identification and controller synthesis framework for precise control of siso and miso HASEL -powered robotic systems. Frontiers in Robotics and AI, 11. doi:10.3389/frobt.2024.1333837

work page doi:10.3389/frobt.2024.1333837 2024
[16]

Xiong, Q., Zhou, X., Li, D., and Yeow, R. (2024). Ac-driven series elastic electrohydraulic actuator for stable and smooth displacement output. arXiv preprint

2024
[17]

, " * write output.state after.block = add.period write newline

ENTRY address author booktitle chapter doi edition editor eid howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sent...
[18]

write newline

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[1] [1]

Acome, E., Mitchell, S., Morrissey, T., Emmett, M., Benjamin, C., King, M., Radakovitz, M., and Keplinger, C. (2018). Hydraulically amplified self-healing electrostatic actuators with muscle-like performance. Science, 359, 61--65

2018

[2] [2]

Cisneros, N., Wu, Y., Rabenorosoa, K., and Le Gorrec , Y. (2025). Dynamic modeling of a curling HASEL actuator using the port H amiltonian framework with experimental validation. Mechatronics, 109, 103342. doi:10.1016/j.mechatronics.2025.103342

work page doi:10.1016/j.mechatronics.2025.103342 2025

[3] [3]

Cisneros, N. (2025). PhD Thesis: Modeling and control of HASEL actuators for micro-robotics applications . Ph.D. thesis, École Nationale Supérieure de Mécanique et des Microtechniques, Besançon, France. Defended on January 29, 2025

2025

[4] [4]

Cisneros, N., Wu, Y., Rabenorosoa, K., and Le Gorrec, Y. (2024). Port- H amiltonian modeling and control of a curling HASEL actuator. In IFAC/IEEE CSS Workshop on Control of Systems Governed by Partial Differential Equations CPDE and XI Workshop Control of Distributed Parameter Systems, volume 58, 143--148. Elsevier / IFAC PapersOnLine. doi:10.1016/j.ifac...

work page doi:10.1016/j.ifacol.2024.08.271 2024

[5] [5]

Ehrlich, J., Löscke, P., Ziegler, J., Lacroix, M., and Böse, H. (2025). High performance HASEL actuators as self-healing trigger devices for biomedical diagnostics. Proceedings of SPIE, 13431, 1343109. doi:10.1117/12.3050100

work page doi:10.1117/12.3050100 2025

[6] [6]

El-Atab, N., Mishra, R.B., Al-Modaf, F., Joharji, L., Alsharif, A.A., Alamoudi, H., Diaz, M., Qaiser, N., and Hussain, M.M. (2020). Soft actuators for soft robotic applications: A review. Advanced Intelligent Systems, 2(10), 2000128

2020

[7] [7]

Hainsworth, T., Schmidt, I., Sundaram, V., Whiting, G.L., Keplinger, C., and MacCurdy, R. (2022). Simulating electrohydraulic soft actuator assemblies via reduced order modeling. In Proceedings of the IEEE International Conference on Soft Robotics (RoboSoft), 21--28. IEEE, Edinburgh, UK

2022

[8] [8]

Kim, S., Laschi, C., and Trimmer, B. (2013). Soft robotics: A bioinspired evolution in robotics. Trends in Biotechnology, 31, 287--294

2013

[9] [9]

Lyko, B., Katzschmann, R.K., M \"u ller, B., et al. (2024). In vitro testing of an artificial muscle for the treatment of incontinence. In Electroactive Polymer Actuators and Devices (EAPAD) XXVI, volume 12945, 34--43. SPIE

2024

[10] [10]

Mitchell, S.K., Wang, X., Acome, E., Martin, T., Ly, K., Kellaris, N., Venkata, V.G., and Keplinger, C. (2019). An easy-to-implement toolkit to create versatile and high-performance HASEL actuators for untethered soft robots. Advanced Science, 6, 1900178

2019

[11] [11]

Ortega, R., van der Schaft , A., Maschke, B., and Escobar, G. (2001). Interconnection and damping assignment passivity-based control of port-controlled H amiltonian systems. Automatica, 38(4), 585--596. doi:10.1016/S0005-1098(01)00278-3

work page doi:10.1016/s0005-1098(01)00278-3 2001

[12] [12]

Perera, O., Liyanapathirana, R., Gargiulo, G., and Gunawardana, U. (2024). A review of soft robotic actuators and their applications in biomedical engineering. Frontiers in Robotics and AI, 11, 524. doi:10.3389/frobt.2024.000524

work page doi:10.3389/frobt.2024.000524 2024

[13] [13]

Rothemund, P., Kellaris, N., Mitchell, S., Acome, E., and Keplinger, C. (2020). HASEL artificial muscles for a new generation of lifelike robots—recent progress and future opportunities. Advanced Materials, 33(19), 2003375. doi:10.1002/adma.202003375

work page doi:10.1002/adma.202003375 2020

[14] [14]

and Maschke, B

van der Schaft , A. and Maschke, B. (2002). H amiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics, 42(1-2), 166--194. doi:10.1016/S0393-0440(01)00077-3

work page doi:10.1016/s0393-0440(01)00077-3 2002

[15] [15]

Volchko, A., Mitchell, S., Morrissey, T., and Humbert, J. (2024). Model-based data-driven system identification and controller synthesis framework for precise control of siso and miso HASEL -powered robotic systems. Frontiers in Robotics and AI, 11. doi:10.3389/frobt.2024.1333837

work page doi:10.3389/frobt.2024.1333837 2024

[16] [16]

Xiong, Q., Zhou, X., Li, D., and Yeow, R. (2024). Ac-driven series elastic electrohydraulic actuator for stable and smooth displacement output. arXiv preprint

2024

[17] [17]

, " * write output.state after.block = add.period write newline

ENTRY address author booktitle chapter doi edition editor eid howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sent...

[18] [18]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...