Theory of Operation
CCW constant-voltage generation cycle from variable capacitance
HASEL actuators are variable capacitors — zipping increases capacitance. In generation mode: prime at high capacitance (zipped), then allow the electrodes to unzip at constant voltage, reducing capacitance and ejecting charge to a storage element. This forms a counterclockwise (CCW) isopotential loop in the Q–V plane.
Generation Cycle
① Priming
Apply V, zip
↑ Capacitance
Apply V, zip
↑ Capacitance
→
② Generation
Unzip at const V
→ eject charge Q
Unzip at const V
→ eject charge Q
→
③ Discharge
Reduce V to 0
at C_min
Reduce V to 0
at C_min
→
④ Reset
Null V,
force subsides
Null V,
force subsides
E_e,T ≈ (C_max − C_min) × V² / 2 ≈ C_max × V² / 2
η_M = E_e / E_m = E_e / (F × Δx)
C(α) = n_pouches × (ε_r × ε_0 × w) / (2t) × l_e(α) [Kellaris 2019]
η_M = E_e / E_m = E_e / (F × Δx)
C(α) = n_pouches × (ε_r × ε_0 × w) / (2t) × l_e(α) [Kellaris 2019]
HASEL Capacitance Parameters
C_maxMax capacitance (zipped)120–528 pF (2-pouch)
C_minMin capacitance (unzipped)30–45 pF (2-pouch)
ε_rRelative permittivity, BOPP film2.2
tFilm thickness12–18 µm
w / L_p / L_eWidth / Pouch length / Electrode length49–53 / 17.0 / 9.37 mm
Energy Summary
E_e,TMax theoretical energy/cycle (6 kV)≈ 9.5 mJ
E_eBest measured energy/cycle (2-pouch)≈ 4.98 mJ
ρ_EExp. energy density (fluid vol.)2.0 mJ/cm³
ρ_E,TTheoretical energy density (fluid)4.2 mJ/cm³
η_MMax mechanical efficiency≈ 23%
Circuit Design
Adapted from Duranti (2017) dielectric fluid transducer circuit
High-voltage reed relays switch between priming (from storage capacitor C_p), generation (onto C_p), and discharge phases. The Pico Electronics 5VV10-P provides 2000× HV amplification. Architecture adapted from Duranti (2017) constant-voltage circuit for dielectric fluid transducers.
C_pStorage capacitor — primes HASEL and receives generated charge4.7 nF
R_preloadMaintains 20% Pico load (voltage regulation)250 MΩ
R_limitCurrent limiter, varies to maintain 80% Pico load5–15 MΩ
R2 = R3Protect reed relay contacts (max 5 mA)2 MΩ each
S1,S2,S3HV reed relays (Cynergy3 DAT72415P) — 24V coil, 15 kV isolation, SPST-NO~300 ms delay
R_measureSeries resistor + Fluke 80K40 probe → 6000:1 reduction (measuring C_p voltage)5 GΩ + 1 GΩ
HV AmpPico Electronics 5VV10-P — non-isolated, 2000×, 5W max at 2–10 kV2–10 kV
Voltage measurement: Direct probe on C_p gives τ = 1GΩ × 4.7nF = 4.7s — too short to measure. Series resistors → ~5 GΩ total → τ ≈ 23.5s. Trade-off: 30:1 additional signal reduction.
Pico regulation: Unregulated supply — voltage drops at low load. Fixed by 250 MΩ preload parallel with C_p and variable R_limit in series to maintain ≥20% current draw at all times.
Experimental Results — Paper 1
Net energy per cycle across 4×5 voltage × force matrix
Published as "Generating Electricity with HASELs and Their Mechanics" in Energies (MDPI). Full dataset: N ≈ 10–20 per point. Co-authors: Blake Boren & Stephen Chamot (NREL). First experimental demonstration of HASEL energy generation.
4.98 mJ
Max net energy/cycle (6kV, 2000g)
2.49 mJ
Max per single pouch
2.0 mJ/cm³
Experimental energy density
23%
Max mechanical efficiency
Net Energy (mJ) — Full Test Matrix
| Voltage | 200 g | 500 g | 1000 g | 1500 g | 2000 g |
|---|---|---|---|---|---|
| 3 kV | 0.33 ± 0.10 | 0.68 ± 0.09 | 1.04 ± 0.08 | 1.28 ± 0.10 | 1.80 ± 0.14 |
| 4 kV | 0.58 ± 0.19 | 1.16 ± 0.19 | 1.76 ± 0.54 | 2.14 ± 0.16 | 2.96 ± 0.17 |
| 5 kV | 0.77 ± 0.27 | 1.63 ± 0.30 | 2.58 ± 0.29 | 3.11 ± 0.28 | 4.17 ± 0.28 |
| 6 kV | 0.83 ± 0.38 | 1.90 ± 0.27 | 3.15 ± 0.37 | 3.74 ± 0.48 | 4.98 ± 0.37 |
Energy formula: E_e = −½ C_h V₃² + ½ C_p(V₄² − V₃²) + ½ C_l V₄². States 3→4 = generation phase. Priming energy consumed (negative); generation energy recovered (positive).
Comparison to Other Electrostatic Generators
| Metric | HASEL (This Work) | DFT – Duranti 2017 | DEG – Moretti Review |
|---|---|---|---|
| Exp. energy/cycle | 2.49 mJ/pouch | 4.8 mJ | — |
| Exp. energy density (fluid) | 2.0 mJ/cm³ | — | — |
| Exp. energy density (film mass) | 85 mJ/g | 179 mJ/g | up to 780 mJ/g |
| Mechanical efficiency | 23% | ~30% | — |
| Self-healing | Yes (dielectric fluid) | Yes | No (solid film) |
Power Output & Frequency Study
NREL MEGSRP Appointment — Jan–Jul 2025
Investigates cyclic energy harvesting and power density vs. cycling frequency (0.5–20 Hz, 2–5 kV). Key question: does power scale linearly as P = E·f, or do viscous losses or circuit limits reduce performance at higher frequencies?
Hypothesis
Linear P vs. Frequency
If HASEL is in the inertial regime (Rothemund 2020), energy/cycle is constant and P = E·f is linear. Artimus confirmed this. Experiment will verify quantitatively.
Circuit Innovation
AC Coupling for Self-Sensing
HV DC priming + low-amplitude high-freq AC superimposed. Coupling capacitor = generator bank AND AC conduit. Sensing is never lost during open-circuit generation phase.
Hardware
Motorized Test Bench
ClearPath servo motor + ball screw (5.08 mm/rev, 800 cts/rev, 7 mm free stroke). NI cRIO DAQ + Labview at 1 kHz. Raspberry Pi controls motor PWM. Data to USB as TDMS.
Circuit Limits
Frequency Constraints
Reed relay ~300 ms → ~3 Hz limit (fully switched). RC: τ = 4.7 nF × 2 MΩ = 9.4 ms → 106 Hz limit. HASEL inertial/viscous regime per oil viscosity and geometry.
Test Matrix (Paper 2)
| Independent Variable | Range | Dependent Variables |
|---|---|---|
| Cycling frequency | 0.5 – 20 Hz | Net energy/cycle, power output (P = E·f) |
| Priming voltage | 2 – 5 kV | Energy per cycle, power density |
| Timing: scheduled vs. sensor feedback | Fixed / feedback-controlled | Energy deficiency vs. ideal schedule |
Rothemund (2020): HASEL is inertial if τ_v/τ_i = μwL^½/Mg^½ ≪ 1. In the inertial regime, t_n ∝ L^½, independent of viscosity. Artimus commercial HASELs operate here — linear P vs. f expected.
Capacitive Self-Sensing
AC impedance sensing for real-time deformation feedback
By superimposing a low-amplitude, high-frequency AC signal on the driving voltage, capacitance — and therefore deformation — can be read in real time without additional sensors. Known as Data-over-Power / Power Line Communication. Artimus Robotics demonstrates single-digit gram sensitivity on commercial HASELs.
X_C = 1 / (ω · C) · Z = √(R² + X_C²) · C ≈ 1 / (2π f X_C)
Key Challenge
Sensing During Open-Circuit Generation
Standard DEG self-sensing fails when the device is disconnected from the HV supply. The dual-purpose coupling capacitor (C_p = generator bank) keeps the AC path active — sensing never interrupted.
Signal Processing
Rizzello RLS Algorithm
Recursive Least Squares on discretized RC circuit state equation extracts capacitance each time step. Issues above ~2 Hz from filtering delay. Separate model branches for generation and discharge phases.
Artimus Guidance
Implementation Notes
Target differential (not absolute) capacitance. Supply AC on low side (Ly 2021). Use ≥10 kHz for low impedance. Thin-film capacitors (not ceramic) — ceramic capacitance drops significantly with voltage.
HASEL Memcapacitance
Nonlinear C vs. V characterization with hysteresis — April 2026
Goal: map the HASEL's nonlinear capacitance as a function of voltage with hysteresis — producing Q vs. V and C vs. V plots at different bias frequencies. This characterizes the memcapacitive behavior (capacitance depends on voltage history) and is key to understanding frequency-dependent energy harvesting.
Method (Acome 2018 approach): Superimpose a low-amplitude triangular wave (~100 Hz) onto a large-amplitude sinusoidal bias (~1 Hz, ±5 kV). Since I_c = C·dV/dt, the triangular wave induces a square-wave current whose amplitude is proportional to capacitance. As the bias sweeps, the AC current amplitude traces C vs. V — including hysteresis from internal fluid dynamics.
Signal Parameters
BiasLow-freq sinusoidal carrier±5 kV, ~1 Hz
AC probeHigh-freq triangular wave (probes capacitance)~5% carrier amp, ~100 Hz
Freq ratioAC / bias (should be ≫ 1 for quasi-static bias)~100×
LoadApplied weight to partially stretch HASEL~100 g
VariableVary bias frequency to map frequency-dependent hysteresisMultiple runs
Equipment
AmplifierTrek 10/10B-HS — 1000 V/V, ±10 kV, ±10 mA, slew >700 V/µs
HASEL2-pouch Peano-HASEL (old style)
Signal genWaveform generator (bias + triangular wave outputs)
DAQOscilloscope or DAQ for current + voltage measurement
Physical interpretation: Hysteresis in C vs. V arises because internal fluid dynamics have a finite response time — at high bias frequencies, fluid cannot fully redistribute before voltage reverses, so capacitance traces a different path on charge vs. discharge. Slower bias → more equilibrium → less hysteresis.
Connection to energy harvesting: The area enclosed by the Q–V loop is the net electrical energy harvested per cycle. Memcapacitance measurements directly visualize this quantity and how it changes with frequency and voltage — linking to the power vs. frequency MEGSRP study.
Nebula EH on Bending Structure
Gantry base-excitation experiments — Oct–Dec 2025
Integrates HASEL energy harvesting with bending motion — simulating a robotic fish in a Kármán vortex street. The gantry provides sinusoidal base excitation; HASEL pouches on the bending structure generate electricity. DIC captures the zipped area as a proxy for capacitance change. The phase relationship between base excitation and HASEL strain governs when to trigger the EH cycle.
First attempt (Oct 2025) — failed: No energy generated. The front HASEL was broken, and the timing code was phased for it — experiments ran 180° out of phase. Subsequent FRF sweeps showed π/2 phase offset between base excitation and HASEL strain at 1 Hz. Corrected for second trial.
Dec 3, 2025
Natural Frequency Identification
Modal impact hammer: ωₙ ≈ 12 Hz (5 mm TPU + HASELs), ≈ 9 Hz (slacked). New 2.5 mm skeleton → ωₙ ≈ 6 Hz. Bending visually confirmed at 6 Hz excitation.
Dec 17, 2025
DIC Energy Harvesting Tests
HASEL slacked with standoffs for more strain per bend. ωₙ ≈ 4 Hz. Square wave actuation (180° offset, 4 Hz, 5 kV). Phase offset φ ≈ −0.43 ± 0.05 rad measured via DIC.
Model
FEA Under Base Excitation
FEA predicts capacitance change as a function of frequency, amplitude, and phase. Used to design optimal EH cycle timing and predict power output across a frequency sweep.
Key Insight
Resonance Maximizes Power
At resonance, large deformation → large capacitance swing → more energy/cycle. Optimal phase offset between EH trigger and base excitation shifts with frequency per the FRF.
Gantry Experimental Settings
LDV BWVibrometer bandwidth1 kHz
Velo rangeMax ~0.38 m/s at 13 rad/s × 0.03 m1 m/s
Disp rangeMax 60 mm peak-to-peak100 mm
DAQdSpace + Artimus 8-ch ARDI supply192.168.202.220
Env.October: 18°C 60% RH · November: 22°C 45% RH—