Legless soft robots capable of rapid, continuous, and steered jumping

The study addresses the challenge of enabling soft terrestrial robots to achieve both high single-jump performance (height and distance) and high-frequency continuous locomotion for efficient obstacle crossing. Existing soft jumpers either store energy (springs, SMAs, magnetic, light-driven, DEAs) achieving large jumps but with slow cycles and complex mechanisms, or use direct bending actuation (DEAs, PVDF) to jump rapidly but with insufficient height (<0.25 body height) for obstacle traversal. Electrohydraulic HASEL actuators can actuate rapidly and continuously but previously produced primarily vertical jumps and suffered from isotropic liquid flow that cancels forward momentum, slow restoration due to gravity-driven backflow, and limited single-jump performance without stacking. The paper proposes a legless soft jumping robot (LSJR) using a soft electrohydrostatic bending actuator (sEHBA) that leverages anisotropic dielectric liquid redistribution and a prebent ring frame to convert electrohydraulic action into rapid, repeatable forward and vertical propulsion, enabling rapid, continuous, and steered jumping with improved obstacle-crossing ability.

The paper reviews soft and partially soft jumping robots driven by integrated springs, SMAs, magnetic actuators, light-powered actuators, DEAs, pneumatic, chemical, motorized systems, and PVDF actuators. Energy-storing approaches achieve high single-jump performance but suffer from prolonged energy storage that lowers frequency and landing stability. Direct-bending soft robots (DEAs, PVDF) enable rapid cycles but insufficient jump heights for obstacles. HASEL actuators offer high strain, high strain rates, and high specific power; stacked quadrant donut HASELs achieve vertical jumping (~1.67 body heights), yet isotropic liquid flow cancels forward propulsion, partial pouch expansion causes unstable take-off, and gravity-driven liquid return slows restoration. Prior DEA designs using saddle-shaped bending via frames inform the current strategy to combine electrohydrostatic actuation with a prestrained ring frame to realize efficient, repeatable propulsion.

Design and principle: The LSJR employs a soft electrohydrostatic bending actuator (sEHBA) constructed from two flexible semicircular pouches (BOPP film) heat-sealed into a semicircular separated HASEL structure. The front pouch contains dielectric liquid and has electrodes; the rear pouch contains air (same volume) without electrodes. A flexible PVC ring frame is fixed around the perimeter and prestrained to guide deformation into a saddle-shaped bend. Applying high voltage creates Maxwell stress that squeezes the dielectric liquid from the electrode-covered outflow region into the non-electrode inflow region, producing rapid, anisotropic flow that imparts forward kinetic energy and drives frame bending. The prebent frame directs vertical and horizontal ground reaction forces for take-off and stores elastic energy for immediate post-landing restoration, enabling rapid cycle times (~10 ms actuation). Design iterations and comparisons: Initial SCS-HASEL and liquid–air variants showed forward jumping due to anisotropic flow but unstable partial pouch expansion and poor restoration. Adding a prebent ring frame constrained deformation, enabled regular saddle-shaped bending, higher and further jumps, and rapid restoration; the liquid–air actuator with prebending corresponds to the final sEHBA. Fabrication: Conductive graphene ink is screen-printed on 16 μm BOPP films; electrodes cure at room temperature (12 h). Two BOPP-electrode films are heat-sealed to form two semicircular pouches (55 mm diameter), leaving fill ports. The front pouch is filled with 1 mL of transformer oil; the rear pouch with equal-volume air; bubbles are expelled and ports sealed. A laser-cut PVC ring frame (0.5 mm thick; inner 58 mm; outer 62 mm) is inserted between films, predeformed and heat-sealed to impart desired prebend (controlled by displacement during heat setting). Final perimeter heat seals and trimming complete the 1.1 g, 65 mm-long LSJR; aluminum tapes connect electrodes. Materials: BOPP film (dielectric breakdown ~700 V/μm; tensile strength ~300 N/mm²), transformer mineral oil (favorable dielectric properties, low viscosity), graphene conductive ink electrodes (~20 μm), and PVC ring frame (low density, good mechanical properties) are used. Control strategy: For single jumps, the LSJR tail electrodes contact copper pads; a square-wave high voltage (10 ms on) triggers a single jump as the connection breaks on take-off. Polarity is reversed between tests and a 60 s wait used to mitigate charge retention. For continuous locomotion, wired connections are used; square-wave actuation with 10 ms on-time at 0.25–8 Hz; polarity alternation reduces charge accumulation. For turning, two LSJRs are coupled side-by-side; square-wave voltage (4 Hz, 10 ms on) is selectively applied to one unit to induce turning. Obstacle tests use 10 kV, 4 Hz, 10 ms on. Experimental setup: A high-speed camera (for single jumps) and DSLR/smartphone cameras (for continuous and obstacle tests) record motion. Substrate surface textures are characterized by confocal microscopy. A high-voltage amplifier and relays, controlled by a microcontroller board, supply actuation. Parametric studies: The effects of electrode area to non-electrode area ratio (r = 2:1, 1:1, 1:2), applied voltage (0–10 kV), load (0, 1, 2 g), and prebending level (body height BH = 2, 4, 6 mm) on jump distance (JD) and height (JH) are characterized. Continuous forward jumping speed (CFJS) is measured on substrates with different roughness (glass, paper, PVC, wood) across frequencies and voltages. Turning speed (TS) of dual-body LSJR is measured across substrates and voltages. Obstacle crossing is evaluated over slopes, wires, steps, multiple steps, gravel mounds, and ring obstacles.

- Performance summary: 1.1 g, 65 mm LSJR achieves single-jump JH = 30.7 mm (7.68 body heights) and JD = 95.0 mm (1.46 body lengths) at 10 kV with r = 1:1 (front pouch electrode:non-electrode area), and continuous forward jumping speed CFJS = 390.5 mm/s (6.01 BL/s) at 10 kV, 4 Hz on wood. - Rapid actuation and restoration: Actuation time ~10 ms; rapid elastic restoration enables ~4 Hz continuous cycles with stable landing (low profile, no capsizing). - Parametric effects: • Electrode coverage ratio r: r = 1:1 yields highest JD and JH; r = 2:1 reduces flexibility and flow volume, diminishing performance. • Loads: 1 g load (0.91 body weight) reduces JD to 56.0 mm and JH to 20.0 mm (59% and 65% of no-load); 2 g load (1.82 BW) reduces JD to 33.7 mm and JH to 8.1 mm (35% and 26%). • Prebending (BH): With 10 kV, RJH (JH/BH) = 9.4 (BH 2 mm), 7.7 (BH 4 mm), 4.2 (BH 6 mm); BH = 4 mm maximizes JD and JH. - Continuous locomotion on substrates (10 kV): At 4 Hz, average CFJS: wood 390.5 mm/s; PVC ~250.1 mm/s (example run; angle deviation per jump <8°); paper intermediate; glass 95.6 mm/s due to low friction. Frequencies >8 Hz may trigger in-air actuation, impairing performance. - Steering with dual-body LSJR: Turning speed (TS) up to 138.4°/s at 10 kV, 4 Hz on wood; on glass 27.9°/s. Example: 80° turn in 1.23 s at 10 kV, 4 Hz on PVC (65.0°/s). - Obstacle crossing (10 kV, 4 Hz): • Single LSJR: climbs 3° glass slope at 16.3 mm/s; crosses 6.3 mm diameter wire; jumps an 8 mm step; surmounts continuous steps (8 mm + 5 mm). Maximum obstacle height crossed (tested at 4 mm intervals): 14 mm for cuboids; 18 mm for triangular prisms and cylinders. Traverses gravel mound (3–6 mm gravel). • Dual-body LSJR: straight and steered jumps over 5 mm round step; crosses ring obstacle (height 8 mm; inner diameter 77 mm; outer diameter 83 mm). - Precision: In continuous forward jumping on PVC at 250.1 mm/s (4 Hz, 10 kV), per-jump angle deviation <8°, enabling near straight-line travel. - Comparative advantage: Achieves large relative JH (7.68 BH) with rapid cycles (~0.01 s on-time) and fastest reported soft-robot turning (138.4°/s), overcoming limitations of prior HASEL jumpers (no forward/steered jumps, limited single-jump without stacking, slow restoration).

The LSJR leverages anisotropic electrohydrostatic liquid redistribution and a prestrained ring frame to convert electrostatic forces into forward and vertical ground reaction forces for take-off, resolving the trade-off between jump height and cycle time seen in energy-storing soft jumpers. Rapid fluid motion and elastic frame recoil provide both propulsion and quick restoration, enabling continuous, efficient locomotion and steering with simple control. The design addresses prior HASEL limitations by directing liquid flow to generate forward momentum, stabilizing deformation via the ring frame for repeatable, high jumps, and enabling fast backflow independent of gravity. Demonstrations across varied substrates and obstacles show practicality for agile navigation in unstructured terrains. However, performance depends on surface friction; smooth surfaces reduce CFJS and TS, indicating potential for enhancements (e.g., electroadhesion). The modular dual-body configuration offers precise direction control and improved obstacle negotiation, highlighting the approach’s relevance to fast, multimodal soft robotic mobility.

This work introduces a tethered legless soft jumping robot (LSJR) based on a soft electrohydrostatic bending actuator that achieves rapid, continuous, and steered jumping with high single-jump performance (7.68 BH; 1.46 BL) and fast continuous speed (6.01 BL/s), and state-of-the-art turning (138.4°/s). The combination of anisotropic dielectric liquid flow and a prebent ring frame enables short actuation times (~10 ms), stable landings, and robust obstacle crossing over varied terrains and obstacles. Future directions include: scaling and parametric optimization of sEHBA for enhanced performance; developing an untethered LSJR and its applications; integrating additional sensing for environmental monitoring; and extending sEHBA to other soft robotic platforms (wall-climbing, swimming, flapping-wing robots).

- Dependence on substrate friction: Smooth surfaces (e.g., glass) reduce continuous speed (95.6 mm/s) and turning speed (27.9°/s), limiting performance; potential mitigation via electroadhesion on the rear pouch. - Tethered operation: Current demonstrations require external high-voltage supply; untethered power and control remain future work. - Charge retention: Requires polarity reversal and wait times (60 s in single-jump tests) to alleviate residual charge, complicating control at high duty cycles. - Frequency constraints: At >8 Hz, in-air actuation can occur before landing, degrading performance; closed-loop timing or adaptive waveforms are needed. - Load sensitivity: Added mass significantly reduces JD and JH (up to ~70% with 2 g load), constraining payload capacity. - Maximum obstacle height below max JH: Due to leaping posture and interaction with obstacles, maximum surmountable obstacle height is less than peak jump height.