Jumping robots offer significant advantages in traversing challenging environments, extending navigation range, and overcoming obstacles. However, achieving both rapid continuous jumping and directional control remains a significant engineering challenge. Current soft jumping robots often excel in single-jump performance (jumping height and distance) but compromise on jumping frequency due to energy storage mechanisms. Conversely, robots using pneumatic, chemical, or motor actuation often feature complex structures and navigation strategies. Lightweight robots using dielectric elastomer actuators (DEAs) or PVDF actuators demonstrate high jumping frequencies but lack sufficient jump height and distance for obstacle crossing. Hydraulically amplified self-healing electrostatic (HASEL) actuators present a promising alternative due to their linear motion capabilities, high actuation strains, and rapid strain rates. However, the isotropic liquid flow in donut HASEL actuators limits their use in forward or steered jumping due to energy loss. Previous HASEL jumpers struggle to achieve enhanced single-jump performance without stacking, rapid restoration, and the ability to generate forward and steered jumping motions. This research addresses these limitations by redesigning the actuator structure to induce anisotropic liquid flow and utilize the generated kinetic energy for forward jumping. Inspired by the saddle-shaped bending in DEA-based locomotion, the researchers incorporate a frame-membrane structure to enhance jumping performance. The resulting electrohydrostatically driven tethered legless soft jumping robot (LSJR) incorporates a soft electrohydrostatic bending actuator (sEHBA) to achieve rapid, continuous, steered jumping, and obstacle-crossing capabilities.

The paper reviews existing soft jumping robots, categorized by their actuation methods: integrated springs, shape memory alloys (SMAs), magnetic actuators, light-powered actuators, DEAs, pneumatic actuators, chemical actuators, motors, and PVDF actuators. Energy-storing jumping robots, often utilizing springs or SMAs, prioritize single-jump performance at the expense of jumping frequency. Robots with pneumatic, chemical, or motor actuation exhibit complex structures and navigation, while lightweight DEA and PVDF-based robots achieve high frequency but limited jump height. HASEL actuators show potential for continuous actuation but lack the ability to generate forward or steered jumps due to isotropic liquid flow. The authors highlight the need for a design that balances high single-jump performance and rapid jumping frequency, which is lacking in existing robots.

The researchers developed a soft electrohydrostatic bending actuator (sEHBA) to address the limitations of existing HASEL actuators. This involved creating a semicircular separated HASEL (SCS-HASEL) actuator, replacing the rear semicircular pouch's dielectric liquid with air, and removing the rear pouch electrodes to achieve anisotropic liquid flow. Experiments compared different actuator configurations, including those with and without pre-bent frames, demonstrating the improved jumping performance with pre-bent frames. The legless soft jumping robot (LSJR) design consists of two flexible plastic semicircular pouches, with the front pouch filled with dielectric liquid and the rear with air. A pre-strained PVC ring frame is fixed to the edge. The application of a high voltage to the electrodes creates Maxwell forces that squeeze the dielectric liquid, generating horizontal kinetic energy. The resulting deformation and frame bending propel the robot forward. The pre-bent frame guides the deformation, enhancing jumping performance and facilitating quick restoration of the initial state after landing. Fabrication involved screen-printing electrodes onto biaxially oriented polypropylene (BOPP) films, heat-sealing the pouches, filling them with dielectric liquid and air, and attaching the pre-bent frame. The experimental setup utilized high-speed cameras to record jumping motions. The control strategy involved applying a high voltage for 10ms to initiate a jump. Single-jump characterization involved varying the electrode area ratio, applied voltage, and load to assess jump distance and height. Continuous jumping tests examined the effect of actuation frequency and substrate surface roughness on continuous forward jumping speed (CFJS). Steered jumping was achieved by connecting two LSJRs abreast and selectively applying voltage to each unit. Obstacle-crossing tests assessed the robot's ability to traverse various obstacles, including slopes, wires, steps, and gravel mounds. The paper includes detailed descriptions of materials, fabrication, and experimental procedures.

The developed LSJR demonstrates significant improvements in jumping performance compared to existing soft robots. Key findings include: * **High Jumping Performance:** The LSJR achieved a jump height of 7.68 body heights and a jump distance of 1.46 body lengths in a single jump. This performance is significantly higher than most previously reported soft jumping robots. * **Rapid Continuous Jumping:** The robot achieved a continuous forward jumping speed of 390.5 mm/s (6.01 body lengths per second) at an actuation frequency of 4 Hz. This speed is substantially higher than that of most existing soft jumping robots. * **Steered Jumping:** Integrating two LSJRs enabled steered jumping with a turning speed of 138.4°/s, the fastest reported for soft jumping robots. * **Obstacle-Crossing:** The LSJR successfully navigated various obstacles including slopes, wires, steps, and gravel mounds, demonstrating its adaptability to unstructured environments. The maximum obstacle height crossed was 18 mm (for triangular prisms and cylinders). * **Lightweight and Compact Design:** The robot has a low profile (0.85 mm thick), lightweight design (1.1 g) and simple control strategy, making it highly modular and cost effective.

The LSJR addresses the limitations of existing soft jumping robots by combining high single-jump performance with rapid continuous jumping and steered locomotion. The innovative sEHBA design, incorporating anisotropic liquid flow and a pre-bent frame, is key to this success. The robot's performance surpasses that of previous soft jumping robots across multiple metrics, demonstrating its potential for applications requiring high agility and speed. The ability to navigate various obstacles, including those larger than the robot itself, highlights the effectiveness of the design. Although tethered in this study, the modular and lightweight design lends itself to future development of untethered versions. The ability to integrate sensors opens possibilities for environmental monitoring and other applications.

This study successfully designed and fabricated a legless soft jumping robot (LSJR) that exhibits superior jumping performance in terms of height, distance, speed, and turning capability compared to existing soft robots. The innovative soft electrohydrostatic bending actuator (sEHBA) is crucial to this achievement. Future work will focus on developing an untethered LSJR and exploring further applications such as wall-climbing and swimming robots, as well as exploring the scalability and parametric optimization of the sEHBA to further enhance performance.

The current study utilizes a tethered LSJR, limiting its applicability in certain environments. The performance of the robot is also affected by substrate surface roughness, with smoother surfaces resulting in lower continuous forward jumping speeds and turning speeds. The exploration of additional surface texture manipulation through electroadhesion is warranted. Finally, while the current design achieved remarkable jumping and turning capabilities, comprehensive analysis of its energy efficiency and the impact of different dielectric liquids would enhance understanding and further optimization.