A Deployable Bio-inspired Compliant Leg Design for Enhanced Leaping in Quadruped Robots
Authors: Yiyang Chen, Yuxin Liu, Jinzheng Zhou, Fanxin Wang, Qinglei Bu, Jie Sun, Yikun Cheng
Organizations: Department of Mechatronics and Robotics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China. · Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Champaign, Illinois, United States.
Quadruped robots are becoming increasingly essential for various applications, including industrial inspection and catastrophe search and rescue. These scenarios require robots to possess enhanced agility and obstacle-navigation skills. Nonetheless, the performance of current platforms is often constrained by insufficient peak motor power, limiting their ability to perform explosive jumps. To address this challenge, this paper proposes a bio-inspired method that emulates the energy-storage mechanism found in froghopper legs. We designed a Deployable Compliant Leg (DCL) utilizing a specialized 3D-printed elastic material, Polyether block amide (PEBA), featuring a lightweight internal lattice structure. This structure functions analogously to biological tendons, storing elastic energy during the robot's squatting phase and rapidly releasing it to augment motor output during the leap. The proposed mechanical design significantly enhances the robot's vertical jumping capability. Through finite element analysis (FEA) and experimental validation, we demonstrate a relative performance improvement of 17.1% in vertical jumping height.
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Fig. 1 : Illustration of the Jumping Actuation Challenge. (Left) The baseline robot, limited by motor torque saturation, fails to reach the critical height. (Right) The proposed system, augmented with DCLs, releases extra stored elastic energy and completes the task (symbolized by the coin).
Fig. 2 : (a-e) Design workflow of the bio-inspired quadruped leaping enhancement; (b) The biological prototype [ 12 ] .
Fig. 3 : Bio-inspired design concept of the robotic leg. (a) The Philaenus spumarius, serving as the biological prototype [ 12 ] . (b) Biological mechanism highlighting the interaction between the rigid hard cuticle and the energy-storing resilin [ 12 ] . (c) The proposed quadruped robot integrated with the SSCMs. (d) Mechanical design overview.
Fig. 4 : The Gyroid lattice structure designed in nTop, shown (A) as a unit cell and (B) implemented as the internal filler of the compliant structure.
Fig. 5 : Operational states of the deployable mechanism. (a) In the Stowed State, the mechanism retracts to eliminate parasitic stiffness. (b) In the Deployed State, the module rotates 90 degrees to align with the femur for ballistic energy storage.
Fig. 6 : Exploded view of the kinematic chain. Key components: (1) SSCM Lattice, (2) Push Rod, (3) Top Cap, (4) Rotating Sleeve, (5) Return Spring, (6) Inner Fixed Post, (7) Guide Pin, (8) Sliding Block, and (9) Locking Pin. The mechanism converts linear input into a precise 90-degree rotation via a helical cam constraint.
Fig. 7 : Rigorous stiffness characterization and operating bounds. FEA raw data (blue circles) validates the structural integrity up to 45∘ . The Analytical Model (solid red line) is a 3rd -order polynomial fitted to the Operating Region ( 0∘ – 29∘ ) with maximize torque 6.8N⋅m . The Safety Margin (blue zone) provides a ≈10∘ buffer before the Design Limit Line (red, 39∘ ), beyond which the structure enters the Densification Region (red zone).
Fig. 8 : The physical experimental setup. (A) The attached tracking balls (each rigid body circled in one color). (B) The established Unitree Go2 model in the Luster FZMotion motion capture system.
Fig. 9 : Composite time-lapse photography of the vertical jumping experiments. (Left) The Baseline group (Unitree Go2 without payload) reaching a peak height of 656.3 mm. (Middle) The Stowed group (passive mass) reaching 654.9 mm, demonstrating negligible parasitic effect (0.33% reduction) from the added mass. (Right) The Deployed group utilizing the PEBA lattice energy release, achieving a peak height of 720.3 mm, a 17.1% increase over the baseline. The white dashed reference line indicates the baseline peak height.
Quadrupedal wheeled-legged robots combine the advantages of legged and wheeled locomotion to achieve superior mobility, but executing dynamic jumps remains a significant challenge due to the additional degrees of freedom introduced by wheeled legs. This paper develops a mini-sized wheeled-legged robot for agile motion and presents a novel motion control framework that integrates the Nonlinear Model Predictive Control (NMPC) for locomotion and the Differential Evolution (DE) based trajectory optimization for jumping in quadrupedal wheeled-legged robots. The proposed controller utilizes wheel motion and locomotion to enhance jumping performance, achieving versatile maneuvers such as vertical jumping, forward jumping, and backflips. Extensive simulations and real-world experiments validate the effectiveness of the framework, demonstrating a forward jump over a 0.12 m obstacle and a vertical jump reaching 0.5 m.
Xuanqi Zeng, Lingwei Zhang, Linzhu Yue +4
Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong
We demonstrate a jumping robot that reaches high (7.6 m) and fast (190 ms stance time) jumps from a single long leg driven by a direct-drive transmission, without elastic energy storage. At 281 g, it achieves the highest jump yet reported for an electrically actuated, spring-free system. The leg uses a new fabric-wrap transmission that provides a variable mechanical advantage, keeping a small electric motor near its peak power output through the stroke while bracing the long, lightweight leg against buckling. A balancing module at the top of the leg uses small propellers to control the leg's orientation on the ground and in the air, where the long leg provides a large moment arm for the control torques. The robot is validated outdoors with vertical jumps, attitude control on the ground and in flight, and tilted jumps.
Gihyeok Na, Justin K. Yim
Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign, IL 61801 USA
We present the design and implementation of HASTA (Hopper with Adjustable Stiffness for Terrain Adaptation), a vertical hopping robot with real-time tunable leg stiffness, aimed at optimizing energy efficiency across various ground profiles (a pair of ground stiffness and damping conditions). By adjusting leg stiffness, we aim to maximize apex hopping height, a key metric for energy-efficient vertical hopping. We hypothesize that softer legs perform better on soft, damped ground by minimizing penetration and energy loss, while stiffer legs excel on hard, less damped ground by reducing limb deformation and energy dissipation. Through experimental tests and simulations, we find the best leg stiffness within our selection for each combination of ground stiffness and damping, enabling the robot to achieve maximum steady-state hopping height with a constant energy input. These results support our hypothesis that tunable stiffness improves energy-efficient locomotion in controlled experimental conditions. In addition, the simulation provides insights that could aid in the future development of controllers for selecting leg stiffness.
Rongqian Chen, Jun Kwon, Kefan Wu +1
George Washington University · General Robotics, Automation, Sensing & Perception Lab at the University of Pennsylvania · University of Connecticut