In recent years, robots have increasingly become integral in enhancing human life, particularly with the growing demand for mobile robots with high payload-to-weight ratios and dynamic capabilities. Traditional wheeled or tracked robots are difficult to operate stably in complex real-world environments, which has driven research on legged robots. Legged robots leverage their distinctive "leg" structures to traverse obstacles and adapt to uneven terrain, demonstrating exceptional mobility when confronted with pronounced undulations or soft ground. However, research on legged robots faces a series of difficulties. From the hardware manufacture perspective, leg structures are required to not only support the robot's weight, but also generate sufficient actuation force to drive the entire system. Furthermore, the impact force generated when the foot lifts off or contacts the ground can affect the internal structure, thereby making impact mitigation a critical consideration in the overall design process. From the control perspective, legged robots exhibit substantially greater kinematic and dynamic complexity compared to wheeled or tracked counterparts. This poses a significant challenge to the control architecture, requiring high-precision, real-time coordination between multiple joints and actuators.
Due to the reasons mentioned above, the construction and analysis of complete legged robotic systems remain inherently complex and challenging. "Compared to the complete multi-legged robots (MLRs), single-legged robots (SLRs) feature simpler configurations and typically admit a dynamic gait: hopping. Its hopping period can effectively characterize the behavior of multi legged and single legged structures, making it easier to tackle structural design and dynamic control problems." said the author Jinyuan Liu, a researcher at Zhejiang University, "Therefore, we systematically review the mechanical structure, applications, modeling, and control strategies of SLRs, and outline key challenges and future directions, with the aim of narrowing the gap between engineering implementation and biomimetic motion."
This article takes the single-leg robot (SLR) as a representative "lower-limb unit" for legged robots and develops a systematic review along four axes—structure, modeling, control, and challenges/prospects. On the hardware side, the article organizes SLRs by structure and actuation–elasticity configuration: (i) telescoping designs, centered on a linear prismatic degree of freedom, feature simple mechanisms and planning and suit planar/spatial jumping and baseline validation; and (ii) articulated designs, which biomimetically incorporate multiple joints and are further subdivided by actuation–elastic coupling into rigid (RALR), parallel elastic (PEALR), series elastic (SEALR), and variable stiffness (VSELR) variants. A performance–cost comparison is provided—for example, SEALR attenuates landing impacts and improves efficiency at the expense of structural complexity, whereas VSELR offers adaptability but increases control difficulty and mechanical heft—and a data-oriented survey of representative quadruped platforms (e.g., ANYmal, SpotMini, Cheetah) is used to bridge the path from single-leg to multi-leg systems. At the modeling level, the article delineates two principal lines for SLR research: the SLIP template models and the articulated reduced models. The former capture the core center-of-mass/ground-reaction dynamics via a spring-loaded inverted pendulum and extend to 1/2/3-DoF and other scenarios; the latter perform controlled structural simplifications that facilitate task-level controller design and comparative evaluation. On the control side, the article systematically compares model-based (e.g., VMC/IDC, MPC) and model-free (e.g., CPG, reinforcement learning) strategies: model-based methods offer interpretability and principled constraint handling but depend on accurate models, are sensitive to noise, and incur notable computational cost; model-free methods exhibit adaptability in high-DoF, nonlinear systems, yet face challenges in training cost, interpretability, and practical deployment—especially in transferring from simulation to hardware. Subsequently, the article summarizes the main Sim-to-Real bottlenecks—performance degradation due to sensor noise, actuation delays, and contact uncertainty—and the prevailing remedies, including domain randomization, high-fidelity simulators, and imitation learning, along with guidance for selecting among control strategies.
Finally, the article outlines a multi-pronged research agenda toward "bionic motion": bio-inspired structures, lightweight fabrication (topology optimization, generative design, multi-material additive processes), auxiliary mechanisms (reaction wheels/tails, grasping, jump-fly hybrids), and new materials (high-energy-density elastomers, SMAs/soft actuators), emphasizing tight integration with intelligent control (including privileged-information RL and large-scale planning) to enhance stability, efficiency, and generality in real-world, complex environments.
However, SLRs still face practical gaps—model–reality mismatch under contact uncertainty, complexity–weight and reliability trade-offs in articulated/elastic actuation, energy and thermal limits during high-power transients, real-time compute burdens for whole-body coordination, and limited scalability from SLR templates to multi-leg systems in unstructured terrains. "Therefore, future research should pursue tightly coupled advances in morphology, materials, and control: bio-inspired structures; lightweight fabrication (topology optimization, generative design, multi-material additive processes); auxiliary mechanisms (reaction wheels/tails, grasping, jump-fly hybrids); and new materials (high-energy-density elastomers, SMAs/soft actuators)—all integrated with intelligent control, including privileged-information RL and large-scale planning, to enhance stability, efficiency, and generality in real-world, complex environments," said Jinyuan Liu.
Authors of the paper include Junhui Zhang, Jinyuan Liu, Huaizhi Zong, Pengyuan Ji, Lizhou Fang, Yong Li, Huayong Yang, and Bing Xu.
This work was supported by the National Natural Science Foundation of China (grant no. U24B2049) and the National Natural Science Foundation of China (grant no. U21A20124).
The paper, "Bridging the Gap to Bionic Motion: Challenges in Legged Robot Limb Unit Design, Modeling, and Control" was published in the journal Cyborg and Bionic Systems on Aug. 19, 2025, at DOI: 10.34133/cbsystems.0365.
