Bionic mudskippers are new amphibious robots, however existing designs lag far behind their biological prototypes in cross-medium locomotion and terrestrial adaptability. To bridge this gap, this paper proposes an untethered tensegrity mudskipper robot with water-land bidirectional locomotion, obstacle crossing, and real-time locomotion adjustment via pectoral-caudal fin coordination. We detail its overall structure and tensegrity X-joint body. The pectoral fins feature an asymmetric stiffness design, providing high stiffness during the power stroke and low stiffness during the recovery stroke. Using a validated tensegrity X-joint kinematic model, the robot generates smooth body waves using a single servo motor to drive the caudal fin. We further model and experimentally validate the crawling process facilitated by the variable-stiffness pectoral fins, quantifying its speed and obstacle-crossing height. Extensive tests demonstrate the wide-range adjustability via pectoral-caudal fin coordination: maximum turning speed increased by 302% and minimum turning radius reduced to 0.57 body lengths. Finally, field tests demonstrated its robust adaptability to complex environments: rough terrain, cobblestone path, water-land transitions, like grassy shores.This work not only provides a novel prototype for amphibious robotic research but also offers new insights into the coordination mechanisms of biological appendages, potentially inspiring future designs in cross-medium locomotion control and bio-inspired robotics.

Biomimetic robotic fish offer significant potential for underwater inspection and aquaculture monitoring due to their superior maneuverability and efficiency. However, existing systems often lack diverse operational modes and intuitive human-machine interaction. Inspired by the archerfish's predatory water-shooting behavior, this paper proposes a biomimetic robotic fish featuring controllable water-jetting and gesture-based interaction. The modular mechanical design integrates a micro-pressurized jetting mechanism, a single-joint caudal fin, and pectoral fin pitch adjustment to achieve multi-modal locomotion, including jetting, swimming, and turning. Based on an STM32 microcontroller, the control system leverages MediaPipe for real-time gesture recognition, mapping user gestures to motion commands via serial communication. Experiments, including jet velocity calibration and underwater locomotion tests, demonstrate that the robot stably executes prescribed maneuvers and responds to gesture controls, verifying the feasibility of the proposed design and control scheme.

Accurate and robust state estimation under dynamic and degraded GNSS conditions remains a key challenge for autonomous robotic navigation. Conventional extended Kalman filters commonly rely on Euclidean additive-error linearization, which may not preserve the intrinsic Lie-group geometry of rigid-body motion and can lead to inconsistency, while many existing InEKF formulations rely on a selected invariant-error representation, which limits multi-source fusion. To overcome these limitations, this paper presents a Deep Sequential Invariant Extended Kalman Filter (DS-InEKF) that unifies left- and right-invariant error representations within a sequential fusion framework and incorporates deep-learning-based adaptive covariance estimation. The proposed architecture re-expresses the local posterior covariance between heterogeneous invariant-error coordinates through an explicit common-state representation, while adaptively estimating measurement noise covariances from sensor-quality features. Experiments on real-world vehicle and wheeled-robot datasets demonstrate that DS-InEKF achieves higher localization accuracy and stability than representative conventional and learning-augmented baselines, reducing horizontal position RMSE by up to 20% and reducing yaw and velocity errors on the evaluated sequences. Its robustness is further verified under controlled degradation tests, including injected yaw misalignment and short-term GNSS outage, where the method maintains more stable error behavior in challenging navigation conditions. These results indicate that combining invariant geometry with adaptive noise modeling provides a unified, data-driven framework for reliable state estimation in complex navigation scenarios.

Abstract Cross-medium multi-rotor aerial robots overcome the limitations of conventional single-medium platforms by adopting adaptive multimodal structural designs. By leveraging adaptive and morphing structures, they achieve flexible switching and collaborative operations among aerial, terrestrial, and aquatic domains. This capability creates new opportunities for challenging missions such as disaster response, environmental monitoring, and ocean exploration. This paper focuses on multiple application scenarios of cross-medium multi-rotor aerial robots. It also classifies the robots’ structural designs. In addition, the paper summarizes recent progress and application scenarios for terrestrial–aerial, aerial–aquatic, and terrestrial–aquatic-aerial triphibious multi-rotor robots. Furthermore, the paper analyzes key technical aspects, including modeling and control, endurance, safety, smart structures, and perception. Finally, this paper discusses the challenges and development trends faced by cross-medium multi-rotor aerial robots. It also discusses future research directions.

Magnetic miniature robotic fish present significant potential for targeted drug delivery and non-invasive surgery. However, existing dynamic models assume constant stiffness, which restricts their capability to accurately capture the complex magnetically driven fluid–structure interactions with stiffness variation. This study proposes a novel magnetic miniature robotic fish featuring discrete stiffness variation, designed based on the tensegrity principle. The robot comprises a flexible head and a compliant tail connected through tensegrity rotational joints. The overall body stiffness is varied by adjusting the structural stiffness of the tensegrity joints. A data-driven dynamic model based on the Koopman operator is developed to address the challenges posed by nonlinear stiffness variations and magnetically induced multiphysics coupling. This model incorporates key physical factors, including magnetic field intensity, actuation frequency, and structural stiffness. The model’s distinctive capability lies in providing a unified dynamic representation across multiple stiffness configurations. By selecting optimal basis functions and regularization parameters, the model achieves a balanced trade-off between sparsity and predictive accuracy. The accuracy of the model is validated through straight-line swimming, turning swimming, and cross stiffness tests. Furthermore, simulations are performed to investigate the nonlinear effects of magnetic field intensity, frequency, and structural stiffness on swimming performance. The results reveal that the appropriate selection of these parameters enhances locomotion performance. A model predictive control framework is established based on the data-driven dynamics, and its potential for trajectory tracking is validated through multi-path swimming experiments.

Tensegrity metamaterials are recognized as significant in mechanical engineering due to their exceptional variable stiffness, adaptive load-bearing capabilities, and other distinctive properties. This chapter presented a novel negative Poisson’s ratio tensegrity metamaterial. Its substructure consisted of a D-bar tensegrity structure and a rotating double-square negative Poisson’s ratio structure. Firstly, the D-bar tensegrity structure’s geometric model was established assuming small deformation. The pretension relationship between the structure’s tension elements was obtained. Experiments were carried out to investigate the effects of structural angle, hinge rigidity–flexibility characteristics, and pretension of tension elements on the compressive load-displacement characteristics of the tensegrity metamaterial substructure. Then, the influence of the tensegrity metamaterial substructure’s angle on the energy absorption effect was analyzed. The energy absorption of the tensegrity metamaterial (TM) substructure was compared to that of the rotating double-square (RD) substructure. The results showed that the energy absorption index of the tensegrity metamaterial structure with negative Poisson’s ratio characteristics increased by 47.32

Current millimeter-scale rigid and flexible swimming robots suffer from inherent structural limitations, such as insufficient compliance or restricted load capacity, which hinder their multifunctional integration and broader applications. Here, we propose a whale-inspired, magnetically actuated rigidflexible coupled robotic fish (14 mm in length). To address millimeter-scale manufacturing challenges, a monolithic disk design is employed to significantly reduce the assembly difficulty of rotational tensegrity joints, constructing a coordinated yet antagonistic 3D tension network. Furthermore, to resolve the complex geometric nonlinearity exhibited by the continuous disk under large deformations, a simplified equivalent stiffness model is proposed and experimentally validated, enabling the rapid analytical evaluation of stiffness and its effect on load capacity. Empowered by this architecture, the robot demonstrates multimodal locomotion, remarkably low energy consumption (minimum cost of transport, COT ≍ 2.86 J/kg/m), and high load capacity (≍ 90 N$\cdot$m/kg). Extensive experiments reveal that adjusting the pre-configured stiffness leads to variations of up to 473% in swimming speed and 460% in COT. Additionally, the robot can adaptively roll over various obstacles, achieving a maximum linear rolling speed of 11.3 body lengths per second. Crucially, it overcomes the payload bottlenecks of purely soft robots by transporting cargo comparable to its own weight, while integrated metal components enable controlled remote heating. These combined capabilities highlight the robot's potential for localized biomedical interventions, such as therapies within the gastrointestinal tract.

The salamander, as an amphibian, holds significant importance for human research into multimodal locomotion in animals. This paper presents the design of an amphibious salamander robot for multimodal locomotion studies. By altering control parameters, the robot enables the switching between various motions; furthermore, parameter tuning allows for the exploration of additional intriguing robotic motions. To begin with, we built a salamander robot with the ability to adapt to amphibious environments. Then, we established a control platform, equipping the robot with multi-module hardware for environmental perception and remote communication capabilities, while implementing multimodal locomotion through a general kinematic model and sinusoidal function-based control method. Finally, we conducted multi-scenario experimental validation using the robotic prototype, confirming amphibious operational feasibility and evaluating control efficacy across varying motion parameters. The results offer actionable design insights for amphibious biomimetic robotics development.

The wheeled bipedal robots have great application potential in environments with a mixture of structured and unstructured terrain. However, wheeled bipedal robots have problems such as poor balance ability and low movement level on rough roads. In this paper, a novel and low-cost wheeled bipedal robot with an asymmetrical five-link mechanism is proposed, and the kinematics of the legs and the dynamics of the Wheeled Inverted Pendulum (WIP) are modeled. The primary balance controller of the wheeled bipedal robot is built based on the Linear Quadratic Regulator (LQR) and the compensation method of the virtual pitch angle adjusting the Center of Mass (CoM) position, then the whole-body hybrid torque-position control is established by combining attitude and leg controllers. The stability of the robot’s attitude control and motion is verified with simulations and prototype experiments, which confirm the robot’s ability to pass through complex terrain and resist external interference. The feasibility and reliability of the proposed control model are verified.

Physical intelligence for aerial robots greatly enhances grasping and perching performance, but remains in emerging stages. This letter proposes a novel bistable soft gripper for aerial robots with high response speed (0.11s), large holding force (23.47N), and active/passive adaptive grasping and perching. The soft gripper is constructed by four bistable fingers, tension nets, and a bidirectional actuation system. The soft finger evolves from a simple bistable rotational joint. Tension nets inspired by spider webs are proposed to improve the energy barrier and grasping performance. Experiments are conducted to measure the gripper's potential energy variation and grasping performance. One peak and two local minima in the energy curve indicate the gripper's bistability. Experimental results show that tension nets can enhance the gripper's energy barrier, response speed, and maximum holding force by 915.07%, 38.55%, and 62.08%, respectively. The gripper's adjustability of the energy barrier is validated, enabling it to switch active/passive modes as needed. The experiments demonstrated static/dynamic grasping and perching for various daily objects with different shapes, sizes, and stiffness for the gripper and aerial robot. Finally, the robot can transport objects outdoors, and can be aerially manipulated by external force, demonstrating its great potential in aerial application

Body and/or caudal fin (BCF) fish mainly use their body and tail fin as propulsors, and tune their stiffness during swimming to enable rapid and efficient locomotion. However, current variable-stiffness biomimetic robotic fish with high-frequency actuation mainly focuses on the effect of tail fin stiffness. In this paper, we develop a freeswimming tensegrity robotic fish with multi-tensegrity joints, to experimentally study the effect of online body stiffness variation in fish-like swimming with high actuation frequency. We detail its remote high-frequency driving mechanism and fast stiffness adjustment system. We validate the wide-range and fast stiffness adjustment for the tensegrity joint. The robotic fish can dynamically alter various body stiffness distributions online by changing its joints' stiffness. The experimental results illustrate the nonlinear and dramatic effects of the driving frequency, body stiffness, and swimming state. The ability to adjust body stiffness online in swimming is demonstrated, enabling large range and fast changes in swimming speed and thrust. Compared to other biomimetic robotic fish, the tensegrity robotic fish's swimming performance is at an upper-middle level, and its variable stiffness ability is outstanding. This work offers valuable insights for the future optimization online of the swimming process in biomimetic fish design.

Robotic fish can enhance swimming performance through bistability, enabling rapid response and increased force. Existing bistable robotic fish are typically classified as either purely soft or purely rigid, which may constrain their performance. This letter introduces the rigid-soft coupled tensegrity robotic fish. The potential energy parameters, such as the energy barrier, are modified by adjusting the preload of the tension elements. An intermittent gear transmission scheme is proposed to accommodate the bistable state snapping. Experiments with the robotic fish were conducted to measure potential energy, swing speed, swimming performance, and thrust. The experimental results showed that the robotic fish's maximum swimming speed, minimum cost of transport, and maximum thrust were 1.1 BL/s, 10.5 J/kg/m, and 8.77 N, respectively. These metrics rank above the medium level compared to existing bistable robotic fish. Adjusting the energy barrier increases the average angular velocities of the robotic fish's step response and continuous swing by 88.8 $<^>{\circ }$/s and 503 $<^>{\circ }$/s, respectively. Moreover, the maximum thrust increased by 97.2%, and the average thrust increased by 1400%. These findings underscore the potential of mechanisms for adjusting bistable characteristics to improve the swimming performance of robotic fish, providing valuable insights for designing future generations of robotic fish.

Traditional quadruped robots are known for their agile movement and versatility across varied terrains. However, their foot structures struggle to navigate unstructured terrains such as pipes, slopes, and protrusions. This paper proposes a novel tensegrity foot structure consisting of a tensegrity ankle joint and an X-shaped adaptive tensegrity footpad, which enhances the terrain adaptability of legged robots. The equilibrium equation of the ankle joint is established, and the relationship between the translational stiffness of the ankle joint and the spring stiffness is derived. Additionally, a mathematical model for the number of X-shaped tensegrity footpad units and their relationship with the deformation height and length of the tensegrity footpad is established. A physical prototype of the tensegrity foot was fabricated using 3D printing. Experiments are conducted to validate the adaptability of both the ankle joint and the tensegrity footpad. The results indicate that the proposed adaptive tensegrity foot structure exhibits good adaptability on unstructured terrains with varying radii, slopes, steps, S-curves, and spherical surfaces. The tensegrity foot structure can enhance the environmental adaptability of quadruped robots and has excellent impact resistance effects.

Due to its lightweight, impact resistance, and energy absorption, tensegrity is a good candidate for drone protection. Researching its collision resistance can significantly improve drone adaptability. This paper examines the structure-ground interaction and collision dynamics of 6-bar, 12-bar, and 30-bar tensegrity spheres through simulations and experiments. Results show consistency between simulations and experiments, confirming the collision dynamics model's effectiveness. The 6-bar tensegrity structure demonstrates excellent collision resistance. Additionally, the influence of structural materials, pretension, and ground types on the 6bar structure is analyzed, showing that increased cable pretension to certain values reduces peak acceleration during collisions. Drone collision tests with trees and high-altitude drops further confirm the tensegrity sphere's good environmental adaptability and protective effect.

Current bistable grippers are limited in triggering modes, adjustability, high-speed grasping controllability, and impact resistance, which constrains their adaptability to diverse targets and complex environments. This letter presents a tensegrity bistable gripper with five triggering modes, three grasping modes, two adjustable performance parameters, and controllable bistable grasping processes. The gripper's self-adaptive jaw supports envelope, hook, and pinch grasping modes, thereby handling objects with a broad size range (0.1-125 mm) and weight range (4.5 g-9.68 kg). By modeling the potential energy and gripping torque of the tensegrity bistable actuator, the proposed adjustment method increases the maximum gripping torque by 152% and raises the trigger energy barrier by 265 times. The five triggering modes offer adjustable grasping response times (0.04 s-26 s). One of the triggering modes enables controllable bistable grasping, allowing for real-time adjustment of both response time and gripper posture during operation. These features enhance the gripper's adaptive grasping capability. Experiments demonstrate successful adaptation to objects with diverse shapes, weights, stiffnesses, and postures while maintaining robust operation under vibrations and in confined spaces, demonstrating significant potential for robotic applications.

Tensegrity metamaterials are considered superior to many traditional materials in engineering due to their exceptional variable stiffness, adaptive load-bearing capabilities, and adjustable morphing properties. This paper presents a novel negative Poisson's ratio tensegrity metamaterial featuring a substructure composed of a D-bar tensegrity structure and a rotating double-square negative Poisson's ratio structure. Firstly, we establish the geometric model of the D-bar tensegrity structure and determine the pretension relationships among its tension elements. We then describe the composition of the tensegrity metamaterials and their performance metrics. The stress-strain behavior of tension elements is characterized through tensile tests. Further experiments explore the effects of structural angle and pretension on the compressive load-displacement characteristics of the structure. Then, the effect of the structural angle of tensegrity metamaterial substructures on energy absorption is analyzed. Additionally, the impact resistance of tensegrity metamaterials with negative Poisson ratios shows significant compressive and impact durability. Their potential for enhancing drone protection and environmental adaptability is also demonstrated.

Miniature robots are increasingly used in unstructured environments and require higher mobility, robustness, and multifunctionality. However, existing purely soft and rigid designs suffer from inherent defects, such as low load capacity and compliance, respectively, restricting their functionality and performance. Here, we report new soft-rigid hybrid miniature robots applying the tensegrity principle, inspired by biological organisms' remarkable multifunctionality through tensegrity micro-structures. The miniature robot's speed of 25.07 body lengths per second is advanced among published miniature robots and tensegrity robots. The design versatility is demonstrated by constructing three bio-inspired robots using miniature tensegrity joints. Due to its internal load-transfer mechanisms, the robot has self-adaptability, deformability, and high impact resistance (withstand dynamic load 143,868 times the robot weight), enabling the robot to navigate diverse barriers, pipelines, and channels. The robot can vary its stiffness to greatly improve load capacity and motion performance. We further demonstrate the potential biomedical applications, such as drug delivery, impurity removal, and remote heating achieved by integrating metal into the robot.

Joints are the core components of robotic actuation systems. Their performance directly affects the system's dynamic characteristics. However, rigid and flexible joints both face a trade-off between environmental adaptability and response velocity due to their structural properties. A bionic tensegrity joint inspired by biological tensegrity principle is proposed. We present its structural design and stiffness model. The joint features tunable bistability, allowing synergistic optimization between adaptability and response velocity. Experiments show that the joint has negative stiffness and fast response. To validate the effectiveness of the proposed joint design, a gripper and a swimmer were developed. The gripper demonstrates a high response velocity of 56 ms while maintaining a payload capacity of up to 4 kg. Leveraging the bistable tensegrity joint, the swimmer achieves a swimming speed of 1.1 body lengths per second (BL s-1). A novel robotic design framework centered on rotational tensegrity joints has been developed, which demonstrates significant potential for agile locomotion, human-robot interaction, and adaptive manipulation.

Soft robots, inspired by living organisms in nature, are primarily made of soft materials, and can be used to perform delicate tasks due to their high flexibility, such as grasping and locomotion. However, it is a challenge to efficiently manufacture soft robots with complex functions. In recent years, 3D printing technology has greatly improved the efficiency and flexibility of manufacturing soft robots. Unlike traditional subtractive manufacturing technologies, 3D printing, as an additive manufacturing method, can directly produce parts of high quality and complex geometry for soft robots without manual errors or costly post-processing. In this review, we investigate the basic concepts and working principles of current 3D printing technologies, including stereolithography, selective laser sintering, material extrusion, and material jetting. The advantages and disadvantages of fabricating soft robots are discussed. Various 3D printing materials for soft robots are introduced, including elastomers, shape memory polymers, hydrogels, composites, and other materials. Their functions and limitations in soft robots are illustrated. The existing 3D-printed soft robots, including soft grippers, soft locomotion robots, and wearable soft robots, are demonstrated. Their application in industrial, manufacturing, service, and assistive medical fields is discussed. We summarize the challenges of 3D printing at the technical level, material level, and application level. The prospects of 3D printing technology in the field of soft robots are explored.

Nowadays, self‐charging devices using clean energy have raised the potential of portable and wearable power generators. Herein, a novel moisture‐induced self‐powered device based on metal–air redox reaction has been designed which can work under normal humidity conditions. Through bridging two asymmetric electrodes including a carbon nanotube/polyaniline composite electrode and a metal electrode by filter paper with CaCl2, the 1D planar device can be simply fabricated. A single device can provide an open‐circuit voltage of over 1.3 V under normal humidity (40%) within 5 min (the maximum can be up to 1.42 V at 80% humidity) and the harvesting energy can be stored effectively. The device possesses great circularity and stability which can maintain steady and consistent output over at least 6 months. Due to the microelectrolyte, this device can prevent harmful leakage or deformation of the electrolyte completely. What is more, the device shows good extendibility. Three single devices in series using common electrodes can light up two light‐emitting diodes. Besides its application potential in self‐powered portable and wearable electronics, this device can provide a reference for utilization in medical devices due to the response signals under breath with different frequencies.