Abstract

Deformation of flexible robots can be practically assessed using extension/compression, shear, curvature, and torsion. Sensing based on one or more of the above characteristics enables closed-loop control for delicate tasks that require precision and dexterity. Due to the increasing popularity of flexible robotics in recent years, significant research effort has been directed to this burgeoning field. Although numerous studies have addressed soft sensing technologies, their successful integration into flexible robotic systems remains limited. This article provides a comprehensive review of sensing methods, from multidimensional deformation to the underlying principles of deriving hard-to-measure deformation from surrogate parameters. It focuses on sensing modalities such as strain measurement via piezoelectric, capacitive, resistive, and optical techniques. The applications of deformation sensing in industrial and service robotics are described. Future challenges and potential research issues including resolution, conformability, multifunctionality, crosstalk, and miniaturization are discussed. The need for a synergistic approach across disciplines is highlighted, emphasizing the integration of new materials, microstructures, advanced manufacturing technologies, and state-of-the-art signal processing techniques.

Introduction and Methods

In this article, we use the term flexible robots to include both soft robots and continuum robots specifically. Many f lexible robots have displayed remarkable capabilities such as jumping, crawling, shape reconfiguration, and dexter ous manipulation, compared to their conventional coun terparts. Different from traditional robots, flex ible robots with hybrid rigid and soft materials or with hyperredundancy can actively and passively change their shape, color, mechanical properties, or motion characteristics for safe and effective interac tion. For example, in minimally invasive surgery, robots for endoluminal intervention are designed to be flexible enough to navigate through narrow tortuous lumens while maintaining the required rigidity and stability for tissue manipulation.

For precise, intelligent, and safe control of flexible robots, accurate deformation sensing is essential. One challenge is that the contact and interaction between the robot and the surrounding environment are unpredictable due to the intrinsic compliance of the flexible robot and multiple contact points. Another challenge is the nonlin earity of the materials and different actuation methods used. In practice, it is also important to ensure that sensors conform to the soft or continuum body of the robot without affecting its mechanical or dynamic behavior. The sensors need to have high flexibility and a Young’s modulus that ideally matches the robot’s structure or the object to be manipulated. These impose new challenges in terms of sensor design, miniaturization, and material fabrication. The most common deformation sensing techniques used thus far are based on either optical principles or electri cal effects, such as piezoelectric, capacitive, and resistive changes. Direct or indirect indices including extension/compression, shear, curvature, and torsion are useful, and different types of energy conversion, such as light, electrical, thermal, and magnetic effects, can be leveraged. 

With recent advances in materials, manufacturing tech nologies, and flexible electronics, the demand for defor mation sensing is rapidly increasing. Although a myriad of studies have addressed soft sensing technologies, their successful integration into flexible robotic sys tems is still limited. Existing review articles have already focused on the perception of soft robots. For example, Dou et al. discussed soft robotic manipulators in terms of design, actuation, stiffness tuning, and sensing. Wang et al. reviewed the perceptions of soft robots and presented the associated challenges. The scope of this article comple ments the existing literature and focuses on deformation sensing techniques, which have hitherto not been reviewed systematically, neither in terms of their use for flexible robotics. The challenges and opportunities are discussed to outline the potential possibilities of deformation sensing technologies. 

A systematic search covering the period between 2008 and 2025wascarried out, and well-known databases, such as Science Direct, Scopus, and PubMed, were included. The keywords used include “robot” or “flexible robot” or “soft robot” or “continuum robot” and “deformation sens ing” or “curvature sensing” or “torsion sensing” or “exten sion sensing” or “compression sensing” or “shear sensing” or “strain sensing” or “pressure sensing” or “shape sensing” or “sensing” or “perception” or “soft sensor” or “flexible sensor” or “deformation sensor” or “stretchable sensor” or “sensor” or “shape sensor.” Only original research and review articles were selected, and patents and commercial ized systems were not included.

Key Results and Conclusions

In summary, in addition to the above five aspects, devel oping synergistic approaches across different disciplines is also important. The development and performance opti mization of deformation sensing technologies rely on the integration of knowledge and techniques from multiple disciplines, primarily materials science, structural engi neering, manufacturing technology, and electronics. Three potential approaches for the development of such sen sors, leveraging expertise from these diverse fields, can be considered here. First, optimizing electronic performance through microstructure design involves strategies such as significantly enhancing the signal change rate using struc tures like microcracks and micropyramids, as well as improving the spatial distribution and intensity of signals by designing sensors that mimic the multilevel structure of skin. Second, the sensing characteristics of materials can be optimized through electronic signal processing technology. For example, ML processes sensing signals to compen sate for material hysteresis, creep, and nonlinearity, while closed-loop feedback control dynamically adjusts the driving voltage or current to mitigate the hysteresis and creep effects inherent in the materials. Third, the integration of materials and structure can be achieved through advanced manufacturing. By adopting multima terial printing technology to realize integrated printing of the substrate, microstructure, and conductive circuits, the complexity of signal transmission lines and structural lay out can be reduced, thereby optimizing the overall sensor performance. In summary, there is great potential in the future development of deeply integrated design platforms and intelligent manufacturing. For instance, developing a multidisciplinary collaborative design software platform that integrates material libraries, microstructure design tools, circuit simulation, mechanical simulation, and manufacturing process planning, along with artificial intelligence-enabled manufacturing processes to automati cally optimize microstructure parameters, material formu lations, and printing paths, holds promise for achieving optimal sensing performance.

In this paper, the deformation sensing of flexible robots is comprehensively reviewed. The covered deforma tion modes encompass extension/compression, shear, curvature, and torsion, while the sensing technologies are primarily categorized into five classes: optical, piezoelec tric, capacitive, resistive, and other emerging techniques. This review elaborates on the sensing systems from fun damental mechanisms and energy conversion principles to diverse technical configurations. Each sensing strat egy adopts distinct structures, functional materials, and manufacturing processes, aiming to achieve highly stretch able and high-performance sensing capabilities, with the key performance parameters of various sensors systemat ically tabulated for comparison. Subsequently, the appli cations of deformation sensing in flexible robots are synthesized across industrial and service robot domains, demonstrating their practical efficacy and reliability. Finally, the challenges are summarized from five criti cal perspectives, and corresponding prospective research avenues are proposed for each challenge to guide future investigations.

Fig. 1. Schematic illustration of the deformation sensing mechanisms and energy conversion principles. Deformation types include compression/tension, shear, curvature, and torsion, which are mainly sensed by resistive, piezoelectric, capacitive, optical, and other techniques.

Fig. 2. Optical technique-based deformation sensing. (a) Shape and force sensing using a helically wrapped standard single-core FBG fiber (b) Multicore optical fibers with Bragg gratings for shape sensing. (c) Mechanism of the stretchable optical waveguide sensor in four strain scenarios. (d) 3-D shape reconstruction of the continuum manipulator using noncontact X-ray images. (e) Contact information captured by vision-based tactile sensors on a soft robotic hand. (f) Optical waveguide array-based sensing skins for soft grippers enable contact point and force detection.

Fig. 3. Examples of piezoelectric technique-based deformation sensing. (a)–(c) Lead-based piezoelectric sensors. (d) Organic lead-free piezoelectric sensors. (e) Organic/inorganic composite lead-free piezoelectric sensors.

Fig. 4. Examples of capacitive technique-based deformation sensing. (a) Capacitive sensor with carbon-based electrode layers. (b) and (c) Capacitive sensor with metallic electrode layers. (d) Capacitive sensor with LM electrode layers. (e) Capacitive sensor with high toughness and large measurement range based on conductive ink. (f) Capacitive sensor with ionically conductive electrode layers.

Fig. 5. Examples of resistive technique-based deformation sensing. (a) and (b) Carbon-based resistive-type sensors. (c) and (d) Metallic-based resistive-type sensors. (e) LM-based resistive-type sensors. (f) Conductive hydrogel-based resistive-type sensors.

Fig. 6. Examples of other techniques for deformation sensing. (a) TENG sensor for real-time gesture interaction. (b) Hydrogel-based TENGs for energy harvesting and tactile sensing. (c) Fibrous inductive sensors for passive inductance textile sensing. (d) Soft magnetic composite compression sensors for wearable technology. (e) Acoustic-based sensing in soft pneumatic actuators. (f) Surface haptic sensing through surface temperature changes.

Fig. 7. Applications of deformation sensors for flexible robots. (a) and (b) Industrial robot applications. (c) Domestic service robot application. (d) Rehabilitation robot application. (e) Surgical robot application. (f) Underwater robot application.

https://ieeexplore.ieee.org/document/11268283