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A Variable Curvature Continuum Kinematics for Kinematic Control of the Bionic Handling Assistant
Abstract
We present a new variable curvature continuum kinematics for multisection continuum robots with arbitrarily shaped backbone curves assembled from sections with three degrees of freedom (DoFs) (spatial bending and extension, no torsion). For these robots, the forward kinematics and the differential forward kinematics are derived. The proposed model approach is capable of reproducing both the constant and variable backbone curvature in a closed form. It describes the deformation of a single section with a finite number of serially connected circular arcs. This yields a section model with piecewise constant and, thus, a variable section curvature. Model accuracy and its suitability for kinematic real-time control applications are demonstrated with simulations and experimental data. To solve the redundant inverse kinematics problem, a local resolution of redundancy at the velocity level through the use of the robot’s Jacobian matrix is presented. The Jacobian is derived analytically, including a concept for regularization in singular configurations. Experimental data are recorded with Festo’s Bionic Handling Assistant. This continuum robot is chosen for experimental validation, as it consists of a variable backbone curvature because of its conically tapering shape.
... For example, Santina et al. [33] analyzed the properties of parameterized soft robot system states based on the PCC model with emphasizing its use in model-based control. Mahl et al. [34] used the PCC kinematic method to model multisection continuum robots with randomly shaped spatial curves. However, these PCC kinematic modeling methods are rarely focused on developing material mechanics models. ...
... Based on the calculated elastic potential energy, the work done by fluidic pressure, and the work done by external forces in Sections III-B-III-D, we can obtain the potential energy as Correspondingly, we can obtain the actuator's equilibrium deformation by minimizing the potential energy using the MPE method as N ], which yields 7N nonlinear equations. By resolving (34), k ′ i can be numerically solved. It should be noted that (33) only has the first two terms when there are no external forces acting on the actuator, and the variable k i = (e 11(i) , e 22(i) , e 33(i) , q (i) , κ 1(i) , κ 2(i) , φ i ) can be solved in the same way as k ′ i . ...
... The experimental results are obtained by capturing the motion of markers with two high-definition cameras, and the theoretical results are computed by MATLAB 2016a (MathWorks Inc., USA). We first calculate the principal curvature and principal curvature orientation of each segment using (34), the modeled deformation of each segment is fit to helical shape using helix in Origin 2024 (OriginLab Inc., USA), and the least-square method is used to fit the whole actuator's morphology. It can be observed that the actuator with a single segment and two segments can match the actuator morphology approximately, but there is a little discrepancy in the middle of the actuator. ...
Soft helical actuators, characterized by high compliance, flexibility, and dexterity in the three-dimensional (3-D) space, are particularly promising candidates in complex and unstructured applications. However, there are few researches on the large deformation of the helical actuators, and the existing modeling methods for helical actuators are based on the constant curvature assumption and only the load applied to the end of the actuator is considered. When the helical actuators are subjected to complicated environmental loads, the constant curvature model can no longer describe its actual morphology and deformation. In this article, a class of laminated composite actuators made up of four different layer material is proposed, whose multiple kinds of helical deformation can be tailored by changing orientated direction and volume fraction of the fibers of the fiber reinforcement layer. Based on the piecewise constant curvature (PCC) model and the minimum potential energy (MPE) method, we propose a segmented modeling method for the large deformation of the helical actuator under external loads. The geometric and mechanical models are established to characterize the large deformation of the proposed helical actuator under input pressure and external loads. Finally, both finite element (FE) analysis and experiments are conducted to verify the validation of the theoretical model, which reveals a consistency between the predicted deformation of the helical actuators and the experimental results.
... Developing a thorough description of the behavior and the morphology of continuum robots are the first major step that is needed to derive precise kinematic models, which themselves help to simulate the movements and the behavior of these robots. Therefore, several models have been proposed by researchers for the geometric description of continuum robots assuming constant curvature [13][14][15][16][17][18][19][20] and variable curvature [21][22][23][24]. ...
... However, the constant curvature does not show a better imitation of the central axis of the continuum robot. For this reason, recent research has opened new doors to modeling the central axis of the continuum robot, which describe in detail the deformation of each unit of the robot as an arc of a circle, typically called variable curvature [21]. ...
... (23) must be expressed in terms of the cable lengths ℓ _ i,j,k instead of ℓ i,j,k . Therefore, according to the assumption mentioned before; each conical shape unit is modeled as an inextensible arc with its individual arc parameters and deforms at small angles, the relationship between these two cable lengths is given by the law of cosines [21]: ...
Continuum robots are progressively dwarfing traditional rigid robots in many areas (surgery, inspection, and rescue under buildings...etc), due to their outstanding flexibility and the easy adaptation to almost any kind of trajectory, yet their kinematic modeling is presented as a drawback, in particular for multi-sections and variable curvature continuum robots, which curbs the full benefit of these kinds of robots.
In this context, this chapter presents the description of continuum robots and their kinematic modeling in detail.
Firstly, the description of the behavior and forward kinematic models are presented for continuum robots with constant curvature and variable curvature, as well as their workspaces. Then, to calculate the inverse kinematic model of continuum robots, an artificial neural networks approach and metaheuristic optimization technique have been used for the sake of obtaining the inverse kinematic model of single-section and multi-section continuum robots, respectively. In the same context, to validate the utility of the proposed techniques, different trajectories are proposed to be followed by considered continuum robots. It is found that the developed techniques are powerful tools to deal with the high complexity of non-linear equations, in particular when it comes to solving the inverse kinematic model of multi-section continuum robots with variable curvature. To have a closer look at the efficiency of the developed techniques during the follow-up of the proposed trajectories, 3D simulation examples through Matlab have been carried out with different configurations.
... Compared to cylindrical structures, conical structures have a more reasonable load distribution, and the manipulator's end is more flexible and lightweight. They have been widely applied in pneumatic soft robotic arms [17][18][19]. Based on this concept, this paper proposes a structure for a CDHM, as illustrated in figure 1(A). ...
... Combining equations (18) and (19), it can be concluded that | δl δφ | decreases with the increase of ∆r. The relationship between δl δε and ∆r is complex to solve through formulas. ...
The cable-driven hyper-redundant manipulator (CDHM), distinguished by its high flexibility and adjustable stiffness, is extensively utilized in confined and obstacle-rich environments such as aerospace and nuclear facilities. This paper introduces a novel CDHM inspired by the trunk of elephants, which changes the arm structure from cylindrical to conical. This alteration diminishes the arm’s self-weight, reduces the moment arm of gravity, decreases the volume of the end joint, narrows the stroke of the driving cables, and boosts the maximum joint speed of the manipulator. Additionally, this study examines the impact of the manipulator’s taper on its overall performance from both dynamic and kinematic perspectives. Finally, three prototype manipulators with varying tapers are confirmed, and tests are conducted on each manipulator’s motion performance and cable tension. By comparing experimental data, the accuracy of the theoretical analysis and the rationality of the conical structure are confirmed. The results suggest that the proposed new configuration offers certain advantages in terms of cable stroke, joint speed and maximum driving force.
... In many continuum robots, constant curvature designs are used for simplified modeling and analysis [9], [17] and reduced design parameters [18], [19]. However, non-constant curvature designs are also employed to improve model accuracy [20], [21], achieve specific bending shapes [22], and enhance the robot's elastic stability [23], [24]. In particular, the initial design of the robot is crucial in determining the robot's configuration space, as the tip position and direction of continuum robots are controlled in a coupled manner according to this design. ...
... To relate δτ and δs i (which is a component of δx i ), we refer to (20). We assume ϵ i is corrected by updating T i , s i , and f i as described in Section IV-C. ...
This paper presents the first kinematic modeling of tendon-driven rolling-contact joint mechanisms with general contact surfaces subject to external loads. We derived the kinematics as a set of recursive equations and developed efficient iterative algorithms to solve for both tendon force actuation and tendon displacement actuation. The configuration predictions of the kinematics were experimentally validated using a prototype mechanism. Our MATLAB implementation of the proposed kinematic is available at https://github.com/hjhdog1/RollingJoint.
... As the number of segments increases, the errors accumulate and propagate to the end effector thus deteriorating the fidelity of forward/inverse kinematics. Although researchers have developed variable curvature models [26], which model a single segment as n segments of CC, most of them are designed to cope with non-constant curvature deformations caused by geometric structures rather than external forces or interactions. ...
... Assumption 2: Torsional deformation is negligible. These assumptions have been verified to be reasonable on many soft arms [33], [26], [32], while for some other manipulators, for example, whose body is made of silica gel, torsion is not negligible [13], [34]. Here we focus on the former case. ...
... Subsequently, researchers proposed customized pneumatic actuators with origami structures to achieve higher contraction ratio and load-bearing capabilities [32], [33]. The pneumatic parallel continuum robot has thus become a relatively popular design of PCRs based on soft actuators [21], [34]- [37]. Nevertheless, the actuation principle (large deformation caused by non-servo-controlled air supply) suffers from difficulties in positioning and loadcarrying. ...
... The attitude obtained by the IMUs is used to inversely solve the actuator lengths as the current feedback, using the constant curvature assumption, resulting in amplified measurement errors. The visual servo control is another popular method for position control of soft robots [37], [42]- [44]. With multiple reflective target points attached, the sensing accuracy of this method can be high. ...
Parallel continuum robots (PCRs) based on soft actuators have been recently proposed to take advantage of both, soft robots in flexible, diverse actuation, parallel robots in stable, and precise motion. Although various designs have been exhibited, most of them suffer from positioning inaccuracy, especially under uncertain payloads, due to the lack of strong actuation and effective integrated sensing methods. Here, we introduce a vacuum-driven PCR that can simultaneously perform multimode motion, high positioning accuracy, and high load-carrying capacity, on the basis of the mechanical feature of origami. With a soft-rigid hybrid 3-D printing method, the origami linkages of the PCR can be constructed at one time. This forms soft but less stretchable pneumatic chambers that can generate strong actuation based on origami folding. The vacuum-driven linkages exploit the contraction-twisting coupled folding characteristic of the Kresling origami pattern. The length of each linkage can be determined by recording the twisting angles. Theoretical models for both the self-sensing linkage and the PCR with three individually actuated linkages, as well as a closed-loop feedback control strategy, have been presented for the motion control of the PCR. The experimental results of a PCR prototype demonstrate its multimode motion, including contraction/extension, omnidirectional bending, and circular swing. The combination of the design and fabrication methods, the sensing strategy, and the feedback control enables the prototype to perform high positioning accuracy with various trajectories, even under a 2-kg payload. The design concept and comprehensive guidelines in this work aim to expand the capacities of PCRs or soft robots for broader applications, and facilitate the usage of origami and multimaterial 3-D printing in building robotic structures.
... These deviations can reduce the fidelity of the forward kinematic model, especially under external loads, contact constraints, or non-planar configurations. Consequently, for applications requiring high-precision modeling or robust environmental interaction, incorporating variable curvature model [28] or data-driven correction methods could provide improved accuracy without excessively increasing computational complexity. ...
This paper presents a comprehensive evaluation of Particle Swarm Optimization (PSO) variants for trajectory tracking of a cable-driven continuum robot, utilizing descriptive statistical metrics along with parametric and non-parametric methods for performance assessment. The forward kinematic model of the robot was derived using the constant curvature approach, and the trajectory tracking problem was formulated as an optimization task. Five PSO variants, namely Standard PSO (S-PSO), Weighted PSO (W-PSO), Quantum PSO (Q-PSO), Sine-Cosine PSO (SC-PSO), and Constricted PSO (C-PSO), were reviewed and applied to two optimization scenarios: achieving a target point without considering end-tip orientation as a basic optimization problem and achieving both position and orientation as a more complex optimization problem. To evaluate their effectiveness and robustness, each algorithm was run 30 times per scenario to optimize the arc parameters necessary for tracking 500 randomly selected end-tip poses within the robot’s workspace. Descriptive statistics, as well as parametric and non-parametric statistical tests, including one-way ANOVA, Kruskal-Wallis, and Dunn’s post hoc test with Holm-Bonferroni correction, were used to compare the PSO variants based on tracking error, execution time, and number of iterations. The analysis showed that for simpler trajectory tracking problems, S-PSO and W-PSO were preferred, but as task complexity increased, these variants became less effective, with Q-PSO and SC-PSO performing better in more complex scenarios. Meanwhile, C-PSO consistently underperformed across all scenarios.
... Traditional lengthbased modeling approaches, such as piecewise constant curvature methods [24], are not well-suited for cone-shaped robots. Adaptations for variable-curvature designs [25] offer improved flexibility but are complex to derive. ...
The logarithmic spiral is observed as a common pattern in several living beings across kingdoms and species. Some examples include fern shoots, prehensile tails, and soft limbs like octopus arms and elephant trunks. In the latter cases, spiraling is also used for grasping. Motivated by how this strategy simplifies behavior into kinematic primitives and combines them to develop smart grasping movements, this work focuses on the elephant trunk, which is more deeply investigated in the literature. We present a soft arm combined with a rigid robotic system to replicate elephant grasping capabilities based on the combination of a soft trunk with a solid body. In our system, the rigid arm ensures positioning and orientation, mimicking the role of the elephant's head, while the soft manipulator reproduces trunk motion primitives of bending and twisting under proper actuation patterns. This synergy replicates 9 distinct elephant grasping strategies reported in the literature, accommodating objects of varying shapes and sizes. The synergistic interaction between the rigid and soft components of the system minimizes the control complexity while maintaining a high degree of adaptability.
... The concept of continuum robots has been proposed since the 1960s and, after years of research and exploration, continuum robots can currently be divided into three types: internal body drive, external body drive, and hybrid drive, according to the distribution of the drive source among the robots [11]. The internal drive is mostly dominated by the pneumatic/hydraulic drive and the SMA drive [12][13][14][15], and the pneumatic/hydraulic power source device can be used as the robot skeleton at the same time, adjusting the gas or liquid pressure to change the bending deformation of the robot. Zhao et al. [16] developed an ultra-redundant elephant trunk robot with a servoelectric cylinder as the backbone to simulate the elongation and torsion of an elephant trunk by controlling the gas pressure in the cylinder. ...
Most trunk-like robots are designed with distributed actuators to mimic the envelope-grasping behavior of elephant trunks in nature, leading to a complex actuation system. In this paper, a modular underactuated elephant trunk-imitating robot based on the combined drive of the cable and shape memory alloy (SMA) springs is designed. Unlike the traditional underactuated structure that can only passively adapt to the envelope of the object contour, the proposed elephant trunk robot can control the cable tension and the equivalent stiffness of the SMA springs to achieve active control of the envelope morphology for different target objects. The overall structure of the elephant trunk robot is designed and the principle of deformation envelope is elucidated. Based on the static model of the robot under load, the mapping relationship between the tension force and the tension angle between modules is derived. The positive kinematic model of the elephant trunk robot is established based on the Debavit–Hartenberg (D–H) method, the spatial position of the elephant trunk robot is obtained, and the Monte Carlo method is used to derive the robot’s working space. The active bending envelope grasping performance is further verified by building the prototype to perform grasping experiments on objects of various shapes.
... In 2014, the German company Festo introduced a flexible elephant trunk robotic arm composed of pneumatic muscles, with a length of 850mm and a maximum diameter of 130mm [5]. They proposed a novel variable curvature continuum kinematics for multi-segment continuum robots with arbitrary-shaped backbone curves assembled from segments with three degrees of freedom . ...
The research on bionic robotic arms originates from the aspiration to imitate and replicate the structure and functions of the human arm. With advancements in technology, particularly in the rapid development of robotics, sensor technology, and materials science, robust technical support has been provided for the study of bionic robotic arms. Additionally, as people's demands for a higher quality of life increase, so does the need for mechanical devices that can undertake arduous, hazardous, or high-precision tasks in place of humans. Especially in fields such as industrial production, healthcare, and military security, the research and application of bionic robotic arms have become a focal point in today's technological landscape. This article presents a comprehensive overview of the research background, development trajectory, and future prospects of three specific areas: flexible robotic arms for confined space operations, bionic robotic arms for rotorcraft, and bionic jellyfish robotic arms. The aim is to provide theoretical support and technical references for research and engineering applications in related fields
... This assumption facilitates theoretical calculations but inevitably introduces model errors. In addition, Mahl et al [33] believed that forces (like the inertia force or gravity) can also affect kinematic model accuracy. Figure 12(b) illustrates the comparison results of tip trajectory in the x direction and y direction. ...
The exploration of adaptive robotic systems capable of performing complex tasks in unstructured environments, such as underwater salvage operations, presents a significant challenge. Traditional rigid grippers often struggle with adaptability, whereas bioinspired soft grippers offer enhanced flexibility and adaptability to varied object shapes. In this study, we present a novel bioinspired soft robotic gripper integrated with a shape memory alloy (SMA) actuated suction cup, inspired by the versatile grasping strategies of octopus arms and suckers. Our design leverages a tendon-driven composite arm, enabling precise bending and adaptive grasping, combined with SMA technology to create a compact, efficient suction mechanism. We develop comprehensive kinematic and static models to predict the interaction between arm bending deflection and suction force, thereby optimizing the gripper’s performance. Experimental validation demonstrates the efficacy of our integrated design, highlighting its potential for advanced manipulation tasks in challenging environments. This work provides a new perspective on the integration of bioinspired design principles with smart materials, paving the way for future innovations in adaptive robotic systems.
... The model considers nonlinearities and coupling effects of the continuum robot arm and rigid links, as well as actuation and sensing mechanisms, and was validated through simulations and experiments. The authors Mahl et al. 12 adopted a velocity-based feed-forward motion control using minimum and maximum iterative algorithms to obtain the IKM solution. In Razmjooy et al., 13 an energy modeling approach is adopted to model with the particular kinematics of a solitary segment. ...
The first aspect of the paper focuses on presenting the innovative design of a new continuum robot, which was initially conceptualized using SolidWorks and then brought to life through 3D printing. This section illustrates the construction process, detailing the wiring method and the separator between each section of the robot. A key feature of the newly proposed design is the ball-like shape on the upper side of each disk, allowing each disk to rotate freely and gracefully in conjunction with the next one. To further enhance the design, the disk was optimized using nTopology software, an AI-based solution that reduces weight while maintaining performance. This modern engineering tool proved to be instrumental in addressing engineering challenges effectively. Subsequently, both the original and optimized disks were fabricated using 3D printing technology. In addition to the physical construction, the study employed an Artificial Neural Network (ANN) coupled with Particle Swarm Optimization (PSO) to simulate the developed model by solving its inverse kinematic model. The findings from this research have paved the way for a new continuum robot design that can be trained using the ANN-PSO method. Furthermore, the powerful nTopology tool was demonstrated to be capable of skillfully optimizing any given components without sacrificing performance.
... The morphological computation of compliant bodies established a strong foundation for the working prototypes of worm-like robots (Hauser et al, 2011), (Hauser et al, 2012). Extensive studies have been accomplished on the kinematic & dynamic modeling of complaint continum robots in order to establish the locomotion paradigms (Jones & Walker, 2006), (Webster & Jones, 2010), (Mahl et al, 2012), (He et al, 2013), (Mahl et al, 2014). ...
Although research in the field of worm robotics has taken some stride in recent past, the connotation of such designs was missing the feel of biology in true sense hitherto. Design and firmware of bio-inspired robots have been attempted by several research groups globally but none of those seriously intrude different physiologoical systems of the said biological specimen. Our attempt on technology-driven ideation of the reproductive system of a celebrated biological worm, namely, Caenorhabditis elegans (C.elegans) has culminated into concept-designs of Reproductive Worm Robot. Incidentally, C.elegans is an interesting biological entity that evokes imagination and assertion to create miniature robotic systems, especially by mimicing its reproductive system. In this paper, we have reported the technological concept designs as well as part-hardware of the working prototype of representative Reproductive Worm Robots by naturally inheriting the reproductive mechanism of the biologocal C.elegans worm (notwithstanding the size effect).
... Kinematic and dynamic model-based controllers have been proposed for SPAs. For instance, [15] introduces a variable curvature continuum kinematic model. However, this approach relies on linear approximations of kinematics, which can lead to significant tracking errors, especially for large movements within a control loop cycle. ...
Soft pneumatic actuators (SPAs) offer a promising alternative for biomedical applications requiring high sensitivity and precise manipulation due to their inherent compliance. 3D-printed multi-modal zigzag SPAs exhibit potential in this area by achieving repeatable and precise shape changes due to their chambered design. However, achieving accurate position control remains a challenge. This work proposes a hybrid control strategy for multi-modal zigzag SPAs that combines feed-forward and proportional-integral-derivative (PID) control to enhance positioning accuracy. A Pseudo Rigid Body (PRB) based inverse dynamic model is employed for the feed-forward component. The effectiveness of the controller is evaluated through extensive simulations and experiments. Results demonstrate that the hybrid control strategy achieves up to 29.5% and 31.6% improvement in accuracy compared to the PID and feed-forward controllers, respectively, within the operational bandwidth.
... For instance, in Ref. [13], a follow-the-leader method was used to plan the motion of a three extensible segments continuum manipulator. Based on constant curvature assumptions [14,15], some works have studied the kinematics of continuum manipulator, such as inverse Jacobian method, conformal geometric algebra methods [16][17][18][19] Additionally, modal approaches [20][21][22] are also been used to improve the motion accuracy when the constant curvature model is not suitable. ...
Fast inverse kinematics (IK) algorithm is significant for real-time precise motion control of continuum and soft manipulator. In this paper, we studied an explicit expression of two-segment continuum manipulator based on the constant curvature assumptions and discussed the existence of the IK solutions. This model used pseudo-rigid-body method, unlike 6-axis rigid industrial robot arm, we found that the two-segment extensible continuum manipulators have limited rotation angle around the direction vector of its tip, i.e., this type manipulator has limited dexterity. Then we pre-constrained five degrees of freedom (DOFs) constrained and discussed the definition of the left DOF. The IK solving process is simplified to realize small calculation cost for most applications. This model will provide a robust and real-time way to control the two-segment extensible continuum manipulators.
... A significant number of soft robots or soft body components can be modeled as slender rods with a high length-to-width aspect ratio. Several examples of soft manipulators Cianchetti et al. (2014); Trivedi et al. (2008b); Mahl et al. (2014), grippers Armanini et al. (2021); Hussain et al. (2020); Galloway et al. (2016), and locomotors Armanini et al. (2022a); Arienti et al. (2013); Umedachi et al. (2016), belong to this group. The most general model to analyze a slender rod is the Cosserat rod model. ...
The need for fast and accurate analysis of soft robots calls for reduced order models (ROM). Among these, the relative reduction of strain-based ROMs follows the discretization of the strain to capture the configurations of the robot. Based on the geometrically exact variable strain parametrization of the Cosserat rod, we developed a ROM that necessitates a minimal number of degrees of freedom to represent the state of the robot: the Geometric Variable Strain (GVS) model. This model allows the static and dynamic analysis of open-, branched-, or closed-chain soft-rigid hybrid robots, all under the same mathematical framework. This paper presents for the first time the complete GVS modeling framework for a generic hybrid soft-rigid robot. Based on the Magnus expansion of the variable strain field, we developed an efficient recursive algorithm for computing the Lagrangian dynamics of the system. To discretize the soft link, we introduce state- and time-dependent basis, which is the most general form of strain basis. We classify the independent bases into global and local bases. We propose “FEM-like” local strain bases with nodal values as their generalized coordinates. Finally, using four real-world applications, we illustrate the potential of the model developed. We think that the soft robotics community will use the comprehensive framework presented in this work to analyze a wide range of specific robotic systems.
... However, it is less accurate and not applicable to soft manipulators with variable-cross-section configurations. For the variable-cross-section configuration, general variable curvature continuum kinematics [22], Cosserat exact geometric model [35]- [37], and spring-mass model [38] have been developed to improve the predictive accuracy of kinematic models. However, these methods are currently limited to static analysis of motion deformation and rarely consider the effects of external disturbances, such as self-gravity and applied load. ...
The field of soft manipulators requires a more promising solution, including efficient structures and controllers. This paper presents a novel cable–pneumatic hybrid-driven tapered soft manipulator (TSM) design and control scheme to enhance the performance in actual tasks. This paper is the first to present the design with a Bowden tube as a driving tendon and propose a composite tendon with Bowden tubes and cable tendons (BTCTs). Leveraging the principles of hybrid-driven antagonism, the compact TSM integrates the composite tendon with BTCTs and pneumatically actuated tapered bellows (PATBs). This new hybrid-driven form provides the TSM with excellent resistance to axial extension, tangential bending, and torsion, enhancing the stiffness of the TSM. The variable-stiffness range of the TSM was quantified in tests including axial stiffness (0.57–10.77 N/mm), tangential bending stiffness (0.01–0.45 N/mm), and torsion stiffness (0.02–0.044 Nm/deg) tests. A deep learning-based neural network (NN) approach was utilized to model the inverse kinematics of the TSM. For more precise motion control, using position and orientation feedback from the sensor at the tip, we have designed a closed-loop iterative feedback controller (IFC) incorporating three algorithms. Experiments on spatial point positioning, trajectory tracking with different constraints, orientation control, and disturbance experiments were conducted on the TSM. Experimental results (spatial point positioning error (mean error of stable region: 0.17 mm), circular trajectory tracking error (mean and standard deviation of 100 trials: 0.87
0.57 mm), orientation control error (less than 1
), and the performance in disturbance experiment) demonstrated that our approach has high control accuracy and strong robustness against external disturbances. We conducted experiments involving teleoperation control, collision-free precise operations in cluttered and constrained environments, and disturbance-adaptive board cleaning testing, ensuring both stability and safety during contact with humans. These experiments intuitively demonstrate the potential of this TSM for executing complex tasks in real-world environments, promising to become a safe collaborative assistant for humans in the future.
... Higher dimensional models with increased accuracy have also been proposed. These include the variable Constant Curvature (Mahl et al., 2013;Mahl et al., 2014) (VCC), the Piece-wise Constant Curvature (PCC) (Hannan and Walker, 2003;Li et al., 2018), the Spring-Mass-Damper model (Zheng, 2012), the Cosserat Rod (Renda et al., 2012;Renda et al., 2014), beam-theory models (Camarillo et al., 2009) and Finite Element models (FEM) (Duriez, 2013;Goury and Duriez, 2018). Some of these models can be extended to incorporate dynamic properties. ...
Soft robots exhibit complex nonlinear dynamics with large degrees of freedom, making their modelling and control challenging. Typically, reduced-order models in time or space are used in addressing these challenges, but the resulting simplification limits soft robot control accuracy and restricts their range of motion. In this work, we introduce an end-to-end learning-based approach for fully dynamic modelling of any general robotic system that does not rely on predefined structures, learning dynamic models of the robot directly in the visual space. The generated models possess identical dimensionality to the observation space, resulting in models whose complexity is determined by the sensory system without explicitly decomposing the problem. To validate the effectiveness of our proposed method, we apply it to a fully soft robotic manipulator, and we demonstrate its applicability in controller development through an open-loop optimization-based controller. We achieve a wide range of dynamic control tasks including shape control, trajectory tracking and obstacle avoidance using a model derived from just 90 min of real-world data. Our work thus far provides the most comprehensive strategy for controlling a general soft robotic system, without constraints on the shape, properties, or dimensionality of the system.
... Constant curvature models have allowed researchers to eliminate many computational complexities such as Ref. [8], making them suitable for finding analytical solutions related to dynamic models and real-time control applications. In order to accurately simulate the behavior of real robots and cover their workspace, the concept of variable curvature has been proposed, which is based on dividing each section of the robot into multiple parts with constant curvature [9]. The variable curvature idea theoretically allows for greater flexibility in the robot. ...
This paper tackles the challenges encountered in surgical continuum robotics by introducing a dynamic model tailored for a cable-driven continuum robot. The intricacies of dynamic modeling and control frequently lead to suboptimal outcomes. Prior studies have often lacked comprehensive descriptions of individual robot component movements, thereby impeding control processes, especially in the presence of external disturbances. Although machine learning-based models show promise across different domains, they face hurdles in continuum robotics due to the complexity of the systems involved. Traditional mathematical models, in contrast, offer explicit equations, providing better interpretability, unlike machine learning models that may struggle with generalization, especially in highly nonlinear systems like continuum robots. The developed model adeptly captures the kinematic and dynamic constraints of various robot segments, serving as the foundation for a robust optimized control strategy. This strategy, which integrates computed torque control and particle swarm optimization (PSO-CTC), enables real-time computation of joint torques based on feedback, ensuring precise and stable task execution even amidst external perturbations. Comparative analysis with an optimized proportional integral derivative (OPID) controller unequivocally demonstrates the superiority of the optimized computed torque controller (OCTC) in settling time, overshoot, and robustness against disturbances. This advancement represents a noteworthy contribution to robotics, with the potential to significantly enhance continuum robot performance in surgical and inspection applications, thereby fostering innovative advancements across various fields.
... Troncoso et al. (2022) employed a similar approach for the COBRA system. developed a kinematic model of their continuum robot for maxillary sinus surgery using the variable curvature continuum kinematics method, described by Mahl, Hildebrandt, and Sawodny (2014), and applying the PCC method to some segments of the robot. Recently, also Mavinkurve et al. (2023) exploited the PCC assumption to model the continuum manipulator inspired by the woodpecker tongue, as well as Yang et al. (2023), who proposed a kinetostatic model of the continuum manipulator thought for aero-engine maintenance. ...
Nowadays, the use of robotic systems for inspection and maintenance is gaining importance due to the number of scenarios in which robots can operate.
Indeed, robotic systems provide many advantages in harsh and hostile environments, improving workers' safety and overall efficiency.
Given their ability to perform different tasks, robotic manipulators constitute a significant proportion of the possible robotic systems employed in these environments.
The category of manipulators is a heterogeneous group that comprises many different types of robots: non-redundant, redundant, and hyper-redundant manipulators, the latter being subdivided into discrete-joint manipulators and continuum manipulators.
Among these types of robots, hyper-redundant manipulators play a crucial role in operating in challenging environments due to their ability to perform auxiliary tasks, such as obstacle avoidance and joint limits satisfaction.
Furthermore, manipulators can be made of rigid or soft mechanisms and can be mobile, operating in aerial, ground, and underwater environments.
The objective of this review article is to provide a reference point for researchers interested in modelling and controlling manipulators for inspection and maintenance in challenging environments.
... For the kinematics and statics modeling of soft robots, methods such as the improved Denavit-Hartenberg approach [30], variable curvature [31], and constant methods [32] are commonly used. These approximation methods are effective for soft robots without external loads. ...
The purpose of this research is to present an alternative multibody dynamic model for soft robots and to analyze the intrinsic mechanism of motion. It is difficult to directly apply traditional robot modeling methods due to the large structural deformation of soft walking robots. This paper establishes the dynamic modeling of a soft robot system with contact/impact based on the corotational formulation of the special Euclidean group SE(2). The experiments are designed to verify the dynamic model of the robot. The history of the marked points on the robot prototype is measured in real time by an ARAMIS Adjustable Camera System. Based on the dynamic model, we conducted an in-depth analysis of the entire process through which the robot achieves directional walking utilizing complex friction characteristics. Notably, the robot’s kick-up phenomenon attracted our attention, and an analytical model for predicting the critical drive acceleration is proposed. The conditions and mechanisms of the robot’s kick-up are analyzed, and effective direction is provided for designing new drive laws. Finally, several sets of key parameters affecting the walking efficiency are analyzed using the multibody model, which can provide scientific guidance for the material selection and optimization of the robot. The presented dynamic modeling approach can be freely extended to other soft robots, which will provide valuable references for the design and analysis of soft robots.
... The self-sensing techniques are mainly employed to measure the shape change of a CDCR, which can be classified into the following approaches: (1) vision-based motion capture system for an open and barrier-free environment [130,131]; (2) stretchable sensors arranged along the backbone of a CDCR for an indirect measurement through kinematic mapping [132]; (3) magnetic sensors integrated into a CDCR to estimate its shape changes [133,134]; (4) fiber Bragg grating (FBG) sensors to measure bending of a CDCR's backbone [95,[135][136][137][138][139]. In general, the existing self-sensing techniques only allow for imprecise measurement of the CDCRs shape due to the high flexibility and large deflection of the CDCR's backbone as well as the unknown external loads and disturbances. ...
Rigid robots have found wide-ranging applications in manufacturing automation, owing to their high loading capacity, high speed, and high precision. Nevertheless, these robots typically feature joint-based drive mechanisms, possessing limited degrees of freedom (DOF), bulky structures, and low manipulability in confined spaces. In contrast, continuum robots, drawing inspiration from biological structures, exhibit characteristics such as high compliance, lightweight designs, and high adaptability to various environments. Among them, cable-driven continuum robots (CDCRs) driven by multiple cables offer advantages like higher dynamic response compared to pneumatic systems and increased working space and higher loading capacity compared to shape memory alloy (SMA) drives. However, CDCRs also exhibit some shortcomings, including complex motion, drive redundancy, challenging modeling, and control difficulties. This study presents a comprehensive analysis and summary of CDCR research progress across four key dimensions: configuration design, kinematics and dynamics modeling, motion planning, and motion control. The objective of this study is to identify common challenges, propose solutions, and unlock the full potential of CDCRs for a broader range of applications.
... For closed-loop control of soft manipulators or arms (Figure 1(a) and (b)), wire encoders have been used to measure the states (Mahl et al., 2014;Kapadia et al., 2014;Tamadon et al., 2020). Other studies have combined the kinematics of the robot with the motion data from cameras or motion capture systems (Hannan and Walker, 2005;Kang et al., 2013;Dalvand et al., 2016;Ansari et al., 2017;Del Giudice et al., 2017;Werner et al., 2020). ...
This study proposes a modularized soft robotic arm with integrated sensing of human touches for physical human–robot interactions. The proposed robotic arm is constructed by connecting multiple soft manipulator modules, each of which consists of three bellow-type soft actuators, pneumatic valves, and an on-board sensing and control circuit. By employing stereolithography three-dimensional (3D) printing technique, the bellow actuator is capable of incorporating embedded organogel channels in the thin wall of its body that are used for detecting human touches. The organogel thus serves as a soft interface for recognizing the intentions of the human operators, enabling the robot to interact with them while generating desired motions of the manipulator. In addition to the touch sensors, each manipulator module has compact, soft string sensors for detecting the displacements of the bellow actuators. When combined with an inertial measurement unit (IMU), the manipulator module has a capability of estimating its own pose or orientation internally. We also propose a localization method that allows us to estimate the location of the manipulator module and to acquire the 3D information of the target point in an uncontrolled environment. The proposed method uses only a single depth camera combined with a deep learning model and is thus much simpler than those of conventional motion capture systems that usually require multiple cameras in a controlled environment. Using the feedback information from the internal sensors and camera, we implemented closed-loop control algorithms to carry out tasks of reaching and grasping objects. The manipulator module shows structural robustness and the performance reliability over 5,000 cycles of repeated actuation. It shows a steady-state error and a standard deviation of 0.8 mm and 0.3 mm, respectively, using the proposed localization method and the string sensor data. We demonstrate an application example of human–robot interaction that uses human touches as triggers to pick up and manipulate target objects. The proposed soft robotic arm can be easily installed in a variety of human workspaces, since it has the ability to interact safely with humans, eliminating the need for strict control of the environments for visual perception. We believe that the proposed system has the potential to integrate soft robots into our daily lives.
The combination of flexible structures, external forces, and various soft material blends commonly causes complex deformations in continuum robots, making their modeling challenging. In this paper, we propose a bending model for pneumatic soft actuators. The chamber layer is being modeled as two states: (1) Free space expansion: using a modified virtual work principle, that is, algebraic calculation of the deformed volume of the chamber; (2) Contact expansion: Finite-strain membrane theory for modeling chamber layers. Modeling of constrained layers using Euler-Bernoulli finite-strain hyperelastic beam theory. Influence of gravity and axial tension is taken into account in the model; the model only requires input material parameters, structural parameters, and pressure for both the constraint and chamber layers. The data are then used to predict the bending behavior of soft actuators in free space. Soft actuators with different combinations of constraint and chamber layers were produced to carry out the experiment, enabling the validation of theoretical predictions. Additionally, the results were compared with those obtained via finite element analysis models. The proposed approach applies to Soft PneuNet Actuators (SPNA) with similar structures.
This paper investigates decoupled motion control and dimension optimization of composite notched continuum mechanisms. In general, the end-effectors of endoscopic surgical robots predominantly consist of rigid articulated actuators, which exhibit limited maneuverability and face challenges in constrained operational environments. The introduction of continuum mechanisms has emerged as a key solution to address these limitations. In this paper, the design, analysis, and development of a novel six-degree-of-freedom (6-DOF) composite continuum surgical robot are presented. Kinematic modeling of the continuum mechanisms is performed, and a decoupled kinematic model of the composite continuum mechanisms is constructed. Furthermore, based on the local and global dexterity of the composite continuum mechanisms, the optimization of the 2-segment lengths of the composite continuum mechanisms is completed. Subsequently, both the forward and inverse kinematic models of the 6-DOF composite continuum surgical robot are developed. Finally, through a series of motion control experiments, the decoupled kinematic model of the prototype is proved to be effective. The prototype has a certain load capacity and can accomplish simple trajectory planning motion, which has potential application in the field of single-hole interventional minimally invasive surgery.
Should robots be stiff to resist external mechanical perturbations or should they adapt to and maybe exploit the interaction with their environments? Soft robotics is an approach to design and develop deformable robots that can comply with, and even exploit, interactions for accomplishing their tasks. Soft robotics is then the use of soft materials or deformable structures to build robots. Though a young field, a wide range of techniques and technologies exist today for designing and building soft robots, including methods for fabrication, technologies for actuation and sensing, as well as control techniques. Together with such technological development, soft robotics technologies enable robot abilities that were not possible before, like squeezing, stretching, morphing, stiffening, growing, self-healing, evolving. They open up new scenarios for robotics, leading towards robots that can effectively and efficiently adapt to their environments and tasks. It becomes possible to pursue applications of soft robots in several fields that range from explorations in unstructured environments to biomedical applications, where a soft interaction with human patients is required.
The milking manipulator is the primary operator of the Automatic Milking System (AMS), capable of automating processes such as cup attachment, teat massage, and milking to reduce labor intensity and enhance production quality and efficiency. However, current manipulators generally suffer from issues such as excessive size, insufficient flexibility, and low efficiency. This paper mainly presents a dexterous manipulator with a Rigid-Flexible Coupling End-Effector (RFCE), featuring flexible finger mechanisms that can switch between various states to accommodate different cup attachment stages and adapt to teats in various spatial orientations. Firstly, through an introduction to the structural design, hardware architecture, and software system of the robot, the design philosophy and operational principle of the robot system are comprehensively elucidated. Subsequently, the forward kinematic model of the manipulator is proposed and the inverse kinematic model based on the semi-analytical method is established. The workspace, dexterity, and efficacy of the inverse solution algorithm were analyzed through simulation. Then, a static model of the flexible joint was formulated based on the Cosserat theory. The deformation behavior of the flexible joint was analyzed, and the kinematic model was adjusted accordingly. Finally, experiments are conducted to validate the static model, the manipulator's positioning accuracy, and the actual task performance. Experimental data shows that the manipulator's absolute positioning accuracy is 1.32mm, with a single cup attachment time of no more than 6s and a success rate of no less than 95%. Simulation and experimental results indicate that the developed dexterous manipulator possesses excellent flexibility and the capability to perform milking operations.
This paper addresses the kinematic control of a redundant soft robotic arm. Kinematic full pose control for soft robots is challenging because direct application of the classical controllers developed based on rigid robots to soft robots could lead to unreliable or infeasible motions. In this study, we explore the manipulability property of soft robotic arm and develop an advanced resolved-rate controller which prioritize position over orientation control and switches its modes and gains based on position and orientation manipulabilities, enabling stable motion even when the robot is close to singular and near-singular configurations. The simulation and experimental results indicate that our proposed method outperforms previous methods in terms of both accuracy and smoothness during operations.
In this chapter, we discuss some practical issues in deploying soft robots. Specifically, we describe the practical advantages and problems arising from the conversion of industrial concrete hoses into soft continuum hose robots, for 3D printing of cement in the construction industry. “Robotizing” the inherent flexibility and maneuverability of hoses offers the potential for the creation and high fidelity repair of more complex structures than currently feasible. However, the inherent softness present in the hose structures presents practical problems. Hose compression can reduce the accuracy of the concrete print. We discuss this phenomenon, along with practical measures taken to address the issue.
The flexible or continuum manipulators present excellent dexterity in confined space, which is beneficial to wide application prospects in many fields. In this paper, we establish the kinematic model and propose a trajectory planning algorithm for multi-segment continuum manipulators. The multi-level mapping from the actuator variables to manipulator tip is described. A novel modal kinematic method is proposed to overcome the singularity problem generated by the piecewise constant curvature kinematics modeling method. Then, the improved particle swarm optimization algorithm (IPSO) is proposed to solve the problem of redundant inverse kinematics and realize the trajectory tracking of the manipulator tip. In addition, the configuration parameters are restricted by the constraint functions, so that the precise shape of the multi-segment manipulator can be controlled. Finally, a series of numerical simulations are conducted to implement the investigation. Simulation results demonstrate that the proposed modal kinematic method and the trajectory planning algorithm are effective for multi-segment continuum manipulator.
Soft manipulators, renowned for their compliance and adaptability, hold great promise in their ability to engage safely and effectively with intricate environments and delicate objects. Nonetheless, controlling these soft systems presents distinctive hurdles owing to their nonlinear behavior and complicated dynamics. Learning‐based controllers for continuum soft manipulators offer a viable alternative to model‐based approaches that may struggle to account for uncertainties and variability in soft materials, limiting their effectiveness in real‐world scenarios. Learning‐based controllers can be trained through experience, exploiting various forward models that differ in physical assumptions, accuracy, and computational cost. In this article, the key features of popular forward models, including geometrical, pseudo‐rigid, continuum mechanical, or learned, are first summarized. Then, a unique characterization of learning‐based policies, emphasizing the impact of forward models on the control problem and how the state of the art evolves, is offered. This leads to the presented perspectives outlining current challenges and future research trends for machine‐learning applications within soft robotics.
Soft robots are high-dimensional nonlinear systems coupled with both geometric and material nonlinearity. Control of such a system is complex and time-consuming. In this study, a real-time trajectory tracking control framework is established based on the reduced order extended position-based dynamics. In contrast to the common nonlinear model order reduction methods that require to collect a large number of data to create the motion subspace, this article's motion subspace is constructed based on the model configuration and material properties. The linear modes of the model and the related modal derivatives provide the reduced order matrix, which streamlines and increases the efficiency of model construction. Then, coupled with the instantaneous optimal control, a real-time reduced order model-based control framework of soft robots can be constructed. Experiments on trajectory tracking of a soft manipulator are conducted to verify the accuracy and efficiency of the proposed controller. The average error of all experiments is within 1 cm; and the single-step calculation time of the controller is about 0.057 s, which is less than the sampling period 0.1 s.
Full text: https://www.sciencedirect.com/science/article/pii/S0094114X24002295?dgcid=coauthor
In this letter, we aim to develop an efficient and accurate kinematic model of a soft wrist that consists of pneumatic bellows configured in parallel, toward dexterous manipulation in confined space. The challenge arises from the distributed nature and deformation-dependency of the generated pneumatic actuation forces along the air chamber, making it difficult to obtain the equivalent generalized forces. To achieve a trade-off between accuracy and computational efficiency, we first establish a simplified geometric model of local deformation of the bellow by using the global state variables, based on simulations and experimental observations of bellow -type actuators. Then we define the deformation gradient of the chamber's wall. Subsequently, we develop forward and inverse kinematics by utilizing the principle of minimum potential energy. The analyses of the wrist's workspace and payload limit are conducted, and trajectory tracking experiments are performed to validate the proposed kinematics. The average error for the circle and tetrahedron trajectories with no load reaches about 2.40% and 5.25% of the characteristic length of the trajectory, respectively, with an average computation time of 0.17 s and 0.16 s per point, and the model maintains a certain level of accuracy under a permissible range of loads. Finally, we mount a suction cup at the end of the soft wrist and successfully perform the pick-and-place task in confined space.
3D tracking of single‐port continuum surgical tools is an essential step toward their closed‐loop control in robot‐assisted‐laparoscopy, since single‐port tools possess multiple degrees‐of‐freedom (DoFs) without distal joint sensors and hence have lower motion precision compared to rigid straight‐stemmed tools used in multi‐port robotic laparoscopy. This work proposes a novel markerless 3D tracking framework for continuum surgical tools using a proposed surgical tool partial pose estimation network (STPPE‐Net) based on U‐Net and ResNet. The STPPE‐Net estimates the segmentation and a 5‐DoF pose of the tool end‐effector. This network is entirely trained by a synthetic data generator based on domain randomization (DR) and requires zero manual annotation. The 5‐DoF pose estimation from the STPPE‐Net is combined with the surgical tool axial rotation from the robot control system. Then, the entire pose is further refined via a region‐based optimization that maximizes the overlap between the tool end‐effector segmentation from the STPPE‐Net and its projection onto the image plane of the endoscopic camera. The segmentation accuracy and 6‐DoF pose estimation precision of the proposed framework are validated on the images captured from an endoscopic single‐port system. The experimental results show the effectiveness and robustness of the proposed tracking framework for continuum surgical tools.
Organisms can adapt to various complex environments by obtaining optimal morphologies. Plant tendrils evolve an extraordinary and stable spiral morphology in the free-growing stage. By combining apical and asymmetrical growth strategies, the tendrils can adjust their morphology to wrap around and grab different supports. This phenomenon of changing tendril morphology through the movement of growth inspires a thoughtful consideration of the laws of growth that underlie it. In this study, tendril growth is modeled based on the Kirchhoff rod theory to obtain the exact morphological equations. Based on this, the movement patterns of the tendrils are investigated under different growth strategies. It is shown that the self-interference phenomenon appears as the tendril grows, allowing it to hold onto its support more firmly. In addition, a finite element model is constructed using continuum media mechanics and following the finite growth theory to simulate tendril growth. The growth morphology and self-interference phenomenon of tendrils are observed visually. Furthermore, an innovative class of fluid elastic actuators is designed to verify the growth phenomena of tendrils, which can realize the wrapping and locking functions. Several experiments are conducted to measure the end output force and the smallest size that can be clamped, and the output efficiency of the elastic actuator and the optimal working pressure are verified. The results presented in this study could reveal the formation law of free tendril spiral morphology and provide an inspiring idea for the programmability and motion control of bionic soft robots, with promising applications in the fields of underwater rescue and underwater picking.
The seahorse's tail is renowned for its exceptional bending ability and strength owing to its unique biological structures. Inspired by this, this letter presents a novel modular cable-driven continuum robot with remarkable load capacity. By employing an asymmetric structure with both flexible and rigid connections in different directions, the proposed robot adaptively grasps objects of various sizes and shapes while handling substantial loads. To study the impact of cable length variations on the robot's motion, an equivalent model is developed to derive the robot's forward kinematics under ideal conditions, which is subsequently validated through experimental analysis. Moreover, stiffness analysis is executed to clarify the structural stability in different directions. Experiment results show that the proposed robot can grasp objects sized from 60 mm to 250 mm and a maximum weight of 3500 g. In summary, the robot exhibits remarkable resilience against impact loads, which is suitable for robust grasping of non-cooperative objects.
We evaluate the use of continuum kinematics with constant curvature as a kinematic model for Festo's “Bionic Handling Assistant” (BHA). We introduce a new, elegant, and parameterless method to deal with geometric singularities in stretched positions, which allows to capture pure elongations that are not naturally expressed by the toroidal deformations underlying the constant curvature assumption. The stability of the method is shown with numeric simulations. We evaluate how well this model describes the BHA by using real-world position measurements as quantitative ground truth and find a good match between model and real BHA, with only 1% relative error. The model provides a practical, and highly efficient tool for the simulation and experimentation with continuum robots and is available as free software library1.
This work deals with the sensorization of continuum soft robots for reconstructing their spatial configuration. Since at the present time the proprioceptive perception is prevalently achieved using external 3D optical methods, an embedded system is needed for the improvement of the performances of this promising kind of robots. The idea is to use stretch sensors to reconstruct the spatial configuration of a robotic structure: differential measurements on strain values can be used to derive local curvatures performed by the arm. Strain values have been extracted using a conductive textile that presents very high elasticity and lightness. The main feature is that its electrical resistance depends on its mechanical strain and it has been characterized in order to derive this strain-resistance relation. The reconstruction method that allows to obtain spatial configuration from material deformations is then reported. A practical application on reconstructing the configuration of an octopus-inspired robot arm is finally shown and discussed.
This paper describes and discusses the history and state of the art of continuous backbone robot manipulators. Also known as continuum manipulators, these robots, which resemble biological trunks and tentacles, offer capabilities beyond the scope of traditional rigid-link manipulators. They are able to adapt their shape to navigate through complex environments and grasp a wide variety of payloads using their compliant backbones. In this paper, we review the current state of knowledge in the field, focusing particularly on kinematic and dynamic models for continuum robots. We discuss the relationships of these robots and their models to their counterparts in conventional rigid-link robots. Ongoing research and future developments in the field are discussed.
Quaternions without unity constraint are used as configuration variables for rotational degrees of freedom of Cosserat rod models, thereby naturally incorporating inflation as well as bending, twisting, extension, and shear deformations of elongate robotic manipulators. The configuration space becomes isomorphic to a subspace of 7-D real-valued functions; thus, an unconstrained local minimizer of total potential energy is a static equilibrium. The ensuing calculus of variations is automated by computer algebra to derive weak-form integral equations that are easily translated to a finite-element package for efficient computation using internal forces. Discontinuities in strain variables are handled in a numerically reliable way. Inextensible, unshearable rod models are derived simply by taking limits of corresponding stiffness parameters. The same procedure facilitates unified software code for both flexible and rigid segments. Simulation experiments with an inflating tube, a helical coil, and a magnetic catheter produce good-quality results and indicate that the computational effort of the proposed method is about two orders of magnitude less than common 3-D finite-element models of large deformation nonlinear elasticity.
Recently, continuum manipulators have drawn a lot of interest and effort from the robotic community, nevertheless control and modeling of such manipulators are still a challenging task especially because they require a continuum approach. In this paper, a general mechanical model with a geometrically exact approach for tendon-driven continuum manipulators is presented. This model can be applied to a wide range of manipulators thanks to the generality of the parameters which can be set. The approach proposed could as well be a powerful tool for developing the control strategy. The model is also capable of properly simulating the coupled tendon drive, because it takes into account the torsion of the robot arm rather than neglecting it, as it is common practice in other existing models.
This paper presents a novel and unified analytic formulation for kinematics, statics, and shape restoration of multiple-backbone continuum robots. These robots achieve actuation redundancy by independently pulling and pushing three backbones to carry out a bending motion of two-degrees-of-freedom (DoF). A solution framework based on constraints of geometric compatibility and static equilibrium is derived using elliptic integrals. This framework allows the investigation of the effects of different external loads and actuation redundancy resolutions on the shape variations in these continuum robots. The simulation and experimental validation results show that these continuum robots bend into an exact circular shape for one particular actuation resolution. This provides a proof to the ubiq-uitously accepted circular-shape assumption in deriving kinematics for continuum robots. The shape variations due to various actuation redundancy resolutions are also investi-gated. The simulation results show that these continuum robots have the ability to redis-tribute loads among their backbones without introducing significant shape variations. A strategy for partially restoring the shape of the externally loaded continuum robots is proposed. The simulation results show that either the tip orientation or the tip position can be successfully restored.
This paper introduces a method for computing the shape of a continuously-flexible (continuum) robot in 3-D space which includes gravity loading by applying Cosserat rod theory to a continuum robot. With this theory, the shape of the rod can be determined using force-torque balance equations obtained from a simple free body diagram that represents the continuum robot. Real-time performance of 125 Hz makes this approach viable for the control of a continuum robot, enabled by avoiding boundary-value conditions in the solution.
A new approach to steerable needle design is proposed for use in minimally invasive surgery. The technology is based on sets of curved concentric tubes. By rotating and extending the tubes with respect to each other, the position and orientation of the needle tip, as well as the shape of the inserted length, can be controlled. A mechanics model is presented for computing the shape of the needle. Forward and inverse kinematic equations are also derived. In addition, experimental results are presented as validation of the approach.
Continuum robotics has rapidly become a rich and diverse area of research, with many designs and applications demonstrated. Despite this diversity in form and purpose, there exists remarkable similarity in the fundamental simplified kinematic models that have been applied to continuum robots. However, this can easily be obscured, especially to a newcomer to the field, by the different applications, coordinate frame choices, and analytical formalisms employed. In this paper we review several modeling approaches in a common frame and notational convention, illustrating that for piecewise constant curvature, they produce identical results. This discussion elucidates what has been articulated in different ways by a number of researchers in the past several years, namely that constant-curvature kinematics can be considered as consisting of two separate submappings: one that is general and applies to all continuum robots, and another that is robot-specific. These mappings are then developed both for the single-section and for the multi-section case. Similarly, we discuss the decomposition of differential kinematics (the robot’s Jacobian) into robot-specific and robot-independent portions. The paper concludes with a perspective on several of the themes of current research that are shaping the future of continuum robotics.
A novel approach toward construction of robots is based on a concentric combination of precurved elastic tubes. By rotation and extension of the tubes with respect to each other, their curvatures interact elastically to position and orient the robot's tip, as well as to control the robot's shape along its length. In this approach, the flexible tubes comprise both the links and the joints of the robot. Since the actuators attach to the tubes at their proximal ends, the robot itself forms a slender curve that is well suited for minimally invasive medical procedures. This paper demonstrates the potential of this technology. Design principles are presented and a general kinematic model incorporating tube bending and torsion is derived. Experimental demonstration of real-time position control using this model is also described.
This paper introduces three algorithms which are essential for the practical, real-time implementation of continuum robots. Continuum robots lack the joints and links which compose traditional and high-degree-of-freedom robots, instead relying on finite actuation mechanisms to shape the robot into a smooth curve. Actuator length limits shape the configuration or joint space of continuum manipulators, introducing couplings analyzed in this paper which must be understood to make effective use of continuum robot hardware. Based on the new understanding of the configuration space uncovered, this paper then derives the workspace of continuum robots when constrained by actuator length limits. Finally, a tangle/untangle algorithm correctly computes the shape of the distal segments of multisection tendon-actuated continuum robots. These contributions are essential for effective use of a wide range of continuum robots, and have been implemented and tested on two different types of continuum robots. Results and insight gained from this implementation are presented
We introduce a new method for synthesizing kinematic relationships for a general class of continuous backbone, or continuum , robots. The resulting kinematics enable real-time task and shape control by relating workspace (Cartesian) coordinates to actuator inputs, such as tendon lengths or pneumatic pressures, via robot shape coordinates. This novel approach, which carefully considers physical manipulator constraints, avoids artifacts of simplifying assumptions associated with previous approaches, such as the need to fit the resulting solutions to the physical robot. It is applicable to a wide class of existing continuum robots and models extension, as well as bending, of individual sections. In addition, this approach produces correct results for orientation, in contrast to some previously published approaches. Results of real-time implementations on two types of spatial multisection continuum manipulators are reported.
“Hyper-redundant” robots have a very large or infinite
degree of kinematic redundancy. This paper develops new methods for
determining “optimal” hyper-redundant manipulator
configurations based on a continuum formulation of kinematics. This
formulation uses a backbone curve model to capture the robot's essential
macroscopic geometric features. The calculus of variations is used to
develop differential equations, whose solution is the optimal backbone
curve shape. We show that this approach is computationally efficient on
a single processor, and generates solutions in O(1) time for an N
degree-of-freedom manipulator when implemented in parallel on O(N)
processors. For this reason, it is better suited to hyper-redundant
robots than other redundancy resolution methods. Furthermore, this
approach is useful for many hyper-redundant mechanical morphologies
which are not handled by known methods
This paper presents novel and efficient kinematic modeling
techniques for “hyper-redundant” robots. This approach is
based on a “backbone curve” that captures the robot's
macroscopic geometric features. The inverse kinematic, or
“hyper-redundancy resolution,” problem reduces to
determining the time varying backbone curve behavior. To efficiently
solve the inverse kinematics problem, the authors introduce a
“modal” approach, in which a set of intrinsic backbone curve
shape functions are restricted to a modal form. The singularities of the
modal approach, modal non-degeneracy conditions, and modal switching are
considered. For discretely segmented morphologies, the authors introduce
“fitting” algorithms that determine the actuator
displacements that cause the discrete manipulator to adhere to the
backbone curve. These techniques are demonstrated with planar and
spatial mechanism examples. They have also been implemented on a 30
degree-of-freedom robot prototype
“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods.
This paper addresses the design of wire actuated steerable electrode arrays for optimal insertions in cochlear implant surgery. These underactuated electrode arrays are treated as continuum robots which have an embedded actuation strand inside their flexible medium. By pulling on the actuation strand, an electrode array assumes a minimum-energy shape. The problems of designing optimal actuation strand placement are addressed in this paper. Based on the elastic modeling of the steerable electrode arrays proposed in this paper, an analytical solution of the strand placement is solved to minimize the shape discrepancy between a bent electrode array and a given target curve defined by the anatomy. Using the solved strand placement inside the steerable electrode array, an optimized insertion path planning with robotic assistance is proposed to execute the insertion process. Later, an optimization algorithm is presented to minimize the shape discrepancy between an inserted electrode array and a given target curve during the whole insertion process. Simulations show a steerable electrode array bending using the elastic model and robot insertion path planning with optimized strand placement. Two experiments have been conducted to validate the elastic model and algorithms. [DOI: 10.1115/1.4007005]
Mechanics-based models of concentric tube continuum robots have recently achieved a level of sophistication that makes it possible to begin to apply these robots to a variety of real-world clinical scenarios. Endonasal skull base surgery is one such application, where their small diameter and tentacle-like dexterity are particularly advantageous. In this paper, we provide the medical motivation for an endonasal surgical robot featuring concentric tube manipulators, and describe our model-based design and teleoperation methods, as well as a complete system incorporating image guidance. Experimental demonstrations using a laparoscopic training task, a cadaver reachability study, and a phantom tumor resection experiment illustrate that both novice and expert users can effectively teleoperate the system, and that skull base surgeons can use the robot to achieve their objectives in a realistic surgical scenario.
This paper presents a new three dimensional (3D) kinematic model based on mode shape functions (MSF) for multisection continuum arms. It solves the singularity problems associated with previous models and introduces a novel approach for intuitively deriving exact, singularity-free MSFs, thus avoiding mode switching schemes and simplifying error models. The model is able to simulate spatial bending, pure elongation/contraction, and introduces inverse orientation kinematics for the first time to multisection continuum arms. Also, it carefully accounts for physical constraints in the joint space to provide enhanced insight into practical mechanics, and produces correct results for both forward and inverse kinematics. The model is validated through simulations, based on a prototype continuum robotic arm. Proposed approach is applicable to a broad spectrum of continuum robotic arm designs.
We describe and discuss the development of long, thin, continuous “string-like” robots aimed at Space exploration missions. These continuous backbone “continuum” robots are inspired by numerous biological structures, particularly vines, worms, and the tongues of animals such as the anteater. The key novelty is the high length-to-diameter ratio of the robots. This morphology offers penetration into, and exploration of, significantly narrower and deeper environments than accessible using current robot technology. In this paper, we introduce new design alternatives for long thin continuum robots, based on an analysis and extension of three core existing continuum robot design types. The designs are evaluated based on their mechanical feasibility, structural properties, kinematic simplicity, and degrees of freedom.
The Bionic Handling Assistant is a compliant, pneumatically actuated continuum manipulator designed to be used for cooperative manipulation. In 2010, it won the German Federal Presidents prize for achievements in technology and innovation, called Deutscher Zukunftspreis. Unlike most manipulators, its flexible structure is link and actuator at the same time, copying an elephant's trunk. For this robot arm, the forward kinematics is derived and validated by test bench measurements. The forward kinematics is an analytical description of the manipulator's backbone curvature. It describes the manipulator's tool center point pose (position and orientation) dependent of the actuator expansions. The kinematic model is assembled of several in series connected three degrees of freedom parallel mechanisms of type 3UPS-1PU.
Continuum manipulators are continuously bending robots consisting of an infinite number of kinematic degrees of freedom (DOF). To reduce the number of actuators, the manipulators are designed in a way to build several serially connected groups of mechanically coupled DOF. These groups are called sections. For real-time motion control, a kinematic model capable to describe the manipulator's deflection is necessary. A common way to model the manipulator kinematics is to describe the deformation of a single section by a curve with constant curvature. This assumption constitutes an intense constrain with respect to manipulator design or model accuracy. Thus, a new kinematic modeling approach capable to describe the kinematics of continuum manipulators with variable section curvature is proposed in the present work. It subdivides a single section in a finite number of virtual units with piecewise constant curvature. This provides the possibility to shape the modeled section curvature closely to the deformation of any arbitrarily bending continuum manipulator. To demonstrate that this modeling approach is well suited for real-time control applications, simulation results of a Jacobian based feed-forward pose control are presented that are applied to the common class of three actuator continuum manipulators.
Efficient formulations for the dynamics of continuum robots are necessary to enable accurate modeling of the robot's shape during operation. Previous work in continuum robotics has focused on low-fidelity lumped parameter models, in which actuated segments are modeled as circular arcs, or computationally intensive high-fidelity distributed parameter models, in which continuum robots are modeled as a parameterized spatial curve. In this paper, a novel dynamic modeling methodology is studied that captures curvature variations along a segment using a finite set of kinematic variables. This dynamic model is implemented using the principle of virtual power (also called Kane's method) for a continuum robot. The model is derived to account for inertial, actuation, friction, elastic, and gravitational effects. The model is inherently adaptable for including any type of external force or moment, including dissipative effects and external loading. Three case studies are simulated on a cable-driven continuum robot structure to study the dynamic properties of the numerical model. Cross validation is performed in comparison to both experimental results and finite-element analysis.
Purpose
– This review will describe the development of the Bionic Handling Assistant as well as the additive manufacturing (AM) process of robot grippers and its possibilities.
Design/methodology/approach
– AM offers the chance to use the additive processes to produce highly flexible automation parts and systems as the Bionic Handling Assistant in small and medium quantities that can utilize a lot of design advantages provided by the process.
Findings
– A lot of products of today and especially tomorrow could be produced by rapid manufacturing. New categories of products, such as the Bionic Handling Assistant, will occur.
Originality/value
– In the paper, aspects of a visionary scenario for future productions are shown and demonstrated on the Bionic Handling Assistant.
Over the past several years, there has been a rapidly expanding interest in the study and construction of a new class of robot manipulators which utilize high degree of freedom, or continuous, backbone structures. In this paper, we consider some basic properties of these "continuum" or "hyper-redundant" robots. We base our analysis around remotely-driven, tendon-actuated manipulators such as the Rice/Clemson "Elephant's Trunk". We briefly discuss the kinematic model, before detailing how to approach the inverse kinematics for a planar continuum robot by decomposition into either a natural or a wavelet basis. We also examine how a wavelet decomposition method can help resolve redundancy in a planar continuum robot.
This paper presents some problems dealing with the transportation of bulk and liquid materials. The robotization of the transport process by an elastic manipulator of an elephant trunk type is proposed. The design of an experimental stand and some results of statical and dynamical analysis are presented. In conclusion, some proposals describing the possibilities of utilising elastic manipulators for transport purposes are given.
This paper shows a new design and prototyping method for a bending pneumatic rubber actuator and its application to a soft-bodied manta swimming robot. The design is based on optimal design using non-linear finite element method, in which geometrical and material non-linearity are considered and fabrication process is based on a rapid and efficient prototyping system using a CAD/CAM based rubber molding process. In this paper, the characteristics of several possible actuators are analyzed and evaluated to lead to an optimal actuator design. The actuator works very well with smooth and soft motion. The manta swimming robot in which the developed actuators are embedded is also designed based on non-linear finite element method. The developed manta swimming robot is made only of rubber and it swims in water smoothly as if it was a living fish. The experimental results of the manta robot motion show that good agreement with those of analytical results.
Continuum robots, which are composed of multiple concentric, precurved elastic tubes, can provide dexterity at diameters equivalent to standard surgical needles. Recent mechanics-based models of these “active cannulas” are able to accurately describe the curve of the robot in free space, given the preformed tube curves and the linear and angular positions of the tube bases. However, in practical applications, where the active cannula must interact with its environment or apply controlled forces, a model that accounts for deformation under external loading is required. In this paper, we apply geometrically exact rod theory to produce a forward kinematic model that accurately describes large deflections due to a general collection of externally applied point and/or distributed wrench loads. This model accommodates arbitrarily many tubes, with each having a general preshaped curve. It also describes the independent torsional deformation of the individual tubes. Experimental results are provided for both point and distributed loads. Average tip error under load was 2.91 mm (1.5% - 3% of total robot length), which is similar to the accuracy of existing free-space models.
This paper presents a new three dimensional (3D) kinematic model based on mode shape functions (MSF) for multisection continuum arms. It solves the singularity problems associated with previous models and introduces a novel approach for intuitively deriving exact, singularity-free MSFs, thus avoiding mode switching schemes and simplifying error models. The model is able to simulate spatial bending, pure elongation/contr action, and introduces inverse orientation kinematics for the first time to multisection continuum arms. Also, it carefully accounts for physical constraints in the joint space to provide enhanced insight into practical mechanics, and produces correct results for both forward and inverse kinematics. The model is validated through simulations, based on a prototype continuum robotic arm. Proposed approach is applicable to a broad spectrum of continuum robotic arm designs.
Robots consisting of several concentric, preshaped, elastic tubes can work dex- terously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these 'active cannulas' assume piece- wise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that pre- viously reported models are special cases of our formulation, and then explore in detail the implications of torsional exibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models; it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments.
Traditionally, robot manipulators have been a simple arrangement of a small number of serially connected links and actuated joints. Though these manipulators prove to be very effective for many tasks, they are not without their limitations, due mainly to their lack of maneuverability or total degrees of freedom. Continuum style (i.e., continuous "back-bone") robots, on the other hand, exhibit a wide range of maneuverability, and can have a large number of degrees of freedom. The motion of continuum style robots is generated through the bending of the robot over a given section; unlike traditional robots where the motion occurs in discrete locations, i.e., joints. The motion of continuum manipulators is often compared to that of biological manipulators such as trunks and tentacles. These continuum style robots can achieve motions that could only be obtainable by a conventionally designed robot with many more degrees of freedom. In this paper we present a detailed formulation and explanation of a novel kinematic model for continuum style robots. The design, construction, and implementation of our continuum style robot called the elephant trunk manipulator is presented. Experimental results are then provided to verify the legitimacy of our model when applied to our physical manipulator. We also provide a set of obstacle avoidance experiments that help to exhibit the practical implementation of both our manipulator and our kinematic model.
Endovascular aortic aneurysm treatment is a minimally invasive surgery (MIS) which requires high dexterity for stentgraft placement. This procedure requires technological improvements. For this purpose we have developed a new tool called MALICA (Multi Active LInk CAtheter). MALICA is an active catheter with a multi continuum micro-robots stack inside its external sheath. In this paper we present a new direct static model formulation of MALICA along with an orientation control scheme using the redundancy property of this robot.
We have developed the snake-like robot since 1972. The body of snake has "the function of an arm" when it holds something by coiling itself and also has "the function of legs" when it moves by creeping. The body of ACM has several functions, which are fulfilled one after another according to the situation. Especially in this paper, it introduces about the various move method realized about the move function using 3-dimensional type ACM, and its feature
Unlike traditional rigid linked robots, soft robotic manipulators can bend into a wide variety of complex shapes due to control inputs and gravitational loading. This paper presents a new approach for modeling soft robotic manipulators that incorporates the effect of material nonlinearities and distributed weight and payload. The model is geometrically exact for the large curvature, shear, torsion, and extension that often occur in these manipulators. The model is based on the geometrically exact Cosserat rod theory and a fiber reinforced model of the air muscle actuators. The model is validated experimentally on the OctArm V manipulator, showing less than 5% average error for a wide range of actuation pressures and base orientations as compared to almost 50% average error for the constant-curvature model previously used by researchers. Workspace plots generated from the model show the significant effects of self-weight on OctArm V.
AMADEUS is a dexterous subsea robot hand incorporating force and
slip contact sensing, using fluid filled tentacles for fingers.
Hydraulic pressure variations in each of three flexible tubes (bellows)
in each finger create a bending moment, and consequent motion or
increase in contact force during grasping. Such fingers have inherent
passive compliance, no moving parts, and are naturally depth
pressure-compensated, making them ideal for reliable use in the deep
ocean. In addition to the mechanical design, development of the hand has
also considered closed loop finger position and force control,
coordinated finger motion for grasping, force and slip sensor
development/signal processing, and reactive world modeling/planning for
supervisory `blind grasping'. Initially, the application focus is for
marine science tasks, but broader roles in offshore oil and gas,
salvage, and military use are foreseen
A new and efficient kinematic position and velocity solution
scheme for spatial hyper-redundant manipulators is presented. The
manipulator's arm has discrete links and universal joints. Backbone
curve concepts and a modal approach are used to resolve the
manipulator's redundancy. The effects of the mode shapes and the slope
of the backbone curve at the starting point on the workspace are
studied. It is shown that the usage of conventional mode shapes limits
the workspace of the hyper-redundant arm. By introducing new mode
shapes, an improved workspace is obtained. A simple and efficient
recursive fitting method is introduced to avoid complications involved
with solving systems of nonlinear algebraic equations. This method also
guarantees the existence of solutions for the inverse kinematic problem
at the velocity level. Velocity properties of the backbone curve are
investigated and the inverse velocity propagation is solved for the
spatial hyper-redundant arm. The velocity propagation scheme is
recursive and is efficiently applicable to any number of links
It is proposed to use weighted least-norm solution to avoid joint
limits for redundant joint manipulators. A comparison is made with the
gradient projection method for avoiding joint limits. While the gradient
projection method provides the optimal direction for the joint velocity
vector within the null space, its magnitude is not unique and is
adjusted by a scalar coefficient chosen by trial and error. It is shown
in this paper that one fixed value of the scalar coefficient is not
suitable even in a small workspace. The proposed manipulation scheme
automatically chooses an appropriate magnitude of the self-motion
throughout the workspace. This scheme, unlike the gradient projection
method, guarantees joint limit avoidance, and also minimizes unnecessary
self-motion. It was implemented and tested for real-time control of a
seven-degree-of-freedom (7-DOF) Robotics Research Corporation (RRC)
manipulator
German future award: Laureates 2010
- Geschä Deutscher
Geschä Deutscher Zukunftspreis. (2010). German future award: Laureates 2010. [Online]. Available: http://www.deutscher-zukunftspreis.de/en/preistraeger/laureates-2010
The bionic handling assistant: A
- A Grzesiak
- R Becker
- A Verl
A. Grzesiak, R. Becker, and A. Verl, " The bionic handling assistant: A
Analytic formulation for kinematics, statics, and shape restoration of multibackbone continuum robots via elliptic integrals
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