In numerous applications, extracting a single rotation component (termed “planar rotation”) from a 3D rotation is of significant interest. In biomechanics, for example, the analysis of joint angles within anatomical planes offers better clinical interpretability than spatial rotations. Moreover, in parallel kinematics robotic machines, unwished rotations about an axis – termed “parasitic motions” – need to be excluded. However, due to the non-Abelian nature of spatial rotations, these components cannot be extracted by simple projections as in a vector space. Despite extensive discussion in the literature about the non-uniqueness and distortion of the results due to the nonlinearity of the SO(3) group, they continue to be used due to the absence of alternatives. This paper reviews the existing methods for planar-rotation extraction from 3D rotations, showing their similarities and differences as well as inconsistencies by mathematical analysis as well as two application cases, one of them from biomechanics (flexural knee angle in the sagittal plane). Moreover, a novel, simple, and efficient method based on a pseudo-projection of the Quaternion rotation vector is introduced, which circumvents the ambiguity and distortion problems of existing approaches. In this respect, a novel method for determining the orientation of a box from camera recordings based on a two-plane projection is also proposed, which yields more precise results than the existing Perspective 3-Point Problem from the literature. This paper focuses exclusively on the case of finite rotations, as infinitesimal rotations within a single plane are non-holonomic and, through integration, produce rotation components orthogonal to the plane.

Optical microrobots are activated by a laser in a liquid medium using optical tweezers. To create visual control loops for robotic automation, this work describes a deep learning-based method for orientation estimation of optical microrobots, focusing on detecting 3-D rotational movements and localizing microrobots and trapping points (TPs). We integrated and fine-tuned You Only Look Once (YOLOv7) and Deep Simple Online Real-time Tracking (DeepSORT) algorithms, improving microrobot and TP detection accuracy by $\sim 3$% and $\sim 11$%, respectively, at the 0.95 Intersection over Union (IoU) threshold in our test set. Additionally, it increased mean average precision (mAP) by 3% at the 0.5:0.95 IoU threshold during training. Our results showed a 99% success rate in trapping events with no false-positive detection. We introduced a model that employs EfficientNet as a feature extractor combined with custom convolutional neural networks (CNNs) and feature fusion layers. To demonstrate its generalization ability, we evaluated the model on an independent in-house dataset comprising 4,757 image frames, where microrobots executed simultaneous rotations across all three axes. Our method provided mean rotation angle errors of $1.871^\circ$, $2.308^\circ$, and $2.808^\circ$ for X (yaw), Y (roll), and Z (pitch) axes, respectively. Compared to pre-trained models, our model provided the lowest error in the Y and Z axes while offering competitive results for X-axis. Finally, we demonstrated the explainability and transparency of the model’s decision-making process. Our work contributes to the field of microrobotics by providing an efficient 3-axis orientation estimation pipeline, with a clear focus on automation.

Extensible continuum robots (ECRs) offer distinct advantages over conventional continuum robots due to their ability to enhance workspace adaptability through length adjustments. This makes ECRs particularly promising for applications that require variable lengths involving the manipulation of objects in challenging environments, such as risky, cluttered, or confined. The development of ECRs necessitates careful consideration of mechanical structures, actuation methods, methods of stiffness variability, and control methods. The selection of papers is based on their relevance to ECRs within the period of 2010 to 2023 in the databases of Scopus and Web of Science. Distinguishing itself from other review papers, this paper aims to deliver a comprehensive and critical discussion about the advantages and disadvantages of ECRs concerning their mechanical structures, actuation methods, stiffness variability, and control methods. It is a beneficial resource for researchers and engineers interested in ECRs, providing essential insights to guide future developments in this field. Based on the literature, existing ECRs exhibit an inherent trade-off between flexibility and structural strength due to the absence of systematic design methods. Additionally, there is a lack of intelligent and effective controllers for achieving complex control performance and autonomous stiffness variability.

The inverse dynamics model of an industrial robot can predict and control the robot’s motion and torque output, improving its motion accuracy, efficiency, and adaptability. However, the existing inverse rigid body dynamics models still have some unmodelled residuals, and their calculation results differ significantly from the actual industrial robot conditions. The bootstrap aggregating (bagging) algorithm is combined with a long short-term memory network, the linear layer is introduced as the network optimization layer, and a compensation method of hybrid inverse dynamics model for robots based on the BLL residual prediction algorithm is proposed to meet the above needs. The BLL residual prediction algorithm framework is presented. Based on the rigid body inverse dynamics of the Newton–Euler method, the BLL residual prediction network is used to perform error compensation on the inverse dynamics model of the Franka robot. The experimental results show that the hybrid inverse dynamics model based on the BLL residual prediction algorithm can reduce the average residuals of the robot joint torque from 0.5651 N·m to 0.1096 N·m, which improves the accuracy of the inverse dynamics model compared with those of the rigid body inverse dynamics model. This study lays the foundation for performing more accurate operation tasks using industrial robots.

This paper presents the novel concept of a singularity-free tube (SFT) in the constant orientation workspace of a spatial parallel manipulator. The concept is developed and demonstrated in the context of a $6$-$6$ spatial parallel manipulator, namely, the semi-regular Stewart platform manipulator. Given two points in the said workspace, the SFT is a tubular volume which contains these points and is free of gain-type or forward-kinematic singularities. The purpose of identifying such regions in space is to allow abundant freedom to the path-planner to connect the said points by a path, which can be free of gain-type singularities simply by remaining inside the SFT at all times. To demonstrate the concept, two smooth paths obtained by formulating two different optimisation problems have been presented as examples. The SFT can be of great help in singularity-free path-planning in many similar manipulators.

In this work, we propose a novel approach for tomato pollination that utilizes visual servo control. The objective is to meet the growing demand for automated robotic pollinators to overcome the decline in bee populations. Our approach focuses on addressing this challenge by leveraging visual servo control to guide the pollination process. The proposed method leverages deep learning to estimate the orientations and depth of detected flower, incorporating CAD-based synthetic images to ensure dataset diversity. By utilizing a 3D camera, the system accurately estimates flower depth information for visual servoing. The robustness of the approach is validated through experiments conducted in a laboratory environment with a 3D printed tomato flower plant. The results demonstrate a high detection rate, with a mean average precision of 91.2 %. Furthermore, the average depth error for accurately localizing the pollination target is impressively minimal, measuring only 1.1 cm. This research presents a promising solution for tomato pollination, showcasing the effectiveness of visual-guided servo control and its potential to address the challenges posed by diminishing bee populations in greenhouses.

The cable-driven parallel mechanism (CDPM) is known as an interesting application in industry to pick and place objects owing to its advantages such as large workspaces. In addition to the advantages of this mechanism, there are some challenges to improving performance by considering constraints in different components, such as the behavior of cables, shape, size of the end effector and base, and model of pulleys and actuators. Moreover, the impact of online geometry reconfiguration must be analyzed. This paper demonstrates the impact of these constraints on the performance of reconfigurable CDPM. The methodology is based on the systematic review and meta-analysis guidelines to report the results. The databases used to find the papers are extracted from Scopus and Google Scholar, using related keywords. As a result, the impact of physical constraints on system performance is discussed. A total of 90 and 37 articles are selected, respectively. After removing duplicates and unrelated papers, 88 studies that met the inclusion criteria are selected for review. Even when considering the physical constraints in modeling the mechanism, simplifications in designing a model for the reconfigurable CDPM generate errors. There is a gap in designing high-performance controllers to track desired trajectories while reconfiguring the geometry, and the satisfaction of physical constraints needs to be satisfied. In conclusion, this review presents several constraints in designing a controller to track desired trajectories and improve performance in future work. This paper presents an integrated controller architecture that includes physical constraints and predictive control.

This paper proposes a seat support mechanism to solve the problem of misalignment between the chest examination and probe scanning areas when the patient is bent in a seated-style echocardiography robot. To guide the patient to an appropriate body position where their chest is within the examination range of the chest examination unit while minimizing the physical load of the patient, the posture of the patient must satisfy the three following conditions. (i) The breech must be in contact with the seat surface, (ii) the legs must be vertical to the floor, and (iii) the chest and mechanism must be parallel while the probe scanning and chest examination ranges must match. The human body was modeled to derive a posture that satisfies the aforementioned conditions for the height of each individual, and a seat support mechanism with four degrees of freedom was installed to guide the user to the derived posture. By installing this mechanism, the body load of the left biceps brachii, right biceps brachii, left latissimus dorsi, and right latissimus dorsi was reduced to 64.7%, 52.7%, 86.4%, and 80.2%, respectively. The sharpness of the image contours was improved to 103.8%.

Continuum robot-based surgical systems are becoming an effective tool for minimally invasive surgery. A flexible, dexterous, and compact robot structure is suitable for carrying out complex surgical operations. In this paper, we propose performance metrics for dexterity based on data density. Data density at a point in the workspace is higher if the number of reachable points is higher, with a unique configuration lying in a small square box around a point. The computation of these metrics is performed with forward kinematics using the Monte Carlo method and, hence, is computationally efficient. The data density at a particular point is a measure of dexterity at that point. In contrast, the dexterity distribution property index is a measure of how well dexterity is distributed across the workspace according to desired criteria. We compare the dexterity distribution property index across the workspace with the dexterity index based on the dexterous solid angle and manipulability-based approach. A comparative study reveals that the proposed method is simple and straightforward because it uses only the position of the reachable point as the input parameter. The method can quantify and compare the performance of different geometric designs of hyper-redundant and multisegment continuum robots based on dexterity.

This paper presents an eight wire-driven parallel robot (WDPR-8) designed to serve as a suspension manipulator for aircraft models during wind tunnel testing. The precision of these tests is significantly influenced by the system’s stability and workspace, both of which are shaped by the geometric configuration of the structure and the tension in the wires. To acquire the efficiency principle of the suspension scheme design for the model, a kinematics model for a WDPR-8 was established. Based on the kinematics model, the stiffness of a WDPR-8 was theoretically studied, and the analytical expression of stiffness matrix of a WDPR was deduced. The stiffness matrix was composed of two terms, one of which is determined by the configuration of suspension system and the other term is determined by the wire tension. Based on the analysis result, a set of suspension scheme was discussed under the calculation of stiffness matrix and workspace analysis. In the discussion process, in addition to the stiffness-maximum calculation, another criterion as force closure is presented, which is useful for increasing the stiffness and workspace of the robot. Finally, a prototype was established according to the analysis result, and the workspace experiments are conducted. Test results indicate that the workspace meets the design requirements, validating the system suspension design method of a WDPR for aircraft model suspension in wind tunnel test considering of the systematic stiffness and workspace.

Descriptions of various subsets of $\mathbb{SO}(3)$ are encountered frequently in robotics, for example, in the context of specifying the orientation workspaces of manipulators. Often, the Cartesian concept of a cuboid is extended into the domain of Euler angles, notwithstanding the fact that the physical implications of this practice are not documented. Motivated by this lacuna in the existing literature, this article focuses on studying sets of rotations described by such cuboids by mapping them to the space of Rodrigues parameters, where a physically meaningful measure of distance from the origin is available and the spherical geometry is intrinsically pertinent. It is established that the planar faces of the said cuboid transform into hyperboloids of one sheet and hence, the cuboid itself maps into a solid of complicated non-convex shape. To quantify the extents of these solids, the largest spheres contained within them are computed analytically. It is expected that this study would help in the process of design and path planning of spatial robots, especially those of parallel architecture, due to a better and quantitative understanding of their orientation workspaces.

This paper provides the methodology used to simulate and control an icosahedral tensegrity structure augmented with movable masses attached to each bar to provide a means of locomotion. The center of mass of the system can be changed by moving the masses along the length of each of the bars that compose the structure. Moving the masses changes the moments created by gravitational force, allowing for the structure to roll. With this methodology in mind, a controller was created to move the masses to the desired locations to cause such a roll. As shown later in this paper, such a methodology, assuming the movable masses have the required mass, allows for full control of the system using a quasi-static controller created specifically for this system. This system has advantages over traditional tensegrity controllers because it retains its shape and is designed for high-shock scenarios.

This article presents a detailed examination of circular target localization techniques for measuring robot pose and performing online pose correction. The investigated target localization methods include centroiding, ellipse fitting with point data and gradient information, and ellipse fitting methods with augmented and corrected input data. The performance of each method is evaluated in terms of accuracy and precision of measurements through experimental comparison with a laser tracker. This study provides technical and practical insights for selecting an appropriate target localization method in robotic applications. It also introduces a vision-based solution for robot relative error correction, comprising the calibration procedure and a closed-loop control with a proportional–integral-derivative controller for pose correction. Results show enhanced accuracy in robot positioning relative to workpiece, highlighting the effectiveness of the proposed solution in robotic drilling applications.

Controlling the landing position of a spinning ball is difficult when using a table tennis robot. A complete physical model requires the factoring in of aerodynamic elements and object collisions, and inaccurate environmental coefficients would increase the landing position error. This study proposed a landing position control method based on a cascade neural network (CNN) that consists of forward and recurrent neural networks (RNNs). The forward NNs are used to estimate the velocity of the outgoing ball according to the velocity and acceleration of the incoming ball captured by cameras and the desired velocity of the outgoing ball. The RNN is employed to reverse-predict ball displacement based on the state of the incoming ball, desired landing point, and ball flight duration. The experiments verified that the method proposed in this study achieved control of differently spinning balls more effectively than the locally weighted regression (LWR)-based model did. The success rate of the CNN at two of six desired landing points was 25.9% and 32.9% higher, respectively, compared with use of the LWR-based model.

To address the issues of low positioning accuracy and weak robustness of prior visual simultaneous localization and mapping (VSLAM) systems in dynamic environments, a semantic VSLAM (Sem-VSLAM) approach based on deep learning is proposed in this article. The proposed Sem-VSLAM algorithm adds semantic segmentation threads in parallel based on the open-source ORB-SLAM2’s visual odometry. First, while extracting the ORB features from an RGB-D image, the frame image is semantically segmented, and the segmented results are detected and repaired. Then, the feature points of dynamic objects are eliminated by using semantic information and motion consistency detection, and the poses are estimated by using the remaining feature points after the dynamic feature elimination. Finally, a 3D point cloud map is constructed by using tracking information and semantic information. The experiment uses Technical University of Munich public data to show the usefulness of the Sem-VSLAM algorithm. The experimental results show that the Sem-VSLAM algorithm can reduce the absolute trajectory error and relative attitude error of attitude estimation by about 95% compared to the ORB-SLAM2 algorithm and by about 14% compared to the VO-YOLOv5s in a highly dynamic environment and the average time consumption of tracking each frame image reaches 61 ms. It is verified that the Sem-VSLAM algorithm effectively improves the robustness and positioning accuracy in high dynamic environment and owning a satisfying real-time performance. Therefore, the Sem-VSLAM has a better mapping effect in a highly dynamic environment.

The authors seek to design a lower limb exoskeleton to augment human finned swimming; however, data associated with human finned swimming previously did not exist, particularly data that characterizes the active joint torque requirements for human-scale finned swimming motion and the corresponding thrust generation. Since these data are not directly measurable nor easily computed in human subject experiments, the authors instead employed a human-scale robotic platform to characterize the relationship between joint torque, speed, power, and thrust production during flutter kick swimming, specifically at the hip joints. Among the useful insights from this study: (1) the underwater environment can be accurately modeled as a simple viscous load as seen by the hip joints, where viscous coefficient depends on the type of fin; (2) accordingly, for a given fin, movement at any amplitude and frequency is invariant when motion is normalized by amplitude; velocity and torque by the product of amplitude and frequency; and power and thrust by the square of the product of amplitude and frequency; (3) the power-specific thrust is invariant, regardless of fin type, amplitude of motion, and frequency of motion; and 4) the phasing between right and left legs does not have a significant effect on thrust generation (i.e., kicking in-phase and kicking in opposition behave similarly). The authors hope this data will be useful to other researchers interested in developing lower limb exoskeletons to augment underwater human finned swimming.

Soft robotic devices are designed for applications such as exploration, manipulation, search and rescue, medical surgery, rehabilitation, and assistance. Due to their complex kinematics, various and often hard-to-define degrees of freedom, and nonlinear properties of their material, designing and operating these devices can be quite challenging. Using tools such as optimization methods can improve the efficiency of these devices and help roboticists manufacture the robots they need. In this work, we present an extensive and systematic literature search on the optimization methods used for the mechanical design of soft robots, particularly focusing on literature exploiting evolutionary computation (EC). We completed the search in the IEEE, ACM, Springer, SAGE, Elsevier, MDPI, Scholar, and Scopus databases between 2009 and 2024 using the keywords “soft robot,” “design,” and “optimization.” We categorized our findings in terms of the type of soft robot (i.e., bio-inspired, cable-driven, continuum, fluid-driven, gripper, manipulator, modular), its application (exploration, manipulation, surgery), the optimization metrics (topology, force, locomotion, kinematics, sensors, and energy), and the optimization method (categorized as EC or non-EC methods). After providing a road map of our findings in the state of the art, we offer our observations concerning the implementation of the optimization methods and their advantages. We then conclude our paper with suggestions for future research.

The snake robot can be used to monitor and maintain underwater structures and environments. The motion of a snake robot is achieved by lateral undulation which is called the gait pattern of the snake robot. The parameters of a gait pattern need to be adjusted for compensating environmental uncertainties. In this work, 3D motion dynamics of a snake robot for the underwater environment is proposed with vertical motion using the buoyancy variation technique and horizontal motion using lateral undulation. “The neutral buoyant snake robot motion in hypothetical plane and added mass effect is negligible”, these previous assumptions are removed in this work. Two different control algorithms are designed for horizontal and vertical motions. The existing super twisting sliding mode control (STSMC) is used for the horizontal serpentine motion of the snake robot. The control law is designed on a reduced-ordered dynamic system based on virtual holonomic constraints. The vertical motion is achieved by controlling the mass variation using a pump. The water pumps are controlled using the event-based controller or Proportional Derivative (PD) controller. The results of the proposed control technique are verified with various external environmental disturbances and uncertainties to check the robustness of the control approach for various path following cases. Moreover, the results of STSMC scheme are compared with SMC scheme to check the effectiveness of STSMC. The practical implementation of the work is also performed using Simscape Multibody environment where the designed control algorithm is deployed on the virtual snake robot.

This study introduces a hybrid model that utilizes a model-based optimization method to generate training data and an artificial neural network (ANN)-based learning method to offer real-time exoskeleton support in lifting activities. For the model-based optimization method, the torque of the knee exoskeleton and the optimal lifting motion are predicted utilizing a two-dimensional (2D) human–exoskeleton model. The control points for exoskeleton motor current profiles and human joint angle profiles from cubic B-spline interpolation represent the design variables. Minimizing the square of the normalized human joint torque is considered as the cost function. Subsequently, the lifting optimization problem is tackled using a sequential quadratic programming (SQP) algorithm in sparse nonlinear optimizer (SNOPT). For the learning-based approach, the learning-based control model is trained using the general regression neural network (GRNN). The anthropometric parameters of the human subjects and lifting boundary postures are used as input parameters, while the control points for exoskeleton torque are treated as output parameters. Once trained, the learning-based control model can provide exoskeleton assistive torque in real time for lifting tasks. Two test subjects’ joint angles and ground reaction forces (GRFs) comparisons are presented between the experimental and simulation results. Furthermore, the utilization of exoskeletons significantly reduces activations of the four knee extensor and flexor muscles compared to lifting without the exoskeletons for both subjects. Overall, the learning-based control method can generate assistive torque profiles in real time and faster than the model-based optimal control approach.