This paper presents the design, analysis, and validation of a novel redundant planar parallel continuum manipulator (PCM) consisting of four flexible links coupled at the rigid mid-and end-platform. To address complex geometry/static hybrid constraints at the rigid platforms, a general framework is developed for the kinetostatics modeling and analysis. Benefiting from the redundant actuation design, the Cartesian stiffness of the studied PCM can be further adjusted as a secondary task to positioning. Utilizing the proposed deflection-based force sensing method, the external load exerted on the end-effector can also be identified by measuring the pose of rigid platforms. To validate the proposed design, a prototype is built, on which a series of experiments have been conducted. The results show that, with the proposed kinetostatics models, the prototype exhibits a mean position and orientation error of 0.52 mm and 0.41$^{\circ}$. Finally, the capability of stiffness-varying and force-sensing is demonstrated to verify the feasibility and potential applications of the designed redundant PCM.Note to Practitioners—This paper is motivated by the need for more adaptable robotic systems in industrial and interactive settings. In this work, a novel redundant parallel continuum manipulator with variable passive compliance and force-sensing capability is presented. This planar manipulator comprises four flexible limbs, each driven by independent linear modules, thus the redundancy in the actuation can be leveraged for varying Cartesian stiffness. By means of measuring the pose of the end-effector, the interaction force exerted on the end-effector can be identified according to the force sensing model. The structural compliance of the manipulator enhances safety in human-robot collaboration, while variable stiffness accommodates the specific requirements of different interaction tasks. Furthermore, the force-sensing capability allows for precise feedback control, significantly improving safety during interactions with humans. Therefore, the presented PCM has the potential for interactive manipulation applications, including delicate and fragile object handling, as well as human-robot collaboration in assembly tasks.

This paper presents a novel active force-controlled end-effector with passive structural compliance and intrinsic contact sensing capabilities. Slender elastic beams are introduced to provide the end-effector with structural compliance to accommodate inevitable fluctuations through deformation during operation. Meanwhile, flexible strain gauges are embedded into the slender elastic beams to endow the end-effector with intrinsic sensing capability. A kinetostatic model is established in closed-form to map the local deflections of strain gauges to the contact force with the environment. On this basis, model-based feedback control can be readily implemented to actively adjust the contact force between the end-effector and the workpiece. A prototype is developed, on which a variety of experiments are conducted to validate the effectiveness of the proposed end-effector. The results demonstrate that the end-effector can control the contact force accurately, with a maximum error of around 0.65N. Furthermore, a demonstration of robotic grinding using the developed prototype showcases its potential for practical applications.

Flapping wing air vehicles(FWAV) or ornithopters are bio-inspired aerial robots that mimic the flying principles of insects and birds. Autonomous take-off is an important capability for FWAV to enhance its performance and extend its working time, which is equipped by almost every kind of bird. As a common method of take-off for birds, jumping take-off has a great ability to adapt to different terrain and high energy efficiency compared with running and rotor-based take-off. Despite recent research, there is no FWAV capable of jumping take-off to this day. In this paper, we present a process to realize the jumping take-off of a meter-scale FWAV from flat ground. To lower the mechanical complexity, we eliminate the design of traditional robotic legs. Instead, we realize steady standing through a tripod-like structure that consists of two wings and a jumping mechanism. Two flapping wings are directly driven by two independent servos. Three carbon fiber springs are employed to build a lightweight jumping module with high elastic energy. We build the dynamic model to analyze the aerodynamic effect during the jumping phase and realize a stable transition to flapping flight. This work lays the foundation for outdoor flight without human assistance.

Owing to their tremendous adaptability to free-form objects, soft grippers with fin-ray structure have a wide range of applications. However, kinetostatics analysis and contact sensing for such soft grippers are quite a challenge due to large structural deformations. In this article, a model-based method for intrinsic contact sensing, object perception, and interactive manipulation, is proposed for this kind of adaptive grippers. The contributions arise from the integration of compact strain-gauge sensors, that are particularly fabricated for slender flexible beams undergoing large deformations. Using a discretization-based approach, the contact condition can be identified efficiently in light of the local deformations gathered via the deflection sensors. Prototypes are developed using simple materials and manufacturing methods, on which various validation experiments are conducted. Owing to the contact sensing capability, the developed adaptive fin-ray gripper is able to perceive the boundary geometry and structural compliance of unstructured objects. Moreover, sensor-based feed-back control can be accomplished to perform interactive manipulation, in which the contact force between the finger and object can be regulated precisely (around$5\,\%$RMS error) in real-time.

Conventional soft pneumatic actuators (SPAs) are made of soft materials that facilitate safe interaction and adaptability. In positioning and loading tasks, however, SPAs demonstrate limited performance. In this article, we extend the current designs of SPAs upon integrating a tendon-driven parallel mechanism into a pneumatic origami chamber, inspired by the performances and structures of vertebrates. The inner rigid/outer soft actuator exploits the advantages of both, parallel mechanisms to achieve precise, versatile motion, and SPAs, to form a compliant, modular structure. With the antagonistic actuation of tendons-pulling and air-pushing, the actuator can exhibit multimode motion, tunable stiffness, and load-carrying maneuvers. Kinematic and quasi-static models are developed to predict the behavior and to control the actuator. Using readily accessible materials and fabrication methods, a prototype was built, on which validation experiments were conducted. The results prove the effectiveness of the model, and demonstrate the motion and stiffness characteristics of the actuator. The design strategy and comprehensive guidelines should expand the capabilities of soft robots for wider applications, and facilitate the development of robots with rigid-soft hybrid structures.

This paper presents a model-based approach to reconstructing the large deformations of slender flexible beams through strain-gauge deflection sensors. Using the principal axes decomposition of structural compliance, a closed-form kinetostatics model can be obtained to characterize the non-linear force-deformation behavior of the flexible beams under-going large-scale deflection. Owing to analytical derivation of the system Jacobian, the efficient Newton-Raphson method is employed to determine the equilibrium configuration of the flexible beams, as well as the corresponding reaction force. To verify the correctness and effectiveness of the proposed method, an experimental apparatus is built up, on which a variety of experiments are conducted. The results show that for a 300 mm long beam, the tip position can be predicted with an accuracy of 1.27 mm, 4.42 mm, and 1.17°, respectively, for the x, y directions and rotation. Accordingly, the estimation errors for the planar forces and torque are 0.075 N (3.33%), 0.155 N (14.23%), and 0.027 Nm (26.84%), respectively.

We introduce an underactuated differential-based robot gripper able to perform self-adaptive grasping with passive disturbance rejection. The gripper utilises three car differential systems to achieve self-adaptiveness with a single actuator: a base differential for distributing power from the motor to the fingers, and two independent finger differentials for controlling the proximal and distal joints. Linear and torsional springs are cleverly added to these differentials to allow the return of the fingers and the gripper-object system to equilibrium, thus enabling the gripper rejecting unexpected external forces applied to the fingers after securing a grasp. This novel design provides passive disturbance rejection without implementing complicated control systems and is the main contribution of this paper. Moreover, the differentials allow the gripper to perform not only self-adaptive power grasp but also precision grasp, provide it with a large force transmission efficiency, and facilitate the prediction of grasping position. We analyse the static model of the introduced differential system and evaluate the gripper design via four sets of experiments. Numerical and empirical results clearly demonstrate the viability of the proposed grasper.

This paper presents an alternative decomposition of spatial stiffness matrices based on the concept of compliant axes. According to the congruence transformation of spatial stiffness, the coordinate-invariant aspects, which are referred to as the central principal components of the 6 × 6 symmetric positive semidefinite matrices, can be derived uniquely. The proposed decomposition is free from the eigenvalue problems of the 6 × 6 stiffness matrices so that both Plücker's ray and axis coordinates can be utilized to characterize the elastic system's force-deflection behavior. Hence, an arbitrary spatial stiffness matrix can be uniquely decomposed into two sets of orthogonal spring wrenches with finite and infinite pitches, respectively. The decomposed wrenches with finite pitches correspond to the stiffness' wrench-compliant axes, along which linear deformations produce only wrenches parallel to them. As a result, three torsional and three screw springs are required, at the most, to realize a given spatial stiffness. Using the principal axes decomposition, some physical appreciations, such as the center of stiffness, the wrench-compliant axes, and the correspondence of compliance and stiffness, can be derived to reveal the inherent structure of spatial stiffness in an intuitive manner. In order to verify the effectiveness of the proposed method, two numerical examples are intensively studied with comparison to the eigenscrew decomposition. In addition, a potential application of the proposed stiffness decomposition method is also provided for the structural compliance modeling of flexible links in robot manipulators.

This paper presents an analytical approach to determine and eliminate the redundant model parameters in serial-robot kinematic calibration based on the product of exponentials formula. According to the transformation principle of the Lie algebra se(3) between different frames, the connection between the joints' twist errors and the links' geometric ones is established. Identifiability analysis shows that the redundant errors are simply equivalent to the commutative elements of the robot's joint twists. Using the Lie bracket operation of se(3), a linear partitioning operator can be constructed to analytically separate the identifiable parameters from the system error vector. Then, error models satisfying the completeness, minimality, and model continuity requirements can be obtained for any serial robot with all combinations and configurations of revolute and prismatic joints. The conventional conclusion that the maximum number of independent parameters is 4r + 2p + 6 in a generic serial robot with r revolute and p prismatic joints is verified. Using the quotient manifold of the Lie group SE(3), the links' geometric errors and the joints' offset errors can be integrated as a whole, such that all these errors can be identified simultaneously. To verify the effectiveness of the proposed method, calibration simulations and experiments are conducted on an industrial six-degree-of-freedom (DoF) serial robot.