Elastic Cables Research Articles

Design and Experimentation of Tensegrity Jumping Robots

Jumping robots possess the capability to surmount formidable obstacles and are well-suited for navigating through complex terrain environments. However, most of the existing jumping robots face challenges in achieving stable jumping and they also have low energy utilization efficiency, which limits their practical applications. In this work, a two-module jumping robot based on tensegrity structure is put forward. Firstly, the structural design and jumping mechanism of the robot are elaborated in the article. Then, dynamic models, including the two modules’ simultaneous jumping and step-up jumping process of the robot, are established utilizing the Lagrange dynamic modeling method. On this basis, the effects of parameters, including the stiffness of elastic cables and the initial tilt angle of the robot, on the jumping performance of the robot can be obtained. Finally, simulations are carried out and a prototype is developed to verify the rationality of the tensegrity-based jumping robot proposed in this work. The experiment results show that our jumping robot can achieve a stable jumping process and the step-up jumping of each module of the prototype can have higher energy efficiency than that of simultaneous jumping of each module, which enables the robot a better jumping performance. This research serves as a valuable reference for the design and analysis of jumping robots.

A Self-Adaptive Inertia Hybrid Control of a Fully Constrained Cable-Driven Parallel Robot

A Cable-Driven Parallel Robot (CDPR) is a special type of parallel robot actuated by elastic cables instead of rigid links, which brings uncertainties of model nonlinearities and structural friction depending on the payload variation. A precise motion with minimum control effort against an unknown payload has been a challenging task. To conquer it, we propose an adaptive hybrid control approach for the fully-constrained CDPR with an unknown payload in this paper. A Cartesian space position control and a joint space cable force control are designed through inertia estimation to encounter the effect of the uncertain payload. And then, an artificial neural network (ANN) is employed to estimate the end-effector force in Cartesian space for precise force control and consecutive uncertainties compensation. The stability of the proposed controller is proven based on the Lyapunov method and the efficacy is verified by the experiments. As for feasibility results, the proposed adaptive hybrid control-based cable force estimation was evaluated on the Mini CDPR. Compared to the traditional control scheme, the tracking error was decreased approximately 56% and the utilized tension was significantly reduced for the given trajectory tracking test. Furthermore, the investigation of free movements of the helix trajectory and pick-and-place tasks showed that the proposed hybrid adaptive control can control the position and cable force altogether while being able to estimate the inertia of the end-effector. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The study was motivated by the control problem of adjusting cable tensions of a cable-driven parallel robot (CDPR) against varying payloads at the end-effector. Several advanced control approaches were proposed for but limited to CDPR model parameter estimation and did not consider varying payload. This paper suggests a practical methodology capable of both self-adaptation to unknown payload inertia and consequently improving tracking control performance for a CDPR. In this paper, we derived an adaptive control model and proved stability to ensure safety. In order to encounter unmodeled uncertainties such as pulley friction and cable characteristics, we utilized an artificial neural network (ANN) trained by experiments. The experimental results could confirm that the proposed scheme can estimate the payload inertia and generate minimized cable tension while maintaining good trajectory tracking performance. In future research, we will show more practical validation for a scale-up CDPR with heavy objects toward logistics or pick-and-place application in practice.

Model‐reference adaptive and self‐tuning controls of telescopic mobile cranes with the impact of elastic cables, viscoelastic cylinders, and winds

SummaryTelescopic truck crane is an under‐actuated mechanical system with three actuators controlling five outputs. Its complex structure, shape variation, uncertain parameters, elastic cables, and viscoelastic cylinders are great challenges in control design. This article proposes two adaptive robust controllers for such cranes. A control core assures robustness based on back‐stepping and Lyapunov stability. The adaptation is achieved by employing model‐reference adaptive and self‐tuning control approaches. Thus, the benefits of these adaptive techniques are introduced into the control systems. The application to a practical crane shows the effectiveness of the proposed controllers. The crane has robustness and adaptation despite the elasticity and friction of the load‐carrying cable, the viscoelasticity of the cylinders, the variation of crane parameters, and the presence of winds. Comprehensive comparison indicates the state of the art and the shortcomings of the control systems.

Interval type-2 fuzzy sliding mode control for a cable-driven parallel robot with elastic cables using metaheuristic optimization methods

In this paper, a supervisory interval type-2 fuzzy adaptive sliding mode control scheme is addressed for cable robots. In the proposed control scheme, intelligent methods are combined with conventional sliding mode control to achieve optimal adjustment of control parameters. This approach ensures accurate tracking performance, despite the structural constraints of cable robots. These constraints include the production of purely tensile forces and the effects due to inherent elasticity, which will make the design of the controller challenging. For this purpose, the internal force concept is utilized to ensure the tension style of cables. Additionally, considering a compensator part in the proposed controller and applying the singular perturbation theorem, the vibration effects of elastic cables are handled, and stability is proved through the second Lyapunov method. Therefore, the desired performance of the control system will be guaranteed for the movements that stimulate the vibration modes of cables. An interval type-2 fuzzy logic controller is proposed to adjust the control gain, effectively reducing the chattering level. Moreover, a supervisory interval type-2 fuzzy logic control system is introduced to regulate the gains within the sliding surface. The Grasshopper Optimization Algorithm is employed to select the optimal parameters for the membership functions of the fuzzy system. The results of the conducted simulations show that the desired tracking performance is provided, despite different uncertain parameters and the structural constraints of the considered cable robot.

Geometric Control for Load Transportation With Quadrotor UAVs by Elastic Cables

Geometric Control for Load Transportation With Quadrotor UAVs by Elastic Cables

An Improved Method for Swing State Estimation in Multirotor Slung Load Applications

A method is proposed to estimate the swing state of a suspended payload in multirotor drone delivery scenarios. Starting from the equations of motion of the coupled slung load system, defined by two point masses interconnected by a rigid link, a recursive algorithm is developed to estimate cable swing angle and rate from acceleration measurements available from an onboard Inertial Measurement Unit, without the need for extra sensors. The estimation problem is addressed according to the Extended Kalman Filter structure. With respect to the classical linear formulation, the proposed approach allows for improved estimation accuracy in both stationary and maneuvering flight. As an additional contribution, filter performance is enhanced by accounting for aerodynamic disturbance force, which largely affects the estimation accuracy in windy flight conditions. The validity of the proposed methodology is demonstrated as follows. First, it is applied to an octarotor platform where propellers are modeled according to blade element theory and the load is suspended by an elastic cable. Numerical simulations show that estimated swing angle and rate represent suitable feedback variables for payload stabilization, with benefits on flying qualities and energy demand. The algorithm is finally implemented on a small-scale quadrotor and is investigated through an outdoor experimental campaign, thus proving the effectiveness of the approach in a real application scenario.

Spikebot: A Multigait Tensegrity Robot with Linearly Extending Struts.

Numerous recent research efforts have leveraged networks of rigid struts and flexible cables, called tensegrity structures, to create highly resilient and packable mobile robots. However, the locomotion of existing tensegrity robots is limited in terms of both speed and number of distinct locomotion modes, restricting the environments that a robot is capable of exploring. In this study, we present a tensegrity robot inspired by the volumetric expansion of Tetraodontidae. The robot, referred to herein as Spikebot, employs pneumatically actuated rigid struts to expand its global structure and produce diverse gaits. Spikebot is composed of linear actuators that dually serve as rigid struts linked by elastic cables for stability. The linearly actuating struts can selectively protrude to initiate thrust- and instability-driven locomotion primitives. Such motion primitives allow Spikebot to reliably locomote, achieving rolling, lifting, and jumping. To highlight Spikebot's potential for robotic exploration, we demonstrate how it achieves multi-dimensional locomotion over varied terrestrial conditions.

Kinematic Modeling and Optimization of a Clustered Tensegrity Mobile Robot

Abstract Clustered tensegrity mechanisms have elicited extensive attention in recent research due to their easy control system and high stiffness-to-mass ratio. However, modeling and analyzing these mechanisms are still challenging due to the clustering of cables and redundant structural parameters. This article proposes an energy-based kinematic modeling method for a modular clustered tensegrity mobile robot. The design of the clustered tensegrity robot is inspired by the biomechanics of worms, allowing it to achieve two locomotion modes resembling earthworm-like and inchworm-like movements using two motors. Moreover, the clustered and modular structure enables the robot to increase the number of modules as needed without increasing the number of actuators. This feature enhances the robot's terrain adaptability without adding complexity to the control system. The article establishes kinematic models using the energy method and clarifies the motion law of nodes on the sliding cables of the robot, considering multiple structural parameters for both locomotion modes. Based on these models, the article reveals the mapping relationships among various structural parameters (i.e., cable-hole gap, cable-hole friction, stiffness and original length of elastic cables, and ground–robot friction) and locomotion performance (i.e., morphology, displacement, and velocity) of the robot. Furthermore, structural parameter optimization is performed to enhance the kinematic performance of the robot in both locomotion modes simultaneously. To validate the proposed kinematic modeling method, a prototype with two modules is developed, and experiments are conducted to assess the robot's locomotion performance. These experiments demonstrate the effectiveness and rationality of the proposed method.

Experimental measurements of two elastic taut-slack mooring configurations for the multi-float M4 WEC

Moorings are a vital and often problematic component of any floating offshore renewable energy system, whether for wind or wave energy conversion, and here we consider the multi-float WEC system M4 in a 122 configuration. Previous experimental work has shown elastic cables to reduce extreme snap loads by a factor of about 6 when considering single cables between the bow float and a mooring buoy, and between the mooring buoy and the bed [1]. Here we compare results for two alternative configurations designed to reduce the mooring footprint as well as extreme snap loads. The first system, shown in Figure 1 (a), consists of a large surface buoy connected to the seabed with three equi-spaced elastic cables in pre-tension, with a single elastic cable to the bow float. The second system, shown in Figure 1 (b) has a smaller submerged buoy, again connected to the seabed with three equi-spaced elastic cables in pre-tension, however, this is connected to a smaller surface buoy which is subsequently connected to the bow float. Both systems are taut-slack. In this paper we present experimental measurements taken at the COAST laboratory at the University of Plymouth. Both configurations are tested in irregular (JONSWAP) wave conditions up to limiting steepness, with run times of 35 mins at 1:40 scale or about 3.5 hours full scale. Peak, mean and rms bed loads for both configurations are presented along with rms and peak relative angular pitch response with drive train disengaged (free hinge between mid and stern floats).&#x0D; References[1] P. Stansby et al., “Experimental study of mooring forces on the multi-float WEC M4 in large waves with buoy and elastic cables,” Ocean Eng., vol. 266, no. P4, p. 113049, 2022.&#x0D;

A Shape-Changing Wheeling and Jumping Robot Using Tensegrity Wheels and Bistable Mechanism

Tensegrity structures made from rigid rods and elastic cables have unique characteristics, such as being lightweight, easy to fabricate, and high load-carrying to weight capacity. In this article, we leverage tensegrity structures as wheels for a mobile robot that can actively change its shape by expanding or collapsing the wheels. Besides the shape-changing capability, using tensegrity as wheels offers several advantages over traditional wheels of similar sizes, such as a shock-absorbing capability without added mass since tensegrity wheels are both lightweight and highly compliant. We show that a robot with two icosahedron tensegrity wheels can reduce its width from 400 to 180 mm, and simultaneously, increase its height from 75 to 95 mm by changing the expanded tensegrity wheels to collapsed disk-like ones. The tensegrity wheels enable the robot to overcome steps with heights up to 110 and 150 mm with the expanded and collapsed configuration, respectively. We establish design guidelines for robots with tensegrity wheels by analyzing the maximum step height that can be overcome by the robot and the force required to collapse the wheel. The robot can also jump onto obstacles up to 300-mm high with a bistable mechanism that can gradually store but quickly release energy. We demonstrate the robot's locomotion capability in indoor and outdoor environments, including various natural terrains, like sand, grass, rocks, ice, and snow. Our results suggest that using tensegrity structures as wheels for mobile robots can enhance their capability to overcome obstacles, traverse challenging terrains, and survive falls from heights. When combined with other locomotion modes (e.g., jumping), such shape-changing robots can have broad applications for search-and-rescue after disasters or surveillance and monitoring in unstructured environments.

An Adaptive Barrier-Mooring System for Coastal Floating Solar Farms

Floating solar farms in the coastal areas are subjected to more complex environmental loads of tides and waves than lakes or reservoirs with greater challenges to their mooring. At present, mooring systems based on elastic cables are prevalent for coastal floating solar farms, but these cables tend to be expensive and require periodic retuning with higher maintenance costs. In this study, we propose a new alternative of an adaptive barrier-mooring system which is consisted of perimeter pontoons, barriers, clump weights, mooring lines and anchors as a new alternative. The performance of the adaptive barrier-mooring system installed on the leading edge of a coastal floating solar farm is first examined through static analysis. The results showed that the new mooring system enables the floating solar farm to adapt up to 36% of water depth without introducing slack in the mooring cables. In addition, the resulting nonlinear mooring stiffness and lower pulling-out forces on the anchors are also both beneficial to the system design. Subsequently, a floating solar farm model with four different mooring systems, including adaptive barrier-mooring systems as well as elastic mooring cables, were tested for dynamic performance in a wave flume in the laboratory with Froude similarity under both incident waves as well as water level changes. The experimental results demonstrated the good performance of the adaptive barrier-mooring system in terms of higher platform stability over a large tidal range. Finally, the construction and maintenance costs of the adaptive barrier-mooring system should be lower compared to elastic mooring systems due to the use of common materials without the need for periodic tightening. We hope that the adaptive barrier-mooring system can further aid the development of coastal floating solar farms in the future.

Cable failure tolerant control and planning in a planar reconfigurable cable driven parallel robot.

The addition of geometric reconfigurability in a cable driven parallel robot (CDPR) introduces kinematic redundancies which can be exploited for manipulating structural and mechanical properties of the robot through redundancy resolution. In the event of a cable failure, a reconfigurable CDPR (rCDPR) can also realign its geometric arrangement to overcome the effects of cable failure and recover the original expected trajectory and complete the trajectory tracking task. In this paper we discuss a fault tolerant control (FTC) framework that relies on an Interactive Multiple Model (IMM) adaptive estimation filter for simultaneous fault detection and diagnosis (FDD) and task recovery. The redundancy resolution scheme for the kinematically redundant CDPR takes into account singularity avoidance, manipulability and wrench quality maximization during trajectory tracking. We further introduce a trajectory tracking methodology that enables the automatic task recovery algorithm to consistently return to the point of failure. This is particularly useful for applications where the planned trajectory is of greater importance than the goal positions, such as painting, welding or 3D printing applications. The proposed control framework is validated in simulation on a planar rCDPR with elastic cables and parameter uncertainties to introduce modeled and unmodeled dynamics in the system as it tracks a complete trajectory despite the occurrence of multiple cable failures. As cables fail one by one, the robot topology changes from an over-constrained to a fully constrained and then an under-constrained CDPR. The framework is applied with a constant-velocity kinematic feedforward controller which has the advantage of generating steady-state inputs despite dynamic oscillations during cable failures, as well as a Linear Quadratic Regulator (LQR) feedback controller to locally dampen these oscillations.

Stability and control issues of multirotor suspended load transportation: An analytical closed–form approach

In the present paper a fully–analytical framework is outlined to analyze the effects of cable–suspended loads on multirotor platforms. In particular, the dynamics of an isolated vehicle is first investigated by including the complete model of the electric propulsion system. Then, system description is extended to the load, which introduces non–actuated degrees of freedom and is suspended through a linear–elastic cable. In order to provide the complete slung–load system with a closed–loop desired behavior, an auxiliary controller is proposed to recover or improve the initial multirotor dynamic properties, while stabilizing load oscillations. To this end, closed–form equations are derived to design the auxiliary controller gains, based on the knowledge of a limited set of parameters. A test case is proposed relative to a commercial–off–the–shelf hexarotor whose electrical propulsion system has been characterized by an experimental campaign performed at University of Bologna premises.

Modeling and Characterization of Tensegrity Structures Integrating Dielectric Elastomer Actuators

Tensegrity structures, architectures that consist of elastic cables and rigid rods, have attracted attention as a building block of robots because of their compliance, lightweight properties, and mechanical robustness. This article describes a method to create electroactive tensegrity structures that employs a dielectric elastomer actuator (DEA) as the actuation principle. Two different types of DEA‐tensegrities are considered herein: a membrane type and a cable type. In these devices, DEAs are made of an acrylic elastomer (3 m, VHB 4905) and a stretchable conductive film (Adhesives Research, ARcare 90336) used as dielectric and electrode layers, respectively. An analytical model of DEA‐tensegrities is built that guides the fabrication of experimental devices. The fabricated DEA‐tensegrities are characterized by the actuation strain in the height direction. As a result, voltage‐controlled actuation strains of 7.5% and 2.0% are observed at 10 kV for membrane type and cable type DEA‐tensegrity, respectively, while the model prediction captures the actuation characteristics.

Robust inverse dynamics control of a cable-driven underwater manipulator with elastic cables

Robust inverse dynamics control of a cable-driven underwater manipulator with elastic cables

COMPLEMENTARY ENERGY PRINCIPLE FOR CABLE NETWORKS IN TERMS OF FORCE VECTOR VARIABLE

An alternative approach to the variation formulation of static equilibrium problem for cable networks is proposed. The dual minimization principle is derived in terms of force variables. The full vector force in the cable member is chosen as the dual variable. Unlike the previously proposed treatments of the problem using the scalar axial force variable the elastic energy retains the most general form until the closing steps. It is only assumed to be a convex function of the member end-to-end vector. As a result the nonsmooth asymmetric response of the cable does not appear in the form of inequality in the very beginning. Instead it shows up in the final form of the complementary energy functional, which turn out to be non-differentiable for zero member forces. The kinematic relations between member elongations and nodal displacements convert into the force equilibrium conditions in terms of nodal reactions and member force vectors. The Dirichlet boundary conditions appear in the dual form as a linear term in the complementary energy functional. For the linear elastic cables this approach lead to a second-order cone optimization problem with two sets conical constraints. Such formulation provides flexibility and thus can be potentially extended to account for phenomena such as inter-fiber friction and adhesion. Keywords: complementary energy, variational principles, cable networks

Empirical Validation of Free Vibration of Sagging Cables

Sagging cables lack unique natural state, but possess unique equilibrium state under sustained loads. However, for the purpose of predicting their dynamic response, the static equilibrium state of heavy cables under self-weight is assumed to be their initial state. The theory of sagging elastic cables presented earlier by the Authors pertains to weightless cables carrying nodal masses apart from static and inertial forces. For applying the proposed theory for sagging heavy cables, the cable is divided into ten segments of equal length. The initial equilibrium configuration of the cable fixed at both the ends is determined by the weights of these lumped nodal masses applied at ten nodes with one end fixed. The stiffness matrix of the cable is determined from tangent configurational flexibility matrix and tangent elastic flexibility matrix of twenty degree of freedom system. The cable tied at both the ends in an equilibrium state is set into motion by releasing it at one end. The theoretically predicted response of the cable is compared with the experimental data from the two investigations. The first experimental investigation by Fried pertains to the planar undamped vibrations of a sagging elastic cable, in which cable is released from its right end and its configurations are plotted at regular time intervals of 0.001s. In the second investigation by Koh, Zhang and Quek, the configurations of a different cable at regular time intervals of 0.125s during half the vibration cycle is measured. The dynamic tensile force at the fixed end has also been predicted in the latter case. The theoretical prediction of the evolving cable configuration have been found to be compatible with experimental data.

Experimental study of mooring forces on the multi-float WEC M4 in large waves with buoy and elastic cables

Experiments have been undertaken in a wave basin with the hinged attenuator-type wave energy converter M4 in a 6-float configuration with two hinges for power take off (PTO), moored to a single-point buoy. This follows previous experiments with inelastic cables giving very high snap loads. The PTO was disengaged for these tests. The aims are i) to use the elastic mooring cable to reduce the snap loads of the M4 system, with two elastic stiffnesses tested, and ii) to study the system's dynamic response with a basic mooring configuration under intermediate to large waves. Mooring loads at the fairlead and the bed, and relative pitch angle between floats were measured. Numerical simulations using two different models were carried out, and the results were compared against the experiment results. For very large waves, the floats showed occasional deck submergence (dunking) limiting relative angular motion as wave height increases, in effect providing a passive end stop. The largest peak relative angle was just less than 40°. The extreme snap loads were up to 1/6th of those with inelastic cables. Spectral analyses of relative pitch angle and mooring force were made and shown to be quite different and complex.

Design and Validation of a Lightweight Soft Hip Exosuit With Series-Wedge-Structures for Assistive Walking and Running

To overcome the limitations of a traditional soft hip exosuit directly driven by Bowden cables or winding belts at two points, in this article, we propose a new soft hip exosuit design concept based on series-wedge-structures for energy-efficient walking and running during daily activities for elderly individuals. The series-wedge-structure is designed to improve the comfort of the wearer–exosuit interface and to passively adapt to the user's body curvature, with no hindrance during movement. The design and function, including the series-wedge-structure belt, series elastic cable drive actuator, and control scheme, are described. The presented soft exosuit, which is lightweight (1.4 kg) and comfortable, provides assistive torque for hip flexion by folding series-wedge-structures driven by Bowden cables. The series-wedge-structure-based hip exosuit adopts single actuation coupled to the Bowden cable pull mechanism with a series elastic actuator to drive both hip flexions based on the out-of-phase nature of the human legs during walking and running. The exosuit performance test results show that the proposed exosuit improves the comfort of the wearer–exoskeleton interface by minimizing the shear force and maximizing the exosuit–skin interaction force contact area. Three healthy subjects walked at a fixed speed of 1.25 m/s and ran at a fixed speed of 2.2 m/s while wearing the proposed exosuit with/without assistance and without wearing the exosuit to evaluate the biomechanical and physiological effects of the proposed exosuit assistance on locomotion. The metabolic rate with exosuit assistance was reduced by 10.9% for walking and by 6.2% for running compared with not wearing the exosuit.

Geometric Control of Two Quadrotors Carrying a Rigid Rod with Elastic Cables

This paper presents the design of a geometric trajectory tracking controller for an underactuated multi-body system describing the cooperative task of two quadrotor UAVs (unmanned aerial vehicles) carrying and transporting a rigid bar, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that of a similar model with inelastic cables. In this reduced model, we design a controller such that the rod exponentially tracks a given desired trajectory for its position and attitude, under some assumptions on initial error. We then show that exponential tracking in the reduced model corresponds to exponential tracking of the original elastic model. We also show that the previously defined control scheme provides uniform ultimate boundedness in the presence of unstructured bounded disturbances.