Link Robot Research Articles

Practical whole-body elasto-geometric calibration of a humanoid robot: Application to the TALOS robot

The whole-body elasto-geometrical calibration of humanoid robots is critical particularly for their control and accurate simulation. However, it is often not considered probably since it is a nontrivial task due to the mechanical complexity and inherent constraints of anthropomorphic structures. Also, humanoid robots have to sustain great efforts on their support legs, leading to link and joint being deformed, and are prone to auto-collision. Thus, elastic parameters have to be factored in addition to the geometric ones and to improve the precision of the pose of all robot segments. This is much more cumbersome and time consuming than the classical calibration of serial manipulators that deals solely with the estimation of the pose of the end-effector. Finally, due to the complexity of the task, a manual intervention in several steps of the calibration is no longer possible and a thorough automation of the approach is needed. Therefore, we propose to use a stereophotogrammetric system along with embedded joint torque sensors to calibrate the pose of all robot links with a fully automatic procedure. The generation of the minimal set of optimal calibration postures is based on a new iterative optimization process that leads to a stable maximum of an observability index. Then full set of geometrical parameters but also joint and base elastic parameters were calibrated using a single least-square optimization program. The proposed method was validated on a TALOS humanoid robot allowing to obtain an accurate whole-body calibration in less than 10 min. The proposed approach was cross-validated experimentally and showed an average RMS error of the tracked markers of 2.2 mm.

A Screw Approach to Vibration Analysis of Beam Structures With Nonstandard Conditions

Abstract A major advantage of the screw theory is that translations and rotations are treated simultaneously, which can provide greater insight into the vibration phenomena, such as vibration centers and axes. The present study describes how these concepts are extended into beam theory. The stiffness matrix of a beam was derived by incorporating different types of vibrations, such as extension, compression, torsion, and bending, at the same time, which was then used to obtain the equations of motion, including nonstandard forms of boundary conditions. We then presented an analytical method to solve these equations by focusing on two distinct examples, namely the cantilever and robot link. In the first numerical example, the mode shapes of the beam could be regarded as rotations about the vibration centers or axes of the rigid bodies in a discrete system. In the second example, the analytical solutions of mode shapes and natural frequencies of a robot link, for which the revolute joints at both sides are not parallel, were presented to demonstrate the utility of the screw theory. We demonstrated that the screw approach could accurately describe the vibrations of both discrete and continuous systems and that the geometric meaning of the vibration modes of discrete systems can be extended into continuous systems.

Formulation Method of Robot Kinematics Considering Versatility and Mobility of Each Joint

This paper proposes a method of formulating the robot kinematics. The proposed method can be applied to mobile manipulators, parallel link robots, and legged robots by the same procedure. The proposed forward kinematics formulation is based on tree-structured rigid-body system and is compared with the Denavit–Hartenberg method and URDF. The proposed differential kinematics formulation is represented by a block lower triangular matrix, which is a generalized form of the basic Jacobian matrix. In addition, an application example of the proposed formulation to the numerical inverse kinematics method is also shown. The usage of the proposed method is demonstrated by simulation experiments using a dual-arm mobile manipulator and a parallel link robot.

Static Modeling of a Class of Stiffness-Adjustable Snake-like Robots with Gravity Compensation

Stiffness-adjustable snake-like robots have been proposed for various applications, including minimally invasive surgery. Based on a variable neutral-line mechanism, previous works proposed a class of snake-like robots that can adjust their stiffness by changing the driving cables’ tensions. A constant curvature hypothesis was used to formulate such robots’ kinematics and was further verified by our previous work via rigorous force analysis and ADAMS simulations. However, all these models and analyses have ignored the effect of the robot links’ gravity, resulting in significant errors in real systems. In this paper, a static model considering gravity compensation is proposed for the stiffness-adjustable snake-like robots. The proposed model adopts a nonlinear Gauss–Seidel iteration scheme and consists of two parts: gravity update and pose estimation. In each iteration, the former updates the payload of each link caused by gravity, and the latter estimates the pose of the robot by refreshing the angle and position values. This iteration stops when the change in the tip position is less than a pre-set error ϵ. During the above process, the only dependent information is each cable’s tension. Simulations and experiments are carried out to verify the effectiveness of the proposed model. The impact of gravity is found to increase with growing material densities in the simulations. The experimental results further indicate that compared with a model without gravity compensation, our model reduces the tip estimation error by 91.5% on average.

Сравнение результатов работы алгоритмов обратной кинематики на основе FABRIK для многосекционных непрерывных роботов

Flexible bend link robots, also called continuum or soft robots, are an urgent research topic. Various algorithms were developed to solve the inverse problem of the multi-section continuum robot kinematics including those based on the FABRIK (Forward And Backward Reaching Inverse Kinematics) algorithm. This algorithm was originally created to solve the inverse kinematics problem of robots consisting of rigid links connected by spherical joints and could also be used in regard to continuum robots, which are arcs smoothly transiting into each other. To work with the FABRIK algorithm, each bend section is approximated to the virtual rigid link. Two known approaches are known to solve the inverse kinematics problem: the first is based on constructing the tangents (bend section transformation into two tangents), and the second is based on constructing the chords (bend section reduction to a chord). Both approaches demonstrate good results in solving the inverse kinematics problem compared to algorithms based on the Jacobian matrix construction. However, scientific literature misses data on comparing methods that use the FABRIK algorithm. In this regard, two approaches were compared to solve the inverse kinematics problem based on implementing the FABRIK algorithm. Results of numerical experiments with three-, five- and ten-sectional robots are presented. Characteristics of the algorithms and boundaries of their application were determined.

Sliding Mode Control for Fuzzy Networked Semi-Markov Switching Models Under Cyber Attacks

Sliding mode control (SMC) is investigated for nonlinear networked stochastic switching systems subject to semi-Markov parameters, in which the model is formulated based on the Takagi-Sugeno (T-S) fuzzy strategy. The occurrences of actuator failures and deception attacks are considered within the framework of networked semi-Markov switching systems. A common sliding surface is designed to prevent instability caused by repeated jumps. Based on the generally uncertain transition rate, sufficient conditions for stochastic stability of the corresponding system are presented. Moreover, in the consideration of actuator failures and deception attacks, the feasibility of the SMC law drives the states toward the specified sliding region. The presented single link robot arm model demonstrates the effectiveness of the theoretical findings.

Performance Comparison of Se formance Comparison of Several Contr al Control Algorithms for ol Algorithms for Tracking Contr acking Control of P ol of Pantograph Mechanism aph Mechanism

A sort of parallel manipulator known as a pantograph robot mechanism was created primarily for industrial requests that required high precision and satisfied speed. While tracking a chosen trajectory profile requires a powerful controller. Because it has four active robot links and one robot passive link in place of just two links like the open chain does, it can carry more loads than the open chain robot mechanism while maintaining accuracy and stability. The calculated model for a closed chain pantograph robot mechanism presented in this paper takes into account the boundary conditions. For the purpose of simulating the dynamics of the pantograph robot mechanism, an entire MATLAB Simulink has been created. The related Simscape model had been created to verify the pantograph mathematical model that had been provided. Five alternative tracking controllers were also created and improved using the Flower Pollination (FP) algorithm. The PID controller, which is used in many engineering applications, is the first control. An enriched Fractional Order PID (FOPID) controller is the second control. The third control considers an improved Nonlinear conventional PID (NLPID) controller, and the parameters for this controller were likewise determined using (FP) optimization using the useful objective function. Model Reference Adaptive Control (MRAC) with PID Compensator is the fourth control. The Fuzzy PD+I Control is the last and final controller. A comparison of the different control methods was completed. A rectangular trajectory was chosen as the end effector of the pantograph robot's position reference because it displays performance during sharp edges and provides a more accurate study. The proposed controllers were used for this task to analyse the performance. The outcomes demonstrate that the Fuzzy PD+I control outperforms the PID, FOPID, NLPID, and MRAC with PID Compensator controllers in terms of performance. In the case of the Fuzzy PD+I control, the angles end effector has a lower rise time, a satisfied settling time, and low overshoot with good precision.

Dynamic Modeling of Three Links Robot Manipulator (Open Chain) with Spherical Wrist

The study here under describes the impact of adding a nano-scaled ceramic particles on the mechanical and fatigue behaviors of aluminum matrix composites AMCs containing 0.5 ,1.0 ,1.5, and 2 % wt. of nano-scaled B4C and Al2O3 particles were dispersed in molten aluminum by the stir-casting process. Vickers, tensile, and fatigue devices were utilized to evaluate the mechanical behavior of composites in the fabrication process. The results show that increasing the weight percentage of nano-ceramic particles increased the hardness, maximum tensile stress, and fatigue strengths of the base alloy. Furthermore, all of the above behaviors of AMCs reinforced with B4C particles are better than those of AMCs reinforced with Al2O3 particles.

Zero‐sum game‐based security control of unknown nonlinear Markov jump systems under false data injection attacks

In order to solve the security control problem of discrete-time unknown Markov jump systems (MJSs) subject to false data injection attacks, a new zero-sum game-based control method is developed in this paper by using model-free adaptive dynamic programming algorithm. The controller and the attacker are regarded as two players. An optimal cost function of MJSs is firstly introduced based on the evolution of the Markov chain. Then, a critic-action-attack framework is established to approximate the cost function, control input and false data, respectively. Additionally, the boundedness of the neural network (NN) weight estimate errors is guaranteed via Lyapunov theory. In the end, the validity of the proposed approach is verified by simulation of a single link robot arm.

Decentralized adaptive control applied to two links of a five degrees of freedom robot, using the polynomial technique

The objective of this work is to design and implement decentralized adaptive controllers in order to perform the position control of two links of an electromechanical manipulator robot with five degrees of freedom (DOF 5). The manipulator robot is consisted of five rotational joints, four links and a claw. Five DC motors are used to drive the robot and the motion transmission from the motors to the joints is achieved by gear trains. Models of the manipulators robots are obtained using Newton-Euler or Lagrange equations; and are coupled and nonlinear. In this work, the model of the links of the manipulator robot is obtained in real time for each sampling period. The parameters of the links to be controlled are identified by recursive least squares (RLS) method, according to data from the links, and are used in the designs of adaptive controllers for the positions control of the joints of the links under analysis. In the end, the experimental results are presented, like the evaluation of the performance achieved by the manipulator robot links.

Controls and process planning strategies for 5-axis laser directed energy deposition of Ti-6Al-4V using an 8-axis industrial robot and rotary motion

Interest in multi-axis additive manufacturing has grown significantly in recent years due to associated benefits that range from improved quality to support for greater geometric complexity. A method of 5-axis Laser Hot-Wire Directed Energy Deposition is developed and demonstrated in this study using an 8-axis industrial robot, comprised of a 6-axis serial link robot and a 2 degree‐of‐freedom positioner. Coordinated 5-axis motion is used to print Ti-6Al-4V objects predominantly through build plate rotation. Methods of slicing and toolpath generation are presented, including the use of an alternating toolpath direction philosophy and the manipulation of the CAD model surface normal vectors for determining the required build plate tilt angles for maintaining consistent deposition orientations relative to gravity. Another objective of the study was to determine the limits of conventional slicing and layer height control techniques for printing geometries with significant unsupported overhangs. A comparison is made between the behavior of normal and conformal bead alignment in this regard, and the performance of the layer height controller is reported as it relates to process stability and the limits of printing overhang geometries. Unsupported overhangs were successfully printed at 35° without build plate tilt and 45° with build plate tilt. Toolpath velocity and net-shape printing performance are reported as well, with 3D scans of the printed surfaces used for net-shape characterization. In all, the printing of three geometries is presented, including the overhang geometry, a 5-axis toolpath geometry, and a large-scale, multi-bead demonstrator part, which exceeded 500 mm in height and weighed 44 kg (97 lbs).

Adaptive nonlinear motion parameters estimation algorithm for digital twin of multi-link mechanism motion trajectory synthesis

Monitoring systems of automated production lines requires high accuracy and processing speed of acquired data. Nowadays digital twin technologies are rapidly developing as part of Industry 4.0. Digital twin is a virtual representation of a physical system that mimics the behaviour of a real object, and is used in real-time control, monitoring and disturbance prediction, without influence on a real object. Digital twin is being used in many fields of application such as: healthcare, manufacturing, education, city development, etc. Nonetheless, despite the rising popularity of digital twin researches, there is no basic approach to digital twin synthesis. Mostly, in state of the art articles, systems with known parameters are considered. In this paper, approach to development of digital twin, based on internal model for multi-link mechanisms with unknown motion parameters, is presented. Described approach intended to ease the task of production line monitoring and extend digital twin technology application field. In this article adaptive controller design, based on internal model, is presented, theoretical explanations of design process are provided, and application of the control algorithm in the task of multi-link mechanism motion trajectory parameters estimation is described. In this work the experimental synthesis of digital twin for Kuka youBot manipulator based on presented approach in real time is described. Adaptive motion parameters estimation was made for two links of the manipulator for the sake of confirmation of presented approach usage in the task of digital twin for systems with unknown parameters. Motion trajectory parameters of the robot links were defined manually with the use of chaotic generators to estimate the accuracy of the adaptive control system. This approach was used in order to calculate the error of reference tracking by comparing the control signal for digital twin with the reference exogenous input for manipulator links. As the results of the experiment, the graphs of the error reference tracking for both links are presented. As the goal of the experiment, the convergence of reference tracking error to the field [–0.005, 0.005] radian was set, and as can be seen from graphs this goal was achieved. There is a small disturbance of the error convergence on the graphs within the desired field which was caused by noised measurements and delays of the chosen modelling environment real-time simulations. In the conclusion of this paper, further work to reduce the influence of mentioned causes is described. The results of this paper can be used in further digital twin technology researches. Presented approach can be implemented in robots remote control tasks, production lines technical condition monitoring and in general motion trajectory parameters estimation tasks for multi-link mechanisms

Robustness of Interaction Parameters Identification Technique for Collaborative Robots

The work focuses on accuracy of the identification procedure allowing to estimate the force and its application point in human-robot physical interaction. It is assumed that the desired parameters are estimated using data obtained from internal torque sensors embedded in the robot joints as well as 3D geometric models describing the robot link surfaces. In practice, the measurement data are corrupted by the noise, which causes identification errors. To evaluate these errors, the relevant covariance matrix is obtained assuming that the measurement noise is presented as unbiased and independent but not identically distributed random values. Based on the relevant analysis, enhancement of the existing method was proposed, which improves the identification accuracy and its robustness with respect to the measurement noise. Particular attention is paid to singular cases arising when the estimated force action line intersects one or several joint sensor axes or does not intersect the robot body at all. The efficiency of the developed techniques was confirmed via simulation and experimental studies with the KUKA iiwa robot.

Physically Consistent Lie Group Mesh Models for Robot Design and Motion Co-Optimization

With recent advances in rapid prototyping and mechatronics, the problem of simultaneous design and motion optimization, or the co-design problem, is becoming more and more relevant in robotics. For reasons of computational tractability, all existing methods use simplified approximations of a robot’s kinodynamic model. We empirically confirm that any model approximations that are not physically consistent, i.e., the kinodynamic model parameters do not accurately reflect the actual link shapes, can sometimes lead to large errors in the optimization. We then propose a physically consistent, Lie group-based mesh element model for robot links that (i) parametrizes a wide variety of link shapes, and (ii) provides closed-form analytic gradients for the mesh deformations. The latter property is key to developing efficient co-design optimization algorithms that significantly improve numerical convergence and stability. Our co-design methodology is validated through extensive numerical and hardware experiments involving 3D-printed serial and parallel robots.

Three-Dimensional Printable Ball Joints with Variable Stiffness for Robotic Applications Based on Soft Pneumatic Elastomer Actuators.

This paper contributes to a new design of the three-dimensional printable robotic ball joints capable of creating the controllable stiffness linkage between two robot links through pneumatic actuation. The variable stiffness ball joint consists of a soft pneumatic elastomer actuator, a support platform, an inner ball and a socket. The ball joint structure, including the inner ball and the socket, is three-dimensionally printed using polyamide−12 (PA12) by selective laser sintering (SLS) technology as an integral mechanism without the requirement of assembly. The SLS technology can make the ball joint have the advantages of low weight, simple structure, easy to miniaturize and good MRI compatibility. The support platform is designed as a friction-based braking component to increase the stiffness of the ball joint while withstanding the external loads. The soft pneumatic elastomer actuator is responsible for providing the pushing force for the support platform, thereby modulating the frictional force between the inner ball, the socket and the support platform. The most remarkable feature of the proposed variable stiffness design is that the ball joint has ‘zero’ stiffness when no pressurized air is supplied. In the natural state, the inner ball can be freely rotated and twist inside the socket. The proposed ball joint can be quickly stiffened to lock the current position and orientation of the inner ball relative to the socket when the pressurized air is supplied to the soft pneumatic elastomer actuator. The relationship between the stiffness of the ball joint and the input air pressure is investigated in both rotating and twisting directions. The finite element analysis is conducted to optimize the design of the support platform. The stiffness tests are conducted, demonstrating that a significant stiffness enhancement, up to approximately 508.11 N·mm reaction torque in the rotational direction and 571.93 N·mm reaction torque in the twisting direction at the pressure of 400 kPa, can be obtained. Multiple ball joints can be easily assembled to form a variable stiffness structure, in which each ball joint has a relative position and an independent stiffness. Additionally, the degrees of freedom (DOF) of the ball joint can be readily restricted to build the single-DOF or two-DOFs variable stiffness joints for different robotic applications.

Inverse kinematics strategies for physical human-robot interaction using low-impedance passive link shells

AbstractThis paper presents an investigation of the effectiveness of different inverse kinematics strategies in a context of physical human-robot interaction in which passive articulated shells are mounted on the links of a serial robot for manual guidance. The concept of passive link shells is first recalled. Then, inverse kinematics strategies that are designed to plan the trajectory of the robot according to the motion sensed at the link shells are presented and formulated. The different approaches presented all aim at interpreting the motion of the shells and provide an intuitive interaction to the human user. Damped Jacobian based methods are introduced in order to alleviate singularities. A serial 5-dof robot used in previous work is briefly introduced and is used as a test case for the proposed inverse kinematics schemes. The robot includes two link shells for interaction. Simulation results based on the different inverse kinematic strategies are then presented and compared. Finally, general observations and recommendations are discussed.

Workspace-Based Model Predictive Control for Cable-Driven Robots

The control of cable-driven robots is challenging due to the system’s nonlinearity, actuation redundancy, and the unilaterally bounded actuation constraints. To solve this problem, a workspace-based model predictive control (W-MPC) scheme is proposed, which combines the online model predictive control with offline workspace analysis. Using the workspace, a set of convex constraints can be generated for a given reference trajectory. This can then be used to formulate a convex optimization problem for the online W-MPC. Meanwhile, strict recursive feasibility and stability are obtained by taking advantage of the predictive feature of MPC. To demonstrate the effectiveness of the proposed W-MPC, simulation was performed on a 2-link planar cable-driven robot and a spatial cable-driven parallel robot for both nominal and non-nominal scenarios. Hardware experiment was also carried out using a 3 degree-of-freedom planar cable robot. The results show that the controller is efficient and effective to perform motion tracking with the cable force constraints satisfied despite the existence of various model uncertainties.

End-effector trajectory tracking of flexible link parallel robots using servo constraints

We apply the concept of servo constraints to end-effector trajectory tracking control of parallel robots with structural link flexibilities. Such servo constraints deliver the inverse robot model where solution approaches via projections are proposed, which transform the resulting differential-algebraic equations to ordinary differential equations. The applicable solution process depends on the existence and stability of the internal dynamics. When using the exact end-effector of flexible link robots as output, this internal dynamics is usually unstable. Then a two-point boundary value problem is considered in the framework of stable inversion to obtain the noncausal solution offline. This solution is used as a feedforward control, which is initially combined only with actuator feedback control. To also account for errors within the link flexibility, the well-known linear–quadratic regulator is adapted to end-effector trajectory tracking based on differential-algebraic equations. Finally, we propose a systematic input–output feedback linearization approach, which uses servo constraints for flexible link parallel robots. Here a minimum phase system is obtained by tracking a redefined end-effector output, which is an approximation of the exact end-effector position. All control concepts are validated experimentally with a parallel robot having a highly flexible link. The results allow us to compare different control approaches and show the superior performance of controllers that rely on a flexible multibody model in contrast to classical rigid multibody modeling.

A multi-objective optimization design of industrial robot arms

This paper introduces a multi-objective design mechanism to minimize both the initial and running costs of industrial robot arms. The goal of the design problem is to decide the type of material and physical dimensions of the robot arm to withstand high loads at vulnerable locations using stress analysis. Additionally, it selects the material architecture for the robot links based on a vibration analysis to avoid robot failure at or close to the resonance frequency. Hence, a set of design equations based on stress analysis are developed using analytical approaches while the findings are supported by finite element simulations in ANSYS. These decide the type of material, cross-section area, factor of safety (FoS), and maximum deflection of the robot links in terms of the mass-loads. Moreover, the vibration analysis is conducted to enhance the dynamic characteristics of the robot arm. Therefore, the excitation frequency is modified by changing the mass and the robot segment-material to evade working at the natural frequency. Modal analysis is conducted using ANSYS to identify the fundamental frequencies and their modal shapes. Then, a material selection mechanism based on finite element analysis is considered to allow a safe frequency operation range for the robot arm. A customized robot arm structure that combines Magnesium and Aluminum alloy with highly improved FoS and minimizes the initial and operating costs is proposed. In addition to the body structure of the robot arm, the influence of the reducers and motors on the stiffness and vibration of the robot arm is presented. Finally, the motion of the robot arm is optimized using a Genetic Algorithm subject to a set of boundary conditions imposed by the desired mission. The effect of rotation angle value in the power consumption is presented. The coefficients of a developed angular displacement function are optimized to ensure minimum power consumption during the robot missions.

Energy-Based Motion Control for Pneumatic Artificial Muscle Actuated Robots With Experiments

The pneumatic artificial muscle (PAM) is a kind of flexible actuators used to simulate the characteristics of human muscles. Robots actuated by PAMs possess compliance and safety, which can achieve satisfactory man–machine interaction control. Nevertheless, such robots actuated by PAMs tend to have lots of control problems due to the inherent characteristics, such as hysteresis, creep, high nonlinearities, and so on, which is not conducive to accurate modeling and motion control. Moreover, most existing control methods do not consider constraining overshoots, etc.; however, based on safety requirements and actual physical constraints, systems with unconstrained overshoots may have potential risks. In this article, a new energy-based nonlinear control method is proposed for 2-link PAM-actuated robots to realize accurate positioning control. For this purpose, first, the dynamic model of 2-link PAM-actuated robots is presented. Further, a new energy storage function is constructed. Additionally, the overshoots and the terms coupled with control inputs are also constrained reasonably, which can reduce the unnecessary energy loss while improving the system safety. To the best of our knowledge, the proposed method is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> nonlinear control approach for 2-link PAM-actuated robots which is designed and analyzed based upon the original nonlinear dynamics <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization to provide high-performance positioning control with constrained overshoots and eliminated residual oscillations simultaneously. By rigorous analysis, the asymptotic stability of the system is proven. To validate the effectiveness of the proposed method, a series of hardware experimental results are presented based on a self-built 2-link PAM-actuated robot.