A new approach to enhance the stiffness of heavy-load parallel robots by means of the component selection

Stiffness enhancement is one of the most crucial issues for the parallel robots as machine tools. Different from the previous methods including the structural comparison and dimensional synthesis, a new approach to enhance the stiffness of heavy-load parallel robots from the direction of component selection is proposed in this paper. To contain the main parameters of components, an overall stiffness matrix is proposed, where the effects of link deformations and joint clearances are considered. In order to meet the stiffness requirements of the machine tool in practical machining directions, a new stiffness index and an objective function are also derived on the basis of the overall stiffness model. In addition, since the number of component parameters is huge, particle swarm optimization technology is utilized to obtain the appropriate results. Finally, two examples of the A3 head and the Tricept based are presented to demonstrate the practicability of the proposed enhancement approach. According to the results of numerical examples, it shows that the proposed approach is feasible, and it can further enhance the stiffness of parallel robots after the structural comparison and dimensional synthesis.     

Development of a variable stiffness joint drive module and experimental results of joint angle control

Two prototypes of variable stiffness joint drive modules imitating a human joint structure are presented. A human joint is driven by a pair of flexor and extensor muscles that work antagonistically. The stiffness of the joint is adjusted by their co-contraction. Such a structure was given to the joint drive module so that it could achieve a variable stiffness property. The joint is driven by two wires with nonlinear springs. Thanks to the nonlinearity of the springs, the stiffness of the joint can be adjusted by quasi-co-contraction of the wires. With the first prototype, the stiffness adjustability of the joint was empirically confirmed. Regarding joint angle control, a three-layered proportional integral derivative (PID) control algorithm was implemented in the second prototype, and it was verified that the control algorithm worked properly.     

Sample-based synthesis of two-scale structures with anisotropy

A vast majority of natural or synthetic materials are characterized by their anisotropic properties, such as stiffness. Such anisotropy is effected by the spatial distribution of the fine-scale structure and/or anisotropy of the constituent phases at a finer scale. In design, proper control of the anisotropy may greatly enhance the efficiency and performance of synthesized structures.We propose a sample-based two-scale structure synthesis approach that explicitly controls anisotropic effective material properties of the structure on the coarse scale by orienting sampled material neighborhoods at the fine scale. We first characterize the non-uniform orientations distribution of the sample structure by showing that the principal axes of an orthotropic material may be determined by the eigenvalue decomposition of its effective stiffness tensor. Such effective stiffness tensors can be efficiently estimated based on the two-point correlation functions of the fine-scale structures. Then we synthesize the two-scale structure by rotating fine-scale structures from the sample to follow a given target orientation field. The effectiveness of the proposed approach is demonstrated through examples in both 2D and 3D.     

Construction of a Gait Adaptation Model in Human Split-Belt Treadmill Walking Using a Two-Dimensional Biped Robot

A number of studies have measured kinematics, dynamics and oxygen uptake while a person walks on a treadmill. In particular, during walking on a split-belt treadmill, in which the left and right belts have different speeds, remarkable differences in kinematics are observed between normal subjects and subjects with cerebellar disease. In order to construct a gait adaptation model of such human split-belt treadmill walking, we proposed a simple control model and developed a new two-dimensional biped robot walk on a split-belt treadmill. We combined the conventional limit-cycle-based control consisting of joint PD control, cyclic motion trajectory planning and a stepping reflex with a newly proposed adjustment of P-gain at the hip joint of the stance leg. The data obtained in experiments on the robot (normal subject model and cerebellum disease subject model) have highly similar ratios and patterns to data obtained in experiments on normal subjects and subjects with cerebellar disease carried out by Bastian et al. We also showed that the P-gain at the hip joint of the stance leg was the control parameter of adaptation for symmetric gaits in split-belt walking and that P-gain adjustment corresponded to muscle stiffness adjustment by the cerebellum. Consequently, we successfully proposed a gait adaptation model for human split-belt treadmill walking, and confirmed the validity of our hypotheses and the proposed model using the biped robot.     

Estimation of Joint Stiffness Using Instantaneous Loads via an Electromyogram and Application to a Master–Slave System with an Artificial Muscle Manipulator

Master–slave systems and human-assisted systems in which robots can work together with humans have been widely developed. Such systems are necessary to communicate human intentions to a robot. Therefore, it is important for these systems to be able to estimate human joint characteristics such as torque, position and stiffness. In this context, we focus on the myoelectric (ME) potential. In many previous studies, an electric motor has been used as an actuator, and the torque and position are estimated from the ME potential. However, the joint stiffness of humans has not been studied extensively. In this study, we propose a method to estimate the stiffness of the human elbow by using antagonistic muscles when an instantaneous load is applied. Furthermore, we apply our method to a 1-d.o.f. manipulator with an artificial muscle. In the case of eccentric contraction, it has been shown that the stiffness of a joint can be estimated solely by an electromyogram of the triceps. Then, the stiffness and angle control of the artificial muscle manipulator that used it as the slave side is proposed. Furthermore, the estimated joint stiffness is set as a desired value for joint stiffness control of the artificial muscle manipulator. Experimental results of stiffness control indicate that the angle and the stiffness of the 1-d.o.f. artificial muscle manipulator can be adequately controlled for a master–slave system. Safer remote control systems can be developed by using this system.     

机器人串联弹性关节驱动器的刚度控制方法

机器人关节的柔顺性在人机协作过程中具有重要作用，然而固定的关节柔性无法满足动态变化的人机协作需求，因此对机器人的关节驱动器提出了具有刚度调节能力的要求.本文采用阿基米德螺旋线平面涡卷弹簧作为机器人关节的柔性元件，并提出一种可用于具有固定刚度的串联弹性驱动器的刚度控制方法.根据关节刚度的定义，将测量得到的弹簧输出端角度用于计算弹簧的输入端转角，使得机器人关节驱动器的等效刚度可以被调整到所期望的大小.该方法以电机位置控制为内环，关节刚度控制为外环，简化了控制器设计，并实现了解耦控制.对所设计的刚度控制器进行了分析.最后在自主设计的单自由度薄型串联弹性驱动器实验平台上进行了刚度调节实验，包括刚度的双向阶跃、零刚度和正弦变化的刚度，实验结果表明关节等效刚度能准确跟踪期望值，验证了该方法的有效性.     

Static modeling and control of redundant manipulators

This paper develops unified static models for control of a redundant manipulator. We introduce the Premultiplier Diagram to describe the static behavior of a redundant manipulator. This diagram provides insight into the algebra and physics related to redundant manipulators. We derive redundancy expressions for the joint displacement, joint torque and joint stiffness matrix. These redundancy expressions are composed of a particular (net) part and a homogeneous (null) part. Based on the orthogonality property between the net and the null components, we propose an extension of the stiffness control scheme for redundant manipulators. We also show how the decomposed and decoupled static behavior of redundant manipulators can be used to derive an optimal control strategy.     

不确定非线性系统全局渐近自适应神经网络控制

针对一类控制增益为一般函数形式的不确定仿射非线性系统,提出一种能够确保全局渐近稳定的自适应神经控制(adaptiveneural control,ANC)方法.为了保证神经网络逼近的适用性,设计一种可变控增益的比例微分(proportionaldifferential,PD)控制器以全局镇定被控对象.利用状态变换解决由未知控制增益函数导致的控制奇异问题.提出一种连续的自适应鲁棒控制项实现闭环系统的渐近跟踪.与现有的全局渐近跟踪ANC方法相比较,本文方法不仅简化了PD增益的选择,而且减轻了控制输入的颤振问题.仿真结果表明了本文方法的有效性.     

Computer analysis of foldable structures

An approach is presented for the computer analysis of foldable structures. This approach is based on the concepts of the standard stiffness method, where the element stiffness matrix for the basic components of such structures, namely, the uniplets, is derived from the stiffness matrix for a three-noded beam. The derivation of the uniplet stiffness matrix is a process of condensing the rotational degrees of freedom of the three-noded beam. A foldable structure may incorporate other elements such as cables and bars, so an iterative scheme for dealing with cables is described. Two examples are provided to illustrate the basic procedure evolved.     

Equilibrium point control of a robot manipulator using biologically-inspired redundant actuation system

Unlike their robotic counterparts, humans excel at various contact tasks even in unknown environments by utilizing their ability to adaptively modulate the arm impedance. As one of many theories in human motor control, the equilibrium point control hypothesis suggests that multi-joint limb movements can be achieved by shifting the equilibrium positions defined by the central nervous system and utilizing the spring-like property of the peripheral neuromuscular system. To generate human arm-like compliant motion, this study implements the equilibrium point control on a robot manipulator using redundant actuation: two actuators are installed on each joint: one to control the joint position and the other to control the joint stiffness, respectively. With the double-actuator unit, the equilibrium position and stiffness (or impedance) can be independently programmed. Also, it is possible to estimate the contact force based on angle measurement with a user-specified stiffness. These features enable the robot manipulator to execute stable and safe movement in contact tasks. A two-link manipulator equipped with the double-actuator units was developed, and experimental results from teleoperated contact tasks show the potential of the proposed approach.     

A real-time impedance-based singularity and joint-limits avoidance approach for manual guidance of industrial robots

This paper studies real-time manual guidance considering singularity and joint-limits avoidance using impedance control in an industrial scenario. The operator is responsible for keeping the end-effector (EE) away from the robot’s singularity and joint-limits. The proposed approach detects the singularity and joint-limits in real-time. Then, virtual stiffness and damping are added to target stiffness and damping as the robot is getting close to the singularity or joint-limit. A criterion is presented for detection of singularity by combining manipulability ellipsoid and condition number. Also a new joint to Cartesian space transformation is formulated in order to convert joint stiffness and damping to Cartesian stiffness and damping for joint-limits avoidance method. The presented approach is applied on a SCARA robot. An experiment is performed in this paper to investigate singularity and joint-limits avoidance separately as well as together. Increase in stiffness and damping warn the operator of the possibility of singularity or joint-limits allowing the operator to changes the EE path. The proposed approach, eliminates the need for a robotics expert by allowing any operator with no knowledge about robot singularity and joint-limits to interact and teach the robot in a safe, real-time and time-saving manner.     

PD Controller for Manipulator with Kinetic Energy Term

A kinetic energy approach to PD control in joint space of a manipulator in terms of the eigenfactor quasi-coordinate velocity (EQV) vector is considered in this paper. The modified PD controller which contains quantities resulting from decomposition of a manipulator mass matrix is proposed. The obtained equations of motion are based on the eigenvalues and eigenvectors of the mass matrix (Junkins, J. L. and Schaub, H. [7]. It is shown that utilizing the EQV vector one can determine directly the kinetic energy of the manipulator and at the same time realize PD control in its joint space. This energy-based strategy gives an interesting insight into position control. The controller presented here was tested in simulation on a 3 d.o.f. direct drive arm manipulator and via experiment on a 2 d.o.f. manipulator. The results confirmed that one can directly determine the kinetic energy for the total manipulator as well for its each joint. Additionally, time response of the system under EQV controller is faster than for the classical controller if mechanical coupling are strong.     

Multiclass classification of Parkinson’s disease using cepstral analysis

This paper addressees the problem of an early diagnosis of PD (Parkinson’s disease) by the classification of characteristic features of person’s voice knowing that 90% of the people with PD suffer from speech disorders. We collected 375 voice samples from healthy and people suffer from PD. We extracted from each voice sample features using the MFCC and PLP Cepstral techniques. All the features are analyzed and selected by feature selection algorithms to classify the subjects in 4 classes according to UPDRS (unified Parkinson’s disease Rating Scale) score. The advantage of our approach is the resulting and the simplicity of the technique used, so it could also extended for other voice pathologies. We used as classifier the discriminant analysis for the results obtained in previous multiclass classification works. We obtained accuracy up to 87.6% for discrimination between PD patients in 3 different stages and healthy control using MFCC along with the LLBFS algorithm.     

Experimental study on torque control using Harmonic Drive built-in torque sensors

We have proposed the practical torque sensor which utilizes elasticity of harmonic drives. The sensing technique provides joint torque sensing without reducing stiffness of the robot and changing the mechanical structure of the joints. In this article, we examine experimentally the characteristics of joint torque control using this torque sensor. Three types of torque control laws are implemented with a one-link arm to find a control method which provides excellent friction reduction and dynamic response in joint torque. The experimental results of joint torque control show that the torque sensor is very useful to compensate the nonlinear friction. Furthermore the torque control is effective to improve the accuracy of the motion control at low velocity and to suppress the vibration caused by the joint flexibility. © 1998 John Wiley & Sons, Inc.     

An inverse kinematics algorithm for interaction control of a flexible arm with a compliant surface

This paper deals with the problem of controlling the interaction of a multilink flexible arm in contact with a compliant surface. For a given tip position and surface stiffness, the joint and deflection variables are computed using a closed-loop inverse kinematics algorithm. This is based on a suitable Jacobian matrix which includes terms accounting for the static deflections due to gravity and contact force. The computed variables are used as the set-points for a simple joint PD control, thus achieving regulation of the tip position and contact force via a joint-space controller. The scheme is tested in a simulation case study for a planar two-link manipulator.     

Proxy-based position control of manipulators with passive compliant actuators: Stability analysis and experiments

In this work we introduce a position control scheme which is targeted at the enhancement of the safety of compliant joint robots. In addition to the necessity for accuracy and robustness that both serve as prerequisites for the successful performance of various tasks, the ability to safely handle unexpected events, such as communication failures or unintended interactions which may endanger the robot/human safety, is a paramount requirement. To achieve a smooth motion behaviour of compliant systems under different circumstances, damping control actions are essential. To this end, a novel proxy-based approach for compliant joint robots, integrated into a passivity-guaranteed controller, is proposed. The stability analysis of the proposed scheme is presented and the global asymptotic convergence, as well as the passivity of the control scheme, are analytically proven. The performance of the proposed approach is practically evaluated by means of experiments on a spatial robotic arm with passive compliant actuators, and is compared with that of a classical PD approach. Experimental results validate the ability of the proposed approach to inject damping in order to provide smooth and damped recovery when an interruption in task execution occurs.     

Combined Direct and Inverse Kinematic Control for Articulated Figure Motion Editing

A new approach for the animation of articulated figures is presented. We propose a system of articulated motion design which offers a full combination of both direct and inverse kinematic control of the joint parameters. Such an approach allows an animator to specify interactively goal-directed changes to existing sampled joint motions, resulting in a more general and expressive class of possible joint motions. The fundamental idea is to consider any desired-joint space motion as a reference model inserted into the secondary task of an inverse kinematic control scheme. This approach profits from the use of half-space Cartesian main tasks in conjunction with a parallel control of the articulated figure called the coach-trainee metaphor. In addition, a transition function is introduced so as to guarantee the continuity of the control. The resulting combined kinematic control scheme leads to a new methodology of joint-motion editing which is demonstrated through the improvement of a functional model of human walking.     

Humanoid motion analysis and control based on COG viscoelasticity

This paper proposes a concept of center of gravity (COG) viscoelasticity to associate joint viscoelasticity with the inverted pendulum model of humanoid dynamics. Although COG viscoelasticity is based on the well-known kinematic relationship between joint stiffness and end-effector stiffness, it provides practical advantages for both analysis and control of humanoid motions. There are two main contributions. The first is that the COG viscoelasticity allows us to analyze fall risk. In a previous study, the author proposed a fall detection method based on the maximal output admissible (MOA) set, which is computed from feedback gain of the inverted pendulum model. The COG viscoelasticity associates joint viscoelasticity with the feedback gain and allows us to compute the corresponding MOA set when an arbitrary joint viscoelasticity is given. The second contribution is that the COG viscoelasticity can be also utilized in motion control. After we design a feedback gain in the inverted pendulum model utilizing the control theory, the COG viscoelasticity can directly transform it to the joint viscoelasticity. The validity of the COG viscoelasticity is verified with whole-body dynamics simulations.     

Passive joint stiffness in the hip and knee increases the energy efficiency of leg swinging

In the field of minimally-actuated robots, energy efficiency and stability are two of the fundamental criteria that can increase autonomy and improve task-performance capabilities. In this paper, we demonstrate that the energetic cost of leg swinging in dynamic robots can be reduced without significantly affecting stability by emulating the physiological use of passive joint stiffness, and we suggest that similar efficiency improvements could be realized in dynamic walking robots. Our experimental model consists of a two-segment dynamically swinging robotic leg with hip and knee joints. Closed-loop control is provided to the hip using neurally inspired, nonlinear oscillators that do not override the leg’s natural dynamics. We examined both linear and nonlinear, physiologically based stiffness profiles at the hip and knee and a hyperextension-preventing hard stop at the knee. Our results indicate that passive joint stiffness applied at one or both joints can improve the energy efficiency of leg swinging by reducing the actuator work required to counter gravitational torque and by promoting kinetic energy transfer between the shank and thigh. Energetic cost reductions (relative to the no-stiffness case) of approximately 25% can be achieved using hip stiffness, provided that the hip actuation bias angle is not coincident with gravity, and cost reductions of approximately 66% can be achieved using knee stiffness. We also found that constant stiffness combined with a limit on knee hyperextension produces comparable results to the physiological stiffness model without requiring complex implementation techniques. Although this study focused on the task of leg swinging, our results suggest that passive-stiffness properties could also increase the energy efficiency of walking by reducing the cost of forward leg swing by up to 66%. We also expect that the energetic cost of walking could be further reduced by adding stiffness to the ankle to assist in the propulsive portion of stance phase.