Research on variable impedance control of SEA-driven upper limb rehabilitation robot based on singular perturbation method

The flexible joint robot (FJR) typically experiences parametric variations, non-linearities, underactuation, noise propagation, and external disturbances which seriously degrade the FJR tracking. This paper proposes an adaptive integral sliding mode controller (AISMC) based on a singular perturbation method and two state observers for the FJR to achieve high performance. Firstly, the underactuated FJR is modelled into two simple second order fast and slow subsystem by using Olfati transformation and singular perturbation method, which handles underactuation while reducing noise amplification. Then, the AISMC is proposed to effectively accomplish the desired tracking performance, in which the integral sliding surface is designed to reduce chattering based on two state observers with no requirements of the velocity and acceleration measurements in the FJR system. Furthermore, an adaptive laws for switching gains are proposed for both slow and fast subsystems in the FJR to remove the requirements of knowing the up-bound of the disturbances and uncertainties. The closed loop stability of not only slow and fast subsystems but also the overall FJR is proved using the Lyapunov theorem. Finally, the simulation and experimental results demonstrate the superiority of proposed control in terms of less tracking error, significant noise suppression, and strong robustness in comparison with existing controllers.

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed into fast and slow subsystems. The slow dynamic corresponds to the rigid manipulator and the fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2-DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

This article describes the implementation of hierarchical control on a robotic manipulator using fuzzy logic. A decentralized control approach is implemented, i.e., individual controllers control the two links of the robot. The kinematic aspect of the control is treated as the supervisory mode at a higher level, and the joint control is treated as the lower level. Fuzzy logic based rules determine the inverse kinematic mapping, which maps the Cartesian coordinates to the individual joint angles. This scheme is implemented using Togai Infra Logic software and the entire simulation software is implemented using the “C” language. The results of the simulation are discussed. This experiment is a proof of the principle that the fuzzy controller can be used to map the nonlinear mapping, which can be implemented to more complex problems of inverse kinematics of higher degree of freedom robots. A fuzzy PD controller is implemented on a Rhino robot. The performance is compared with a traditional PD controller. The fuzzy controller, being an adaptive technique, gives better performance than a traditional linear PD controller over a typical operational range. The fuzzy controller reaches the desired position with no overshoot, which is unlikely with a PD controller.

The notable performance exhibited by impedance controllers during robotic interaction has led to the widespread use of this control methodology. Improved position and interaction control might be attainable through utilisation of variable impedance control (VIC) techniques. Interactional performance could be further improved by combining structural compliance with VIC. However, utilization of VIC tends to induce energy-injecting elements, which could impact on a robotic system's stability/passivity. Additionally, implementation of active VIC techniques on passively compliant robots has not been investigated (although several works consider VIC using variable stiffness actuators), which renders the existing rigid-joint robot, passivity-inducing control schemes inapplicable to compliant systems. To this end, the work presented here introduces a novel scheme, termed passivity-preservation control (PPC), which suppresses the energy injections that could be introduced into compliant robots, as a result of VIC. Compared to tank-based VIC approaches the PPC scheme is directly applicable to flexible-joint robots, even ones with nonlinear passive stiffness elements, while its performance is independent of the tank-energy levels. Moreover, the proposed scheme permits stable VIC using full-state feedback, thereby enabling impedance modulations relating to both motor and link-side variables. Consequently, full-state feedback gains can be generated via linear quadratic regulator optimisation, thus enabling application of gain-scheduling techniques on flexible-joint robots for enhanced position control. Passivity and stability analyses are performed for joint and Cartesian-space versions of the PPC scheme, which justify their applicability to both interaction and “free-motion” scenarios. The PPC scheme's efficacy, compared to constant gain impedance methods, in terms of convergence and interactional performance, is corroborated via simulation and experimental means involving the Sawyer robot, which is powered by series elastic actuators. Theoretical and experimental results mathematically and practically verify VIC stability, thus enabling flexible-joint robots to more accurately mimic biologically inspired behaviors.

Purpose This paper aims to propose an innovative adaptive control method for lower-limb rehabilitation robots. Design/methodology/approach Despite carrying out various studies on the subject of rehabilitation robots, the flexibility and stability of the closed-loop control system is still a challenging problem. In the proposed method, surface electromyography (sEMG) and human force-based dual closed-loop control strategy is designed to adaptively control the rehabilitation robots. A motion analysis of human lower limbs is performed by using a wavelet neural network (WNN) to obtain the desired trajectory of patients. In the outer loop, the reference trajectory of the robot is modified by a variable impedance controller (VIC) on the basis of the sEMG and human force. Thenceforward, in the inner loop, a model reference adaptive controller with parameter updating laws based on the Lyapunov stability theory forces the rehabilitation robot to track the reference trajectory. Findings The experiment results confirm that the trajectory tracking error is efficiently decreased by the VIC and adaptively correct the reference trajectory synchronizing with the patients’ motion intention; the model reference controller is able to outstandingly force the rehabilitation robot to track the reference trajectory. The method proposed in this paper can better the functioning of the rehabilitation robot system and is expandable to other applications of the rehabilitation field. Originality/value The proposed approach is interesting for the design of an intelligent control of rehabilitation robots. The main contributions of this paper are: using a WNN to obtain the desired trajectory of patients based on sEMG signal, modifying the reference trajectory by the VIC and using model reference control to force rehabilitation robot to track the reference trajectory.

In this paper, active control of a 6-DOF space robot with flexible panels using singular perturbation method is investigated. Dynamic model of the system is established by using the Jourdain’s velocity variation principle. Dynamic equation of the system is decomposed into a slow subsystem and a fast subsystem by using the singular perturbation method. A composite controller is used to make the space robot reach a specified position and suppress the elastic vibration of the panels. Simulation results indicate that the proposed model is effective to describe the dynamics of space robot; the designed composite controller can effectively make the robot reach a specified position and the elastic vibration of the panels may be suppressed simultaneously; the fast controller has a great influence on the control effect of the space robot system.

Chapter 6 - Design of a Composite Control in Two-Time Scale Using Nonlinear Disturbance Observer-Based SMC and Backstepping Control of a Two-Link Flexible Manipulator

This work presents an approach for fault diagnosis of discrete time singularly perturbed systems (SPS) with time-delay, called parity space in order to generate fault detection residual. In fact, to decompose the full system into slow and fast subsystems, we based on singular perturbation method. Then, we can use the reduced residual generated basing on slow subsystem in order to estimate and isolate faults of the global delayed SPS. A numerical example is presented to demonstrate the efficiency of the proposed approach in the case of sensor faults with different values of singular perturbation parameter epsilon.

In this research, properties of variable admittance controller and variable impedance controller were simulated by MATLAB firstly, which reflected the good performance of these two controllers under trajectory tracking and physical interaction. Secondly, a new mode of learning from demonstration (LfD) that conforms to human intuitive and has good interaction performances was developed by combining the electromyogram (EMG) signals and variable impedance (admittance) controller in dragging demonstration. In this learning by demonstration mode, demonstrators not only can interact with manipulator intuitively, but also can transmit end-effector trajectories and impedance gain scheduling to the manipulator for learning. A dragging demonstration experiment in 2D space was carried out with such learning mode. Experimental results revealed that the designed human-robot interaction and demonstration mode is conducive to demonstrators to control interaction performance of manipulator directly, which improves accuracy and time efficiency of the demonstration task. Moreover, the trajectory and impedance gain scheduling could be retained for the next learning process in the autonomous compliant operations of manipulator.

Contact Dynamics and Force Control of Space Robotic Systems

Detailed modelling of contact dynamics involving a flexible space manipulator system and a payload is considered in this paper. The components undergoing direct contact (the end–effector of a manipulator and a payload) are modelled using the finite–element method, while the rest of the system is handled through the usual flexible multi–body formulation. Then, the system dynamics is composed of a set of differential equations subjected to sets of algebraic equations expressing kinematic or contact constraints. This dynamic model is then used to design a composite controller which must simultaneously achieve three goals: (i) trajectory tracking, (ii) force control and (iii) stabilization of the flexible degrees of freedom of the multi–body system. The singular perturbation method is used to obtain two reduced–order models; subsequently, the slow subsystem is used to design a hybrid position/force controller based on impedance control, and the fast subsystem is used to design a linear quadratic regulator (LQR).

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time. Impedance Control provides a universal approach to the control of flexible robots — in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use Hamilton’s principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed to the fast and the slow subsystems. The slow dynamic corresponds to the rigid manipulator and fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2 DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

Variable impedance control has been considered as one of the most important compliant control approaches for its abilities in improving compliance, safety, and efficiency in robot–environment interaction. However, existing variable impedance controllers have deficits in stability guarantee. This article proposes a stability-guaranteed variable impedance control approach for robots with modeling uncertainties based on approximate dynamic inversion (ADI). Novel constraints on variable impedance profiles are given to guarantee the exponential stability of the desired variable impedance dynamics. An ADI-based impedance control law is designed to achieve the desired variable impedance dynamics through the convergence of a variable impedance error. Based on the extended Tikhonovs theorem, it is proven that the closed-loop control system has semiglobal practical exponential stability. The proposed impedance controller can be implemented in a PID form and is appealing for its simple structure, easy implementation, and control stability guarantee. The effectiveness of the proposed variable impedance controller is illustrated by an illustrative example taken on a five-bar parallel robot.

A multirate adaptive composite controller using neural networks is presented in this paper for the trajectory tracking control of a flexible-link robot with a partially known nonlinear dynamics. Based on the singular perturbation method and two time-scale decomposition, the flexible-link robot model is decomposed into two subsystems: the slow subsystem and the fast subsystem. Thus, separate slow and fast control laws can be designed for each subsystem and then combined into a composite control. The slow control is implemented by a neural network-based adaptive controller with novel properties and structure, which is used to control the slow subsystem, an equivalent rigid-link manipulator. The fast control is designed to stabilize the fast subsystem around the equilibrium trajectory set up by the slow subsystem under the effect of the slow control.

针对参数不确定的漂浮基柔性关节空间机器人系统,研究了其动力学建模过程、运动控制律设计及柔性振动的主动抑制.利用系统动量、动量矩守恒关系和拉格朗日方程建立了系统的动力学方程.为克服传统奇异摄动法仅适用于关节弱柔性系统这一局限性,设计了柔性补偿项来等效提高空间机器人系统中柔性关节的刚度.在此基础上,利用奇异摄动法将系统分解为相互独立的慢变子系统和快变子系统,并分别进行控制律设计.所设计的慢变子系统模糊鲁棒滑模控制律可补偿系统中的不确定参数,减小柔性关节引起的转角传动误差,实现系统期望运动轨迹的渐近跟踪;快变子系统控制律可主动抑制柔性关节引起的系统柔性振动.仿真实验结果证明了该混合控制律的有效性.