Feedforward operational stiffness modulation and external force estimation of planar robots equipped with variable stiffness actuators

A variable stiffness actuator (VSA) is considered a promising mechanism-based approach for realizing compliant robotic manipulators. By changing the stiffness of each joint, the robot can modulate the stiffness of the entire system to enhance safety and efficiency during physical interaction with other systems. This paper presents a feedforward method to modulate the operational stiffness of a parallel planar robot with multiple VSAs. A VSA utilizing a lever mechanism was developed, clearly presenting its mechanical design and kinematic model details. A computational model of joint-restoring torque was developed based on deformation measurements and hysteresis loop geometry to estimate the applied torque of each joint in real-time. An algorithm was proposed to compute the joint stiffness solution using the robot's kinematic model for modulating the operational stiffness of the parallel robot. Experiments were performed to evaluate the proposed method by comparing the performances of two DOF serial and parallel robot systems. The results demonstrated the capability of the VSA in both feedforward stiffness modulation and external force estimation.

     

Optimal variable stiffness control: formulation and application to explosive movement tasks

It is widely recognised that compliant actuation is advantageous to robot control once dynamic tasks are considered. However, the benefit of intrinsic compliance comes with high control complexity. Specifically, coordinating the motion of a system through a compliant actuator and finding a task-specific impedance profile that leads to better performance is known to be non-trivial. Here, we propose an optimal control formulation to compute the motor position commands, and the associated time-varying torque and stiffness profiles. To demonstrate the utility of the approach, we consider an “explosive” ball-throwing task where exploitation of the intrinsic dynamics of the compliantly actuated system leads to improved task performance (i.e., distance thrown). In this example we show that: (i) the proposed control methodology is able to tailor impedance strategies to specific task objectives and system dynamics, (ii) the ability to vary stiffness can be exploited to achieve better performance, (iii) in systems with variable physical compliance, the present formulation enables exploitation of the energy storage capabilities of the actuators to improve task performance. We illustrate these in numerical simulations, and in hardware experiments on a two-link variable stiffness robot.     

A Mixed Suspension System for a Half-Car Vehicle Model

Inthis paper we realize the design of a mixed suspension system(an actuator in tandem with a conventional passive suspension)for the axletree of a road vehicle based on a linear model withfour degrees of freedom. We propose an optimal control law thataims to optimize the suspension performance while ensuring thatthe magnitude of the forces generated by the two actuators andthe total forces applied between wheel and body never exceedgiven bounds. The solution we derive takes the form of an adaptivecontrol law that switches between different constant state feedbackgains. The results of our simulations show that the bound onthe active forces is a design parameter useful for establishinga trade-off between performance and power requirement.     

Ankle–knee prosthesis with active ankle and energy transfer: Development of the CYBERLEGs Alpha-Prosthesis

This paper presents the development of the CYBERLEGs Alpha-Prototype prosthesis, a new transfemoral prosthesis incorporating a new variable stiffness ankle actuator based on the MACCEPA architecture, a passive knee with two locking mechanisms, and an energy transfer mechanism that harvests negative work from the knee and delivers it to the ankle to assist pushoff. The CYBERLEGs Alpha-Prosthesis is part of the CYBERLEGs FP7-ICT project, which combines a prosthesis system to replace a lost limb in parallel with an exoskeleton to assist the sound leg, and sensory array to control both systems. The prosthesis attempts to produce a natural level ground walking gait that approximates the joint torques and kinematics of a non-amputee while maintaining compliant joints, which has the potential to decrease impulsive losses, and ultimately reduce the end user energy consumption. This first prototype consists of a passive knee and an active ankle which are energetically coupled to reduce the total power consumption of the device. Here we present simulations of the actuation system of the ankle and the passive behavior of the knee module with and without the energy transfer effects, the mechanical design of the prosthesis, and empirical results from testing of the physical device with amputee subjects.     

Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators

This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple Lyapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities (LMIs). The proposed design method is illustrated by two numerical examples.     

Maximizing biogas production from the anaerobic digestion

This paper presents an optimal control law policy for maximizing biogas production of anaerobic digesters. In particular, using a simple model of the anaerobic digestion process, we derive a control law to maximize the biogas production over a period T using the dilution rate as the control variable. Depending on initial conditions and constraints on the actuator (the dilution rate D(·)), the search for a solution to the optimal control problem reveals very different levels of difficulty. In the present paper, we consider that there are no severe constraints on the actuator. In particular, the interval in which the input flow rate lives includes the value which allows the biogas to be maximized at equilibrium. For this case, we solve the optimal control problem using classical tools of differential equations analysis. Numerical simulations illustrate the robustness of the control law with respect to several parameters, notably with respect to initial conditions. We use these results to show that the heuristic control law proposed by Steyer et al., 1999 [20] is optimal in a certain sense. The optimal trajectories are then compared with those given by a purely numerical optimal control solver (i.e. the “BOCOP” toolkit) which is an open-source toolbox for solving optimal control problems. When the exact analytical solution to the optimal control problem cannot be found, we suggest that such numerical tool can be used to intuiter optimal solutions.     

Design and analysis of a novel variable stiffness actuator based on parallel-assembled-folded serial leaf springs

Variable stiffness actuator (VSA) can significantly improve the dynamic performance of robots and ensure safety in human robot interaction. In this paper, a novel structure-controlled VSA which achieves a lower minimal stiffness while the size and load capacity remain unchanged is introduced. Stiffness variation is implemented by changing the effective length of parallel-assembled-folded serial leaf springs presented in this paper, which makes the adjustment of stiffness easier and driven by an independent motor. A modified analytical model of joint stiffness is built, which takes the gap between leaf springs and rollers into consideration. Experiments prove that the modified model is more accurate comparing with the ideal model which ignores the gap. Further analyses show that the gap can even make serious impacts on leaf spring-based structure-controlled VSA in other performances such as deformability and energy capacity.     

Fault‐Tolerant Control for Flutter of Airfoil Subject to Input Saturation

In this paper, a fault tolerant control is studied for a two‐dimensional airfoil with input saturation and actuator fault. The dynamic equation of airfoil flutter is firstly established, in which the cubic hard spring nonlinearity of pitch stiffness is considered. Then, an adaptive sliding mode fault tolerant control is derived by using an on‐line updating law to estimate the bound of the actuator fault such that no information about the fault is needed. Furthermore, an auxiliary design system is introduced to resolve actuator saturation in control. Next, Lyapunov stability analysis is carried out to prove that the system is asymptotically stable. Finally, the effectiveness of the proposed controller is verified through numerical simulations. Simulation results indicate that the adaptive sliding mode fault tolerant controller is effective in suppressing airfoil flutter under partial loss of actuator effectiveness performance and input saturation.     

Optimal pole-placement for state-feedback systems possessing integrity

A sequential design procedure to design an optimal state-feedback system possessing integrity and good response is presented. A sufficient condition is derived for checking the integrity of the optimal closed-loop system. The matrix Lyapunov equation is used to obtain the optimal state-feedback control law that places the closed-loop poles in specified regions and to derive the sufficient condition for the integrity of the designed system against actuator failures. The effectiveness of the proposed method is demonstrated by illustrative examples.     

Programmable springs: Developing actuators with programmable compliance for autonomous robots

Developing real robots that can exploit dynamic interactions with the environment requires the use of actuators whose behaviour can vary from high stiffness to complete compliance or zero impedance. We will outline our design for an electric actuator, called a programmable spring, which can easily be configured using a high-level programming interface to emulate complex multimodal spring damping systems. The types of behaviour that our actuator can exhibit are explored, including antagonistic actuation, cyclic behaviour and hysteresis. This system is intended as the basis for a cost-effective ‘off-the-shelf’ component for robotics research and development.     

Stability and joint stiffness analysis of legged robot’s periodic motion driven by McKibben pneumatic actuator

A McKibben-type pneumatic actuator is widely used as a convenient actuator for a robot with a simple actuator model and a simple control method. However, the effect of its characteristics on the stability of robot motion has not been sufficiently discussed. The purpose of our research is to analyze the influence that the various characteristics of a McKibben pneumatic actuator has on the stability of movements generated by the actuator. In this study, we focus on a periodic motion, which is one of the common movements of robots. We introduce a stability criterion for periodic motion similar to our previous work, in which stability of musculo-skeletal system was discussed, and show that the criterion is always satisfied. Next, we focus on a redundancy of air pressure inputs. As one of application of the redundancy, we investigate the joint stiffness of a robot and propose a design procedure of inputs based on a reference period trajectory and the desired joint stiffness. The stability analysis and design of joint stiffness are verified not only through numerical simulations but also through experiments with a developed 1-DOF legged robot.     

Robust reliable tracking controller design against actuator faults for LPV systems

A robust reliable tracking controller design method is developed against actuator faults for linear parameter varying (LPV) systems under a passive control framework. This method is based on a newly proposed stability condition for LPV systems, which is a more general condition than the existing results. An important contribution of this method is that it could handle relatively wider range of actuator faults due to the extra freedom degree introduced by a new slack variable in the stability condition. Numerical example shows the effectiveness and superiority of our method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Mechanism and Control of Continuous-State Coupled Elastic Actuation

Focusing on the physical interaction between people and machines within safety constraints in versatile situations, this paper proposes a new, efficient, coupled elastic actuation (CEA) to provide future human-machine systems with an intrinsically programmable stiffness capacity to shape the output force corresponding to the deviation between human motions and the set positions of the system. As a possible CEA system, a prototype of a two degrees of freedom (2-DOF) continuous-state coupled elastic actuator (CCEA) is designed to provide a compromise between performance and safety. Using a pair of antagonistic four-bar linkages, the inherent stiffness of the system can be adjusted dynamically. In addition, the optimal control in a simple various stiffness model is used to illustrate how to find the optimal stiffness and force trajectories. Using the optimal control results, the shortest distance control is proposed to control the stiffness and force trajectory of the CCEA. Compared to state-of-the-art variable stiffness actuators, the CCEA system is unique in that it can achieve near-zero mechanical stiffness efficiently and the shortest distance control provides an easy way to control various stiffness mechanisms. Finally, a CCEA exoskeleton is built for elbow rehabilitation. Simulations and experiments are conducted to show the desired properties of the proposed CCEA system and the performance of the shortest distance control.     

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.     

Augmented Virtual Stiffness Rendering of a Cable-driven SEA for Human-Robot Interaction

Human-robot interaction (HRI) is fundamental for human-centered robotics, and has been attracting intensive research for more than a decade. The series elastic actuator (SEA) provides inherent compliance, safety and further benefits for HRI, but the introduced elastic element also brings control difficulties. In this paper, we address the stiffness rendering problem for a cable-driven SEA system, to achieve either low stiffness for good transparency or high stiffness bigger than the physical spring constant, and to assess the rendering accuracy with quantified metrics. By taking a velocity-sourced model of the motor, a cascaded velocity-torque-impedance control structure is established. To achieve high fidelity torque control, the 2-DOF (degree of freedom) stabilizing control method together with a compensator has been used to handle the competing requirements on tracking performance, noise and disturbance rejection, and energy optimization in the cable-driven SEA system. The conventional passivity requirement for HRI usually leads to a conservative design of the impedance controller, and the rendered stiffness cannot go higher than the physical spring constant. By adding a phase-lead compensator into the impedance controller, the stiffness rendering capability was augmented with guaranteed relaxed passivity. Extensive simulations and experiments have been performed, and the virtual stiffness has been rendered in the extended range of 0.1 to 2.0 times of the physical spring constant with guaranteed relaxed passivity for physical humanrobot interaction below 5 Hz. Quantified metrics also verified good rendering accuracy.      

一种提高RS422通信BIT可靠性的设计方法

电动静液作动器是飞机操纵系统的关键部件,要求有较好的速度平稳性。系统内存在泄漏非线性和摩擦非线性等影响速度平稳性的因素。滑模控制可以有效抑制系统内非线性因素的影响,但是由于抖振现象的存在限制了速度平稳性的进一步提升。针对固定切换增益的滑模控制方法的不足,提出一种基于变结构滤波器的自适应滑模控制方法。采用变结构滤波器估计系统状态信息,估计的系统状态信息用于构建滑模面,采用自适应切换增益来导出控制率,有效减小了抖振幅度。仿真结果证明了自适应滑模控制方法的有效性,采用这种方法提高了电动静液作动器的速度平稳性。     

Robust Tracking Control Of The Variable Stiffness Actuator Based On The Lever Mechanism

This paper is concerned with the design of a robust adaptive tracking control scheme for a class of variable stiffness actuators (VSAs) based on the lever mechanisms. For these VSAs based on the lever mechanisms, the AwAS‐II developed at Italian Institute of Technology (IIT) is chosen as the study object, and it is an enhanced version of the original realization AwAS (actuator with adjustable stiffness). Firstly, for the dynamic model of the AwAS‐II system in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance and input saturation constraints, by using the coordinate transformations and the static state feedback linearization, the state space model of the AwAS‐II system with composite disturbances and input saturation constraints is transformed into an uncertain multiple‐input multiple‐output (MIMO) linear system with lumped disturbances and input saturation constraints. Subsequently, a combination of the feedback linearization, disturbance observer, sliding mode control and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the AwAS‐II system. Under the proposed controller, the semi‐global uniformly ultimately bounded stability of the closed‐loop system has been proved via Lyapunov stability analysis. Simulation results illustrate the effectiveness and the robustness of the proposed robust adaptive tracking control scheme.     

Robust Control for a Class of Uncertain Switched Fuzzy Systems with Saturating Actuators

This paper investigates the robust control problem for a class of uncertain switched fuzzy systems with saturating actuators. The asymptotical stability for fuzzy subsystems subject to actuator saturation is not assumed. Based on the multiple Lyapunov functions method, we design a switching law and a state feedback control law such that the closed‐loop system is asymptotically stable. Additionally, the estimation of the domain of attraction is presented by solving an optimization problem. Finally, simulation results verify the feasibility and effectiveness of the proposed method.