Swing-Up Control of the Pendubot: An Impulse–Momentum Approach

The standard control problem of the pendubot refers to the task of stabilizing its equilibrium configuration with the highest potential energy. Linearization of the dynamics of the pendubot about this equilibrium results in a completely controllable system and allows a linear controller to be designed for local asymptotic stability. For the underactuated pendubot, the important task is, therefore, to design a controller that will swing up both links and bring the configuration variables of the system within the region of attraction of the desired equilibrium. This paper provides a new method for swing-up control based on a series of rest-to-rest maneuvers of the first link about its vertically upright configuration. The rest-to-rest maneuvers are designed such that each maneuver results in a net gain in energy of the second link. This results in swing-up of the second link and the pendubot configuration reaching the region of attraction of the desired equilibrium. A four-step algorithm is provided for swing-up control followed by stabilization. Simulation results are presented to demonstrate the efficacy of the approach.      

Controllability and observability of an n‐link robot with multiple active links

This paper considers an n‐link planar robot moving in the vertical plane with multiple active links. The controllability and observability of the robot around the upright equilibrium point, which are important for the existence of an output‐feedback controller, are investigated in detail. Specific properties of the mechanical parameters are extracted to demonstrate that when there are adjacent active links, the robot is strongly structurally controllable and observable around the upright equilibrium point. When the active links are not adjacent to each other, a necessary and sufficient condition is established to ensure the linear controllability and observability. Finally, the theoretical results are illustrated via several practical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Intelligent control of a three-DOF planar underactuated manipulator

Recently, computational intelligence has been applied extensively in control engineering, especially for systems that cannot easily be controlled by conventional means. In this article, attention is paid to the control of a three-DOF planar underactuated manipulator, also known as the three-link gymnastic robot, by utilizing a neural network (NN) and a genetic algorithm (GA). In an attempt to make the problem more analogous to human gymnastics, constraints are applied to the joint angles. With different swing-up timings, the performance of the proposed controller is investigated and control simulations are performed. Numerical simulations show that the neurocontroller is able to control the system effectively within the constraints and given timings.     

欠驱动三连杆机械臂能量解耦控制策略

针对第二关节为被动的欠驱动三连杆机械臂提出一种能量解耦控制策略.首先,将整个运动空间分为摇起区和平衡区,为了实现快速摇起控制,进一步将摇起区分为摇起子区间一和摇起子区间二;其次,基于Lyapunov函数设计控制律,使第三杆相对于第二杆处于自然伸展的状态,即使第三杆角度和角速度收敛为零,从而解除能量控制与第三连杆姿态之间...     

On simultaneous control of the energy and actuated variables of underactuated mechanical systems – example of the acrobot with counterweight

The energy-based control approach aiming to control both the total mechanical energy and actuated variables of underactuated mechanical systems has generated renewed interest in recent years. Different from the reports of successful applications of this approach, we investigate whether there exists an underactuated mechanical system for which we fail to control both the total mechanical energy and actuated variable(s) to some given desired values by studying a CWA (Counter-Weighted Acrobot), which is a modified Acrobot with its first link having a counterweight and only its second link being actuated. By analyzing globally the solution of the closed-loop system consisting of the CWA and the controller designed via the energy-based control approach, we show that unless the CWA is linearly controllable at the up–up equilibrium, where links 1 and 2 are in the upright position, the controller fails to achieve the goal of controlling the energy to the potential energy at the equilibrium and controlling the actuated joint variable to zero. We also provide corresponding results for the up–down, down–up, and down–down equilibriums of the CWA, where up and down denote that the link is in the upright and downward positions, respectively. We present numerical simulation results to validate the theoretical results.     

Swing-up control strategies for a reaction wheel pendulum

Control of a reaction wheel pendulum, a prototype of an under-actuated system, is easily done using switching control strategies, which combines swing-up control and balancing control schemes. In this article, two novel swing-up control strategies for a reaction wheel pendulum have been proposed. The first swing-up control strategy treats the oscillations of the pendulum as perturbations from the bottom equilibrium point. The second swing-up control is based on interconnection and damping assignment-passivity based control (IDA-PBC). IDA-PBC preserves Euler Lagrangian structure of the system and gives more physical insight about any mechanical system. Any balancing controller can be coupled with the proposed swing-up control strategies to stabilise the pendulum at the top unstable equilibrium position. The control task of balancing the pendulum in top upright position is completed by switching from swing-up scheme to the balancing scheme at the point where the pendulum is very near to the top equilibrium point. Proposed swing-up control strategies have been implemented in real time in switching mode. The two proposed swing-up control schemes provide fast responses as compared to existing energy based schemes.     

A constrained assumed modes method for dynamics of a flexible planar serial robot with prismatic joints

In the present study, for the first time, flexible multibody dynamics for a three-link serial robot with two flexible links having active prismatic joints is presented using an approximate analytical method. Transverse vibrations of flexible links/beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the links. In this study, first, vibration analysis of a flexible link sliding through an active prismatic joint having translational motion is considered. A rigid-body coordinate system is used, which aids in obtaining a new and rather simple form of the kinematic differential equation without the loss of generality. Next, the analysis is extended to include dynamic forces for a three-link planar serial robot called PPP (Prismatic, Prismatic, Prismatic), in which all joints are prismatic and active. The robot has a rigid first link but flexible second and third links. To model the prismatic joint, time-variant constraints are written, and a motion equation in a form of virtual displacement and virtual work of forces/moments is obtained. Finally, an approximate analytical method called the “constrained assumed modes method” is presented for solving the motion equations. For a numerical case study, approximate analytical results are compared with finite element results, which show that the two solutions closely follow each other.     

垂直三连杆欠驱动机械臂通用控制策略设计

本文针对一类含单一欠驱动关节的垂直三连杆欠驱动机械臂提出一种基于振荡衰减轨迹的通用控制策略. 与传统的分区控制策略相比, 本文控制策略无需采用分区方式就能快速地实现将机械臂末端点由垂直向下初始位 置开始移动, 并最终稳定在垂直向上目标位置的控制目标. 首先, 根据驱动连杆的初始和目标状态, 为驱动连杆规划 含可调参数的振荡衰减轨迹. 该轨迹能够在一定调节时间内将驱动连杆直接由初始状态移动至目标状态. 基于连 杆状态间的耦合关系, 利用粒子群优化算法优化轨迹参数使欠驱动连杆在相同调节时间内也运动至目标状态. 接 着, 利用滑模方法设计跟踪控制器使驱动连杆跟踪优化后的振荡衰减轨迹, 这样, 系统末端点将由初始位置移动至 目标位置. 进一步利用极点配置方法设计镇定控制器克服重力的作用将末端点稳定在目标位置. 最后, 通过仿真实 验验证所提控制策略的有效性.     

Comparative study of performance indices for fundamental robot manipulators

In this paper, conventional global and local indices–structural length index, manipulability measure, condition number and Global Conditioning Index (GCI)–have been examined for the workspace optimization of the sixteen fundamental robot manipulators classified by B. Huang and V. Milenkovic [Kinematics of major robot linkages, Robotics International of SME 2 (1983) 16–31]. To find the optimum link length and volumes of these robot manipulators, two design objectives have been used: maximize the workspace area covered by the robot manipulator and maximize the local indices. As an example, a three-link robot manipulator has been studied based on the above design objectives. Also, optimization results of the sixteen robot manipulators have been compared to each other and summarized in tables.     

An adaptive fuzzy strategy for motion control of robot manipulators

This paper makes an attempt to develop a self-tuned proportional-integral-derivative (PID)-type fuzzy controller for the motion control of robot manipulators. In recent past, it has been widely believed that static fuzzy controllers can not be suitably applied for controlling manipulators with satisfaction because the robot manipulator dynamics is too complicated. Hence more complicated and sophisticated neuro-fuzzy controllers and fuzzy versions of nonlinear controllers have been more and more applied in this problem domain. The present paper attempts to look back at this widely accepted idea and tries to develop a self-tuned fuzzy controller with small incremental complexity over conventional fuzzy controllers, which can yet attain satisfactory performance. The proposed controller is successfully applied in simulation to control two-link and three-link robot manipulators.     

A scheme for robust trajectory control of space robots

This paper presents a scheme for robust trajectory control of free-floating space robots. The idea is based on the overwhelming robust trajectory control of a ground robot on a flexible foundation and robust foundation disturbance compensation presented elsewhere. No external jets/thrusters are required or used in the scheme. An example of a three-link robot mounted on a free-floating space platform is considered for demonstrating the efficacy of the control scheme. Bond graph technique has been used for the purpose of modeling and simulation. Robustness of the control scheme is guaranteed since the controller does not require the knowledge of the manipulator parameters.     

Swing-up control of a 3-DOF acrobot using an evolutionary approach

We present a control method for a 3-DOF acrobot which is a model of a gymnast on a horizontal bar with three links, two active joints, and a passive joint. This robot is a nonholonomic and underactuated system. We propose two control methods for the 3-DOF acrobot. First, swing-up control is performed by genetic programming (GP), and stabilizing control is handled by a linear quadratic regulator (LQR). GP can search widely for the optimum input torques for swing-up so that the acrobot is able to reach a near balancing point. The LQR is then switched on to stabilize the system. In the simulation results, the 3-DOF acrobot could swing up to the desired position, and the proposed method could control the acrobot effectively.     

Energy-based modeling and control for grid-side converter of doubly fed wind generator

To avoid dealing with the zero dynamics limitation brought by the bidirectional power flow through the back-to-back converter in a doubly fed wind generator,a new energy-based modeling and control approach for the gridside converter is presented.During the modeling process,the grid-side converter is divided into two subsystems with the feedback interconnection structure,and the interactive matrix of the model takes into account the concrete port structure. Then,an energy-based controller is proposed to realize the grid-side control objectives based on the new model.Simulation studies are carried out in MATLAB/Simulink.Comparative results between the proportional-integral controller and the energy-based controller show that the latter one can obtain faster convergence rate and global stability as the load current varies.Moreover,the energy-based controller is also competent for grid-side control when simulated in a 2 MW wind energy conversion system with random wind.     

Adaptive Fuzzy Switched Swing-Up and Sliding Control for the Double-Pendulum-and-Cart System

In this paper, an adaptive fuzzy switched swing-up and sliding controller (AFSSSC) is proposed for the swing-up and position controls of a double-pendulum-and-cart system. The proposed AFSSSC consists of a fuzzy switching controller (FSC), an adaptive fuzzy swing-up controller (FSUC), and an adaptive hybrid fuzzy sliding controller (HFSC). To simplify the design of the adaptive HFSC, the double-pendulum-and-cart system is reformulated as a double-pendulum and a cart subsystem with matched time-varying uncertainties. In addition, an adaptive mechanism is provided to learn the parameters of the output fuzzy sets for the adaptive HFSC. The FSC is designed to smoothly switch between the adaptive FSUC and the adaptive HFSC. Moreover, the sliding mode and the stability of the fuzzy sliding control systems are guaranteed. Simulation results are included to illustrate the effectiveness of the proposed AFSSSC.      

改进的Backstepping在移动机器人轨迹跟踪中的应用

以四轮移动机器人的运动学模型为研究对象,基于BackStepping的设计思想,通过构造一种简单的中间虚拟反馈变量,同时结合Lyapunov直接法设计了一种移动机器人轨迹跟踪控制律,并证明了系统在设计控制律下的全局稳定性;但控制律中含有未知参数,不同的参考轨迹都要重新调节才能达到良好的跟踪效果,因此利用极点配置的方法对这些参数进行了优化整定,从而保证了控制器的自适应性;文中以直线和圆为参考轨迹做了仿真实验;仿真结果表明该算法具有快速,精确,全局稳定的良好特性。     

Fuzzy-Basis-Function-Network-Based $H_infty$ Tracking Control for Robotic Manipulators Using Only Position Feedback

This paper presents an H _infin fuzzy output-feedback tracking-control scheme for robotic manipulators without measuring joint velocities. The developed controller and observer are based on a fuzzy basis function network (FBFN), which is employed to approximate nonlinear functions in the dynamics of controller and observer. The FBFN-based observer that estimates joint velocities can remove the needs of full-state measurements. According to the inevitable approximation errors and external disturbances, an H _infin auxiliary control signal is used to suppress the effects of the uncertainties. Moreover, all parameters of the fuzzy basis functions (FBFs) and FBF-to-output weights can be tuned online. The proposed controller requires no prior knowledge about the dynamics of the robot manipulator and no offline learning phase. Finally, comparative simulations on a three-link robot manipulator are provided to illustrate the tracking performance of the H _infin FBFN-based output-feedback control approach.     

Chaos-PSO-based Motion Planning and Accurate Tracking for Position-posture Control of a Planar Underactuated Manipulator with Disturbance

Unlike a fully-actuated manipulator, the position-posture control of a planar underactuated manipulator (PUM) is more difficult, but the research on it is significant due to the wide practical applications. The existing control methods consider no external disturbance and are involved in the staged control idea, bringing the problems of nonsmooth control torque and time-consuming. A novel one-stage control approach is proposed in this paper for the position-posture control of a three-link PUM with the first free joint under the external disturbance. By analyzing the coupling relationship between its active joints and free joint, the position-posture control is transformed into the trajectory tracking control. Unlike the general trajectory planning, the trajectories of the active joints are planned to include several parameters. Meanwhile, the parameters are solved using a chaos particle swarm optimization algorithm to guarantee that all joint angles can reach to their desired angles. Then, to obtain the high trajectory tracking accuracy at every moment under the external disturbance, the nonlinear disturbance observer is constructed and a nonlinear fast terminal sliding mode tracking controller is designed. Finally, the feasibility and superiority of this strategy are verified via two simulations.

     

Stability indices for a self-organizing fuzzy controlled robot: A case study

This study developed a model-free self-organizing fuzzy controller (SOFC) for manipulating multiple-input multiple-output systems. The SOFC has an online learning algorithm that can continually update fuzzy rules during the control process, beginning from an empty rule table. The SOFC was used to control a three-link robot with a complex dynamic model in order to evaluate its applicability. Stability and robustness of the SOFC were demonstrated using a state-space approach. Simulation results confirmed that the control performance of the SOFC outperforms that of the fuzzy logic controller for the control of the robot.     

Intelligent Control for an Acrobot

The acrobot is an underactuated two-link planar robot that mimics the human acrobat who hangs from a bar and tries to swing up to a perfectly balanced upside-down position with his/her hands still on the bar. In this paper we develop intelligent controllers for swing-up and balancing of the acrobot. In particular, we first develop classical, fuzzy, and adaptive fuzzy controllers to balance the acrobot in its inverted unstable equilibrium region. Next, a proportional-derivative (PD) controller with inner-loop partial feedback linearization, a state-feedback, and a fuzzy controller are developed to swing up the acrobot from its stable equilibrium position to the inverted region, where we use a balancing controller to catch and balance it. At the same time, we develop two genetic algorithms for tuning the balancing and swing-up controllers, and show how these can be used to help optimize the performance of the controllers. Overall, this paper provides (i) a case study of the development of a variety of intelligent controllers for a challenging application, (ii) a comparative analysis of intelligent vs. conventional control methods (including the linear quadratic regulator and feedback linearization) for this application, and (iii) a case study of the development of genetic algorithms for off-line computer-aided-design of both conventional and intelligent control systems.     

Back handspring of a multi-link gymnastic robot — reference model approach

This paper reports on the first gymnastic robot that can perform back handspring. The robot is a planar and serially connected four-link robot, with its joints actuated by electric servomotors. The paper describes the modeling of the robot and the control framework for a back handspring. The controller is derived from a task-specific reference model and its model matching. The use of a reference model described by global physical quantities such as center of mass or angular momentum allows the gymnastic motion planning of a multi-body system to be intuitive and the model matching controller can be applied directly to the experimental model without obtaining each joint trajectory. The controller effectiveness is confirmed via simulations and experiments of the back handspring. Although there remains the problem of how to systematically design the control parameters, the paper shows the strength of the model-based controller for fast gymnastic motions.