Stability analysis and time-varying walking control for an under-actuated planar biped robot

This paper presents two walking controllers for a planar biped robot with unactuated point feet. The control is based on the tracking of reference motions expressed as a function of time. First, the reference motions are adapted at each step in order to create a hybrid zero dynamic (HZD) system. Next, the stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the HZD. When the controlled outputs are selected to be the actuated coordinates, most periodic walking gaits for this robot are unstable, that is, the eigenvalues of the linearized Poincaré map (ELPM) is larger than one. Therefore, two control strategies are explored to produce stable walking. The first strategy uses an event-based feedback controller to modify the ELPM and the second one is based on the choice of controlled outputs. The stability analysis show that, for the same robot and for the same reference trajectory, the stability of the walking (or ELPM) can be modified by some pertinent choices of controlled outputs. Moreover, by studying some walking characteristics of many stable cases, a necessary condition for stable walking is proposed. It is that the height of swing foot is nearly zero at the desired moment of impact. Based on this condition, the duration of the step is almost constant in presence of initial error, so a method for choosing controlled outputs for the second controller is given. By using this method, two stable domains for the controlled outputs selection are obtained.     

Experimental control of a single-link flexible robot arm using energy shaping

Flexible-link robotic manipulators are mechanical devices whose control can be rather challenging, among other reasons because of their intrinsic under-actuated nature. This paper presents the application of an energy-based control design methodology (the so-called IDA-PBC, interconnection and damping assignment passivity-based control) to a single-link flexible robotic arm. It is shown that the method is well suited to handle this kind of under-actuated device not only from a theoretical viewpoint but also in practice. A Lyapunov analysis of the closed-loop system stability is given and the design performance is illustrated by means of a set of simulations and laboratory control experiments, comparing the results with those obtained using conventional control schemes for mechanical manipulators.     

Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

In this paper, a novel interval type-2 fuzzy fractional order super twisting algorithm (IT2FFOSTA) which is essentially a second order sliding mode controller is presented. The proposed IT2FFOSTA enhances fractional order super twisting algorithm (FOSTA) by taking advantage of an interval type-2 fuzzy fractional order sliding surface (IT2FFOSS) for some classes of fully-actuated and under-actuated nonlinear systems in presence of uncertainty. The FOSTA significantly reduces the amount of chattering and the IT2FFOSS results in decreasing the tracking error, control effort, and chattering level. In order to control under-actuated systems, a hierarchical sliding surface is employed. The multi-tracker optimization algorithm is utilized to adjust the controller’s parameters; this leads to an optimal performance for the IT2FFOSTA. To examine the performance of the IT2FFOSTA, some simulation and experimental tests on three examples of different classes of fully-actuated and under-actuated systems, including ball and plate, inverted pendulum, and ball and beam systems are carried out. The simulation and experimental results demonstrate the superiority of the IT2FFOSTA in reducing the amount of chattering, tracking error, and control effort compared to those of the other control methods.     

Distributed finite-time tracking for a team of planar flexible spacecraft

The paper presents a distributed finite-time controller for multiple under-actuated spacecraft with flexible appendages to track a virtual leader with stationary states under an undirected communication graph. Each spacecraft of concern is simplified as a free-floating hub-beam system, which is an under-actuated Euler-Lagrange system by nature since only the hub is driven. In the undirected communication graph, it is assumed that only one spacecraft can receive the information from the virtual leader. A distributed finite-time control law is presented for such a multi-agent system. The closed-loop system is proven to converge to the desired states within a finite time via Lyapunov theory and homogeneous method. Finally, a comparison is made between the proposed controller and the PD controller to show the better performance of the proposed controller.     

三自由度欠驱动机器人系统的优化设计

以一种串联的欠驱动机器人为研究对象,设计一种优化机器人末端控制机构,并在此基础上建立其运动学模型。提出在确定运动轨迹下,以控制机器人末端对轨迹的跟随性为目标,通过多关节配合,实现机器人末端工具对曲面的柔性跟踪。实验证明:该机器人能够按照指定的轨迹运动,并且在被动轴的作用下,机器人末端可以与跟踪曲面保持良好的柔性接触。     

Robust control of a class of under-actuated mechanical systems with model uncertainty

Robust control of under-actuated mechanical systems (UMSs) with model uncertainty is still a challenging problem. For UMSs, the model parametric uncertainties make it difficult to precisely calculate the isolated equilibrium point corresponding to a fixed input. Without an accurate destination state, many set-point control methods cannot eliminate the positioning errors. An improved sliding mode control (ISMC) method is proposed to solve the robust control problem for a class of UMSs with model uncertainty and input disturbance. A balance variable is introduced in the sliding surface design to compensate for the disturbance caused by the inaccurate destination state, and the ISMC method is proposed to make the system state reach the sliding surface in finite time. Linear matrix inequality approach and particle swarm optimisation algorithm are applied to design the sliding mode surface parameters. The simulation results on an UMS are presented to show the effectiveness of the proposed scheme.     

A robust algorithm for model-following control of under-actuated systems,and its application to a non-holonomic robot and an aircraft

In this paper, we present an algorithm for model-following control of under-actuated systems. To make the algorithm robust, we try to suppress computation errors from approximations which are often encountered in the cases of applying the existing algorithms to the under-actuated systems. In this view, we present an algorithm without any kinds of approximations, even in the cases of under-actuated systems. Finally, we check the examples in which the proposed algorithm is applied to a non-holonomic robot and an aircraft.     

两杆欠驱动机器人的多层嵌套滑模控制方法

目前对于两杆欠驱动机器人的滑模控制方法大多不能保证子滑模趋近各自滑模面的可达性和鲁棒性,表现为系统的稳定过度依赖参数的选取,控制运行拥塞,参数调整难度大,实现困难。为此提出一种多层嵌套滑模控制方法,以改善子滑模趋向各自滑模面的可达性、鲁棒性和快速性。进行了系统滑模面的可达性和稳定性分析,并就Pendubot和Acrobot两类欠驱动机器人进行了位置镇定控制数值仿真。仿真结果表明该方法能够使系统的控制参数调整保持一定的连续性,降低控制拥塞和参数调整难度,并有效地提高子滑模趋向各自滑模面的快速性和鲁棒性。     

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.     

一种新型灵巧手的设计与仿真分析

为了提高BHG-1型灵巧手的自适应性和拟人化,设计了一种欠驱动手指机构,以较少的驱动器数目获得较多的自由度,降低装置对控制系统的要求。采用拉格朗日方程建立了2自由度欠驱动手指的动力学模型,并利用Adams软件对其进行了动力学的仿真与分析。