Stabilization of nonholonomic chained systems via nonregular feedback linearization

This paper addresses the problem of feedback stabilization of nonholonomic chained systems within the framework of nonregular feedback linearization. Firstly, the nonsmooth version of nonregular feedback linearization is formulated, and a criterion for nonregular feedback linearization is provided. Then, it is proved that the chained form is linearizable via nonregular feedback control, thus enable us to design feedback control laws using standard techniques for linear systems. The obtained discontinuous control laws guarantee convergence of the closed-loop system with exponential rates. Finally, simulation results are presented to show the effectiveness of the approach.     

Lyapunov design of global state and output feedback trackers for non-holonomic control systems

In this paper, new results are obtained for the global tracking of a class of non-holonomic dynamic systems via state and output feedback. The tracking controllers are systematically constructed on the basis of a recursive technique and a full exploitation of the system structure. When disturbances occur in a non-holonomic chained system, it is shown how to modify the controller design procedure to yield robust tracking control laws. The proposed method is demonstrated and discussed by means of a benchmark non-holonomic knife-edge mechanical system.     

Non-regular feedback linearization of nonlinear systems via a normal form algorithm

In this paper, the problem of non-regular static state feedback linearization of affine nonlinear systems is considered. First of all, a new canonical form for non-regular feedback linear systems is proposed. Using this form, a recursive algorithm is presented, which yields a condition for single input linearization. Then the left semi-tensor product of matrices is introduced and several new properties are developed. Using the recursive framework and new matrix product, a formula is presented for normal form algorithm. Based on it, a set of conditions for single-input (approximate) linearizability is presented.     

Stabilization of non-holonomic chained systems by gain scheduling

In this paper, a simple method the gain scheduling technique is applied for the stabilization of non-holonomic chained systems, such as mobile robots, front-wheel drive cars, and fire trucks. First, the stabilizing non-holonomic chained systems' problem is formulated as a multi-input multi-state (MIMS) linear parameter-varying system. By choosing a suitable and non-zero control input in the new formulated linear parameter-varying system, the gain scheduling techniques can then easily be applied to design the state feedback stabilizing controller. Simulation results show that the proposed methodology has demonstrated superiority over previous methods and results in much simpler trajectories.     

Non-uniform in time stabilization for linear systems and tracking control for non-holonomic systems in chained form

The paper contains certain results concerning non-uniform in time stabilization for linear time-varying systems by means of a linear time-varying feedback controller. These results enable us to present an explicit solution for the state feedback tracking control problem of non-holonomic systems in chained form under weaker hypotheses than those imposed in earlier existing works.     

New results on non-regular linearization of non-linear systems

This paper presents some new results on non-regular linearization of non-linear systems. Based on a normal form and a non-regular linearization technique developed recently, the paper first provides a set of calculating formulas for the linearization procedure. As an application, the linearization of bilinear systems is investigated. Then, it presents easily verifiable sufficient conditions for the global (semi-global) (approximate) linearization. Finally, an estimate of the region of attraction for the kth degree approximately linearized systems with state feedback control is given, which illustrates one of the advantages of the approximate linearization.     

Finite-time output feedback stabilisation of chained-form systems with inputs saturation

This paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.     

非完整链式系统的输出跟踪控制——动态扩展线性化方法

针对非完整单链和多链系统,利用动态反馈线性化技术设计了输出跟踪控制器.证 明了当满足一定的条件时,通过选择适当的输出变量并利用动态反馈可使非完整链式系统实 现输入-输出完全线性化,从而可设计线性控制器跟踪期望的运动轨迹.最后以移动小车的跟 踪控制为例,通过仿真验证了文中方法的有效性.     

Adaptive stabilization of uncertain dynamic non-holonomic systems

This paper investigates the stabilization problem of uncertain dynamic non-holonomic chained systems with unknown constant inertia parameters. Globally time-varying adaptive stabilizing control laws for such systems are presented. The application of it to a non-holonomic wheeled mobile robot is described. Simulation results show that the proposed approach is effective.     

Formation Control and Tracking for Co-operative Robots with Non-holonomic Constraints

This paper mainly addresses formation control problem of non-holonomic systems in an optimized manner. Instead of using linearization to solve this problem approximately, we designed control laws with guaranteed global convergence by leveraging nonlinear transformations. Under this nonlinear transformation, consensus of non-holonomic robots can be converted into a stabilization problem, to which optimal treatment applies. This concept is then extended to the formation control and tracking problem for a team of robots following leader-follower strategy. A trajectory generator prescribes the feasible motion of virtual reference robot, a decentralized control law is used for each robot to track the reference while maintaining the formation. The asymptotic convergence of follower robots to the position and orientation of the reference robot is ensured using the Lyapunov function which is also generated using chained form differential equations. In order to witness the efficacy of the scheme, simulations results are presented for Unicycle and Car-like robots.     

一类二阶非完整系统的镇定

研究一类二阶非完整系统的镇定问题. 通过状态和输入反馈变换将系统模型转换为二阶链式标准型, 并对标准型给出一种时变光滑指数镇定控制律. 所得结果应用于欠驱动平面刚体的镇定.     

Learning optimal trajectories for non-holonomic systems

Many advanced robotic systems are subject to non-holonomic constraints, e.g. wheeled mobile robots, space manipulators and multifingered robot hands. Steering these mechanisms between configurations in the presence of perturbations is a difficult problem. In fact, the divide et impera strategy (first plan a trajectory, then track it by feedback) has a fundamental drawback in this case: due to the peculiar control properties of non-holonomic systems, smooth feedback cannot provide tracking of the whole trajectory. As a result, it would be necessary to give up either accuracy in the final positioning or predictability of the actual motion. We pursue here a different approach which does not rely on a separation between planning and control. Based on the learning control paradigm, a robust steering scheme is devised for systems which can be put in chained form, a canonical structure for non-holonomic systems. By overparametrizing the control law, other performance goals can be met, typically expressed as cost functions to be minimized along the trajectory. As a case study, we consider the generation of robust optimal trajectories for a car-like mobile robot, with criteria such as total length, maximum steering angle, distance from workspace obstacles, or error with respect to an offline planned trajectory.     

Exponential stabilization of non-holonomic systems: An ENI approach

In this paper, a new canonical form, called extended non-holonomic integrators (ENI), is firstly introduced for non-holonomic systems. Next, a recursive design technique is presented to exponentially stabilize ENI systems. The relationships between the convergence rates of the states and the controller parameters are explicitly given, in particular, the convergence rate of individual state can be specified explicitly. Then, it is shown that non-holonomic systems in ENI form, chained and power forms are equivalent, thus can be dealt with in a unified framework. Finally, a car-like mobile robot is used to demonstrate the effectiveness of the proposed control.     

非完整链式系统的输出跟踪控制 ——动态扩展线性化方法1)

Tracking control of nonholonomic single and multi-chained systems is investigated in this paper.It is shown that the nonholonomic chained systems can be completely linearized by dynamic feedback linearization if the proper output variables are chosen and certain conditions are satisfied,and linear tracking controllers can then be designed for the resulted linearized systems.As an example,a moving cart is simulated to verify the proposed strategy.     

Poincaré Normal Form for a Class of Driftless Systems in a One-Dimensional Submanifold Neighborhood

In this paper, motivated by the restrictive conditions required to obtain an exact chained form, we propose a quadratic normal form around a one-dimensional equilibrium submanifold for systems which are in a chained form in their first approximation. In the case considered here, in contrast to the case of approximated feedback linearization, not all the state and input components have the same approximation meaning. Because of this, we use a very simplified version of dilation, which is a useful way to design a homogeneous control law for driftless systems. Date received: December 2, 1999. Date revised: October 24, 2001.     

精确反馈线性化在移动机器人轨迹跟踪中的应用

本文首先介绍了轮式移动机器人从原始形式到链形式的转换 ,并以此为对象 ,通过动态扩展 ,引入了精确反馈线性化的方法 ,将链形式精确地转换为输入输出线性系统 ,在此基础上 ,设计了反馈控制器对轮式移动机器人的轨迹跟踪进行控制 .仿真结果说明了方法的可行性     

Output consensus for multiple non-holonomic systems under directed communication topology

In this paper, the problem of output consensus for multiple non-holonomic systems in chained form has been investigated. First, an output consensus controller under the strongly connected communication topology is devised by two steps, where a time-varying control strategy and the backstepping design technique are employed. Then, the results are extended to the general directed topology case via graph decomposition, in which the input-to-state stability theory plays a critical role. We prove that the proposed controller can achieve the semi-global output consensus among multiple non-holonomic systems, provided that the interaction graph contains a spanning tree. Finally, numerical examples are provided to illustrate the effectiveness of the designed controller.     

欠驱动机械手的非线性补偿控制的实现

以具有欠驱动关节的水平两自由度机械手为对象,建立了其动力学数学模型。对具有非完全约束机器人的特点进行了分析。利用解非线性方程的有效方法一平均值法对模型进行了处理,得到平均值系统,使模型得到简化。含有非驱动关节的平面二自由度机械手具有不可积分的速度和加速度束。因而是一个二阶非完整系统。通过分析系统的动力学机构,设计了一种非线性补偿控制的方法来对欠驱动关节实现控制。实验结果表明。该控制方法在控制模型、控制算法和反馈控制方法上都是十分有效的。     

Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin

We present a continuous feedback stabilizer for nonlinear systems in the strict-feedback form, whose chained integrator part has the power of positive odd rational numbers. Since the power is not restricted to be larger than or equal to one, the linearization of the system at the origin may fail. Nevertheless, we show that the closed loop system is globally asymptotically stable (GAS) with the proposed continuous (but, possibly not differentiable) feedback. We formulate a condition that enables our design by characterizing the powers of the given system. The condition also shows that our result is an extension of Qian and Lin [Non-lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization, Systems Control Lett. 42 (2001) 185–200] where the power of odd positive integers has been considered. New result on the global finite time stabilization problem is also presented.     

不确定非完整链式系统的鲁棒镇定

不确定非完整链式系统的镇定问题在过去十年中得到了许多有趣的结果, 涌现出了几类模型和相应的控制方法. 目前已经可以对这方面的发展做出总结. 本文给出了非完整链式系统的模型、镇定控制方法和一些结论, 特别是基于视觉传感器得到了一些新的有趣的不确定链式模型. 同时, 利用新的二步法、视觉反馈、状态缩放变换和切换等技术设计了新的不确定链式模型的鲁棒镇定控制器. 希望这项工作可以做到抛砖引玉, 也可以为这个领域的专家做一个较好的参考.