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.     

Cooperative control design for non-holonomic chained-form systems

Consensus and formation control problems for multiple non-holonomic chained-form systems are solved in this paper. For consensus problem, based on cascaded structure of the chained-form systems, it amounts to solving two consensus subproblems of two linear subsystems transformed from the original system. With the obtained consensus protocols and the method of virtual structure, decentralised formation controllers can then be designed. According to different desired motion patterns of the entire group, both the formation tracking and formation stabilisation problems can be considered. The significance of this paper lies in adapting theories from non-autonomous cascaded systems for cooperative control design for non-holonomic chained-form systems. A unique feature of our proposed solution is that all states can be cooperatively controlled to achieve the desired references for non-holonomic chained-form system. Simulation results are included to illustrate the effectiveness of the proposed methods in solving cooperative control problems of non-holonomic chained-form systems.     

非定常完整约束系统的线性映射方法

通过一阶线性映射可以从非定常完整约束系统的位形空间映射出一个时空Π,并诱导出时空Π上的附加几何结构(度规和联络),由此可以写出约束系统在时空Π中的运动方程.当一阶线性映射不可积时,时空Π是一个Riemann Cartan空间;当一阶线性映射可积时,时空Π将退化为一个Riemann空间,且此时由这种线性映射方法得到的时空Π中的运动方程等价于用广义坐标表示的约束系统的Lagrange方程.     

有多余坐标的可控完整力学系统的自由运动与初始运动

对于完整力学系统,若选取的参数不是完全独立的,则称为有多余坐标的完整系统.本文研究有多余坐标的可控力学系统的自由运动与初始运动.首先,需由d′Alembert Lagrange原理并利用Lagrange乘子法建立有多余坐标完整系统的运动微分方程;其次,由约束系统自由运动的定义,令所有乘子为零,得到系统实现自由运动的条件.第三,如果给定运动的初始条件和控制参数,就可以研究系统的初始运动.文末,举例并说明方法和结果的应用.     

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.     

Pattern generation, topology, and non-holonomic systems

We consider the problem of achieving a desired steady-state effect through periodic behavior for a class of control systems with and without drift. The problem of using periodic behavior to achieve set-point regulation for the control systems with drift is directly related to that of achieving unbounded effect for the corresponding driftless control systems. We prove that in both cases, the ability to use periodic behavior, and more generally, bounded behavior, to achieve the desired goal implies, under a certain topological condition, the non-holonomicity of the control systems. We also prove that under a regularity condition, the resulting system trajectories must be area-generating in a precise sense.     

广义坐标的形成史

当力学系统加上约束时,由直角坐标过渡到广义坐标是特别方便的,而且也是十分必要的.引进广义坐标是分析力学的一大特色,而Lagrange方程就建立在广义坐标上的.这个札记提供广义坐标形成的一些史料,并提出一些看法.     

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.     

Stabilization control of non-holonomic systems with application to rider-motorcycle systems

A design method is presented for fuzzy control to stabilize a system subject to non-holonomic constraints. Although a time-varying feedback law has been proposed for stabilizing non-holonomic systems, it results in slow convergence. By contrast, the current study employs fuzzy control designed with sliding modes to stabilize non-holonomic systems. The non-holonomic system becomes input-output linearizable via a proper choice of output function. Fuzzy control is formulated to become a class of variable structure system (VSS) control. Moreover, it is designed with the aid of sliding modes to ensure stability. A rider-motorcycle system, assuming rolling contact between tyres and ground, can be treated as a non-holonomic system. Owing to the motorcycle's static natural instability, stabilization control becomes an important task while riding. Using the proposed method, both hands-off and hands-on rider control are investigated. The effects of stabilization control exerted by the rider are examined according to simulation results.     

Feedback linearization and stabilization of second-order non-holonomic chained systems

This paper presents a theoretical framework for non-regular feedback linearization and stabilization of second-order non-holonomic chained systems. By giving a new criterion for the problem of non-smooth non-regular feedback linearization, it is proved that second-order chained systems are non-regular static state feedback linearizable. A discontinuous control law is obtained based on linear system theory and the inversion technique. The design mechanism is generalized to higher-order non-holonomic chained systems. Simulation studies are carried out to show the effectiveness of the approach.     

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.     

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.     

Structure identification of generalized adaptive neuro-fuzzy inference systems

This paper presents a method to identify the structure of generalized adaptive neuro-fuzzy inference systems (GANFISs). The structure of GANFIS consists of a number of generalized radial basis function (GRBF) units. The radial basis functions are irregularly distributed in the form of hyper-patches in the input-output space. The minimum number of GRBF units is selected based on a heuristic using the fuzzy curve. For structure identification, a new criterion called structure identification criterion (SIC) is proposed. SIC deals with a trade off between performance and computational complexity of the GANFIS model. The computational complexity of gradient descent learning is formulated based on simulation study. Three methods of initialization of GANFIS, viz., fuzzy curve, fuzzy C-means in x/spl times/y space and modified mountain clustering have been compared in terms of cluster validity measure, Akaike's information criterion (AIC) and the proposed SIC.     

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.     

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.     

Multiprocessor platform for partitioned real‐time systems

Two current trends in the real‐time and embedded systems are the multiprocessor architectures and the partitioning technology that enables several isolated applications with different criticality levels to share the same computer. This paper presents a real‐time platform for multiprocessor and partitioned systems, in which communication requirements are also considered. The paper describes the adaptation of MaRTE OS (a monoprocessor real‐time operating system) to the XtratuM hypervisor for the multiprocessor Intel x86 architecture. This adaptation makes two contributions to ease the development process of future mixed‐criticality applications: firstly, it integrates the hypervisor technology and the fully partitioned scheduling in a multiprocessor environment, and secondly, it provides the basis to interconnect partitioned and non‐partitioned applications via a homogeneous communication subsystem. Copyright © 2016 John Wiley & Sons, Ltd.     

Convergence of partitioned adaptive filters for systems with unknown biases

A convergence theorem on performance bounds for partitioned adaptive estimation is extended to include biases among the unknown parameters. The importance and implications of this rarely considered case are briefly discussed.     

A New Algorithm for Generalized Optimal Discriminant Vectors

A study has been conducted on the algorithm of solving generalized optimal set of discriminant vectors in this paper.This paper proposes an analytical algorithm of solving generalized optimal set of discriminant vectors theoretically for the first time.A lot of computation time can be saved because all the generalized optimal ests of discriminant vectors can be obtained simultaneously with the proposed algorithm,while it needs no iterative operations .The proposed algorithm can yield a much higher recognition rate.Furthermore,the proposed algorithm overcomes the shortcomings of conventional human face recognition algorithms which were effective for small sample size problems only.These statements are supported by the numerical simulation experiments on facial database of ORL.