Feedback control strategies for a nonholonomic mobile robot using a nonlinear oscillator

Among control problems for mobile robots, point‐to‐point stabilization is the most challenging since it does not admit designs with smooth static state feedback laws. Stabilization strategies for mobile robots, and nonholonomic systems generally, are smooth, time‐varying or nonsmooth, time‐invariant. Time‐varying control strategies are designed with umdamped linear oscillators but their fixed structure offer limited flexibility in control design. The central theme of this paper lies in use of nonlinear oscillators for mobile robot control. Large numbers of qualitatively different control strategies can be designed using nonlinear oscillators since stiffness and damping can be functions of robot states. We demonstrate by designing two fundamentally different controllers for two‐wheeled mobile robot using two variants of a particular nonlinear oscillator. First controller is dynamic and generates smooth control action. Second controller is almost‐smooth and time‐invariant. While first controller guarantees global asymptotic stability for any desired posture of robot, second controller is stable, and converges robot from almost any posture to desired posture. The only gap in posture space is unstable equilibrium manifold of measure zero. For both control strategies we mathematically establish stability and convergence of mobile robot to desired posture. Simulation results support theoretical claims. ©1999 John Wiley & Sons, Inc.     

Feedback control of nonlinear systems

This paper deals with the design of (memoryless) state-feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs. The purpose of the design is to obtain a (locally) internally stable closed-loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated. Two standard setups are considered: in the first one, the ratio between the energy associated with the penalty variable and that associated with the exogenous input is required to be bounded by a constant 0 < γ this setup includes (to some extent) the standard H_∞ control problem of linear system theory. In the second one, the penalty variable is required to converge to 0 as t ∞; this setup generalizes the so-called servomechanism problem of linear system theory.     

Feedback affinization of nonlinear control systems

In this paper conditions for the nonlinear control system

to have a nonlinear feedback control

u=(x,v), vΩ′R^m′, m′m, 0Ω′

such that the nonlinear system takes a form of an affine system

are presented. All results require algebraic operations and differentiation of functions only.     

Feedback decomposition of nonlinear control systems

By using the recently developed (differential) geometric approach to nonlinear systems, a feedback decomposition for nonlinear control systems is derived.     

Adaptive control for robot manipulators using discrete timeidentification

An adaptive control scheme is proposed for rigid link robots where the control signal computations are performed continuously and the control coefficient computations are performed in discrete time. A global boundedness result is established for the resulting scheme, independent of the sampling rate. It is also shown that the position, velocity, and acceleration tracking errors are of the order of the sampling period. Furthermore, it is shown that, if the reference trajectory is persistently exciting (in a continuous-time sense), then, for a sufficiently fast sampling rate, the tracking errors decay to zero     

带有随机时延的非线性网络控制系统的输出反馈镇定

考虑了一类非线性网络控制系统的输出反馈镇定问题.通过齐次马尔可夫链来描述采样器-控制器和控制器.执行器的时延,将网络控制系统建模为带跳非线性系统.利用Lyapunov方法和线性矩阵小等式技巧,得到了闭环系统随机稳定的充分条件,并给出了镇定控制器的设计方法.     

Feedback passivity‐based control of discrete nonlinear systems with time‐delay for variable geometry truss manipulator

In this paper, the feedback passivity‐based control of nonlinear discrete time‐delay systems for variable geometry truss manipulators is investigated. To determine an appropriate communication channel in the sense of feedback passivation, we first model the dynamics of the variable geometry truss manipulator as a generalized discrete nonlinear system with time‐delay. Then we further prove that when the infinite norm of estimated error is bounded, as long as there is a controller enables the closed‐loop system to be input‐strictly passive, there must be a deterministic equivalent controller to ensure that the system is stochastically quasi passive. After that, on the basis of the conclusion obtained, a more conclusive corollary is addressed for linear plants. Though passivity is a stricter condition than stability, feedback passivation does not impose more restrictions on estimate errors, and therefore does not require more communication channel information than mean square stability. Finally, we simplify the variable geometry truss dynamics to a linear plant to simulate to verify the validity of our method, and also compared the experimental results with the methods in the existing literature.     

Feedback control for a class of discrete event systems with critical time

This paper presents an algebraic approach for control laws synthesis of timed event graphs subjected to strict temporal constraints. This class of discrete event systems is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a linear equations system in Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the Min-Plus algebra. Then, a method for the synthesis of control laws ensuring the respect of constraints is described. We give explicit formulas characterising a control law, which ensures the validity of the temporal constraints. It is a causal feedback control, involving delays. The method is illustrated on an example.     

Feedback control of nonlinear systems by extended linearization

For single-input, multiple-output, nonlinear systems, we consider a design method based on the family of linearizations of the system, parameterized by constant operating points. Nonlinear state feedback control laws and observer/state feedback control laws are designed such that the eigenvalues of the family of linearized closed-loop systems are placed at specified values that are locally invariant with respect to the closed-loop operating point. The method is illustrated by application to the problem of automatically balancing an inverted pendulum.     

Feedback control of multiinput nonlinear systems by extendedlinearization

Control of a nonlinear system is addressed by considering its family of linearizations. Given that a family of linear state-feedback controllers has been designed to meet some (linear) control objective, it is shown how these controllers can be pieced together into an overall, nonlinear, state-feedback controller. The resulting closed-loop system has the property that its linearizations are equal to the desired linearly controlled systems. A similar approach can be used to design nonlinear state estimators. The approach is illustrated by applying it to the control of a planar two-link manipulator     

Minimal time control of a discrete system with a nonlinear plant

This paper treats the problem of minimal time control of a class of pulse-width-modulated (PWM) regulator systems with plants described by a nonlinear second-order differential equation. For the type of nonlinearity considered, it is found possible to carry out the necessary phase plane constructions by making use of the geometric properties of the solutions of the plant differential equation. The resulting optimal strategy is quite simple and is similar to the one for PWM systems with linear second-order plants whose transfer functions have nonpositive poles and no finite zeros [3].     

A CDM-backstepping control with nonlinear observer for electrically driven robot manipulator

This paper presents a CDM-backstepping strategy for motion control of Electrically-driven manipulator under the conditions of uncertainty and the action of external disturbance, while incorporating a nonlinear observer. Based on this model, a systematic analysis and design algorithm is developed to deal with stabilization and trajectory tracking of elbow robot, one feature of this work is employing the backstepping observer to achieve the exponential stability with position and velocity estimations. The results of computer simulations demonstrate that accurate and robust motion control can be achieved by using the proposed approach.     

一类离散非线性时延系统的滑模变结构控制研究

针对时变时滞的离散非线性系统, 利用Takagi-Sugeno模糊模型对其进行线性逼近, 将系统在滑模面上渐近稳定的时滞相关稳定性条件转换为线性矩阵不等式(LMI)的求解问题。由于证明中引入了松弛矩阵变量, 因而所得结果具有较小的保守性。进而采用变速趋近率方法得到滑模变结构控制律。最后, 对具有时变时延的小车—拖车自动倒车系统, 运用T-S模糊模型建模, 实现了小车—拖车系统的自动倒车控制。仿真结果验证了控制器的有效性。     

Decentralized control of robot manipulators: nonlinear and adaptiveapproaches

For robot arm tracking, the authors propose a nonlinear and adaptive approach based on decentralized system structure. Using the passive feature of robots and cubic feedback to treat the nonlinear couplings and quadratic interconnections, the decentralized adaptation is achieved by applying the linear-in-parameters property of the motion equation. The nonlinear feedback improves the performance of PD control from local to global stability and the adaptation reduces its tracking errors. The practical significance of the approaches lies in the fact that they can be implemented in most robots without hardware alteration     

改进的非线性离散系统自适应数据驱动控制

基于同步扰动随机近似的算法, 控制器选取为一个函数逼近器, 并在这里被确定为神经网络. 控制算法中使用了自适应的参数估计, 明显改善了控制性能, 同时也给出了相应的收敛性分析. 最后, 新型的控制算法被应用到了解决非线性离散系统的跟踪控制问题中, 并通过仿真比较结果, 充分验证了这种自适应数据驱动控制策略的可行性和有效性.     

Robust discrete nonlinear feedback control for robotic manipulators

Nonlinear feedback control algorithms for manipulators utilize a complete (coupled and nonlinear) dynamic robot model to decouple the robot joints. In the companion article¹ we outlined the practical problems introduced by modeling inaccuracies, unmodeled dynamics and parameter errors. We then introduced the α-computed-torque nonlinear feedback control algorithm which is robust in the presence of the aforementioned error sources. In this article, we apply the insight gained from the α-computed-torque algorithm to design a robust discrete-time (accelerometer-free) computed-torque robot-control algorithm founded upon our discrete dynamic robot model.² Numerical experiments with the cylindrical robot confirm both the robust disturbance rejection characteristics and the practical applicability of our discrete-time computer-torque control algorithm.     

Feedback classification of nonlinear control systems on 3-manifolds

We consider nonlinear control-affine systems with two inputs evolving on three-dimensional manifolds. We study their local classification under static state feedback. Under the assumption that the control vector fields are independent we give complete classification of generic systems. We prove that out of a singular smooth curve a generic control system is either structurally stable and thus equivalent to one of six canonical forms (models) or finitely determined and thus equivalent to one of two canonical forms with real parameters. Moreover, we show that at points of the singular curve the system is not finitely determined and we give normal forms containing functional moduli. We also study geometry of singularities, i.e., we describe surfaces, curves, and isolated points where the system admits its canonical forms.     

Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems

We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.     

Autonomous mobile robot model predictive control

This paper presents model predictive control of an autonomous vehicle. Simulation and experimental results have been shown and compared with input–output linearization method. The results obtained show that the MPC is an efficient method that allows for accurate control and navigation of an autonomous vehicle. Model based predictive control is tested in simulations for motion on an inclined plane. This is done to prepare future work regarding the avoidance of the violation of the smoothness condition for exact linearization, while at the same time by modifying the input commands the geometric path planning results are conserved. The approach is presented for the wheel-ground slippage and tip-over avoidance of the three-wheeled vehicle for inclined plane motion. A complete three-dimensional dynamic model using Newtonian dynamics is also presented. Simulation results using a three-wheeled vehicle built in our laboratory illustrate the performance of the proposed controller.