An iterative linear quadratic regulator based trajectory tracking controller for wheeled mobile robot

We present an iterative linear quadratic regulator(ILQR) method for trajectory tracking control of a wheeled mobile robot system.The proposed scheme involves a kinematic model linearization technique,a global trajectory generation algorithm,and trajectory tracking controller design.A lattice planner,which searches over a 3D(x,y,θ) configuration space,is adopted to generate the global trajectory.The ILQR method is used to design a local trajectory tracking controller.The effectiveness of the proposed method is demonstrated in simulation and experiment with a significantly asymmetric differential drive robot.The performance of the local controller is analyzed and compared with that of the existing linear quadratic regulator(LQR) method.According to the experiments,the new controller improves the control sequences(v,ω) iteratively and produces slightly better results.Specifically,two trajectories,’S’ and ’8’ courses,are followed with sufficient accuracy using the proposed controller.     

On the controllability of switching linear systems

This note presents a necessary and sufficient condition for small time controllability of a linear switching system (that is, a collection of linear time-invariant control systems, where a trajectory is any concatenation of trajectories of the individual systems). This result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone.     

垂直起降飞机的全局轨迹跟踪控制

研究垂直起降飞机在任意输入耦合作用下的轨迹跟踪控制问题．垂直起降飞机是具有3个自由度、2个控制输入的欠驱动系统．首先通过控制输入和坐标变换,使飞机的动力学方程变换成严格反馈形式;然后基于后推法的思想推导出保证系统渐近收敛于参考轨迹的时变反馈控制规律．该方法将系统分解为低阶子系统来处理,利用中间虚拟控制变量和部分Lyapunov函数筒化了控制器的设计．仿真结果表明所设计的控制器是有效的．     

Global trajectory tracking control of VTOL-UAVs without linear velocity measurements

This paper deals with the position control of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) without linear velocity measurements. We propose a multistage constructive procedure, exploiting the cascade property of the translational and rotational dynamics. More precisely, we consider the force as a virtual control input for the translational dynamics, from which we extract the required (desired) system attitude and thrust achieving the tracking objective. Thereafter, the control torque is designed to drive the actual attitude to the desired one. A nonlinear observer, as well as some instrumental auxiliary variables are used to obviate the need for the linear velocity. Global asymptotic stability of the overall closed loop system is achieved. Simulation results are provided to show the effectiveness of the proposed control scheme.     

Trajectory tracking control for a miniature fixed-wing unmanned air vehicle

This article considers the problem of trajectory tracking control for a miniature fixed-wing unmanned air vehicle (UAV). With the UAV equipped with longitudinal and lateral autopilots, we adopt a kinematic model that takes into account the fact that the heading of the UAV is controlled by its roll motion and the autopilot responses to air speed and roll control commands are first order in nature. Backstepping techniques are applied to derive air speed and roll control commands from known air speed and heading control laws that explicitly account for air speed and heading rate constraints of the UAV. Regarding inaccurately known autopilot constants, a parameter adaptation technique is used to estimate autopilot constants. High-fidelity simulation results on a six degree-of-freedom (DOF) 12-state fixed-wing UAV model are presented to show the effectiveness of our approach.     

Nonlinear feedback control and trajectory tracking of vehicle

This paper mainly studies nonlinear feedback control applied to the nonlinear vehicle dynamics with varying velocity. The main objective of this study is the stabilisation of longitudinal, lateral and yaw angular vehicle velocities. To this end, a nonlinear vehicle model is developed which takes both the lateral and longitudinal vehicle dynamics into account. Based on this model, a method to build a nonlinear state feedback control is first designed by which the complexity of system structure can be simplified. The obtained system is then synthesised by the combined Lyapunov–LaSalle method. The simulation results show that the proposed control can improve stability and comfort of vehicle driving. Moreover, this paper presents a lemma which ensures the trajectory tracking and path-following problem for vehicle. It can also be exploited simultaneously to solve both the tracking and path-following control problems of the vehicle ride and driving stability. We also show how the results of the lemma can be applied to solve the path-following problem, in which the vehicle converges and follows a designed path. The effectiveness of the proposed lemma for trajectory tracking is clearly demonstrated by simulation results.     

On the controllability of linear juggling mechanical systems

This paper deals with the controllability of a class of nonsmooth complementarity mechanical systems. Due to their particular structure they can be decomposed into an “object” and a “robot”, consequently they are named juggling systems. It is shown that the accessibility of the “object” can be characterized by nonlinear constrained equations, or generalized equations. Examples are presented, including a simple model of backlash. The main focus of the work is about linear jugglers.     

四旋翼无人机三维航迹规划及跟踪控制

无人机航迹规划是指根据地形和威胁分布,规划出满足任务要求的合理航迹.为了满足三维空间快速规划的需求,提出了一种基于人工势场的三维航迹规划方法.首先,定义了目标和威胁物的虚拟力函数,推导出了三维空间参数约束方程,并采用联合威胁概念解决三维空间局部极小和振动问题;其次,引入空间圆弧插补技术生成光滑航迹;此外,为方便跟踪控制,提出了航迹时域化方法;最后,利用动态系统全局渐近稳定定理,设计具有全局Lipschitz的闭环系统,实现了具有内外环严格稳定性的双环轨迹跟踪控制.仿真结果验证了航迹规划和跟踪算法的有效性.     

Robust trajectory tracking for a scale model autonomous helicopter

This paper considers the question of obtaining an a priori bound on the tracking performance, for an arbitrary trajectory, of closed‐loop control of an idealized model of a scale model autonomous helicopter. The problem is difficult due to the presence of small body forces that cannot be directly incorporated into the control design. A control Lyapunov function is derived for an approximate model (in which the small body forces are neglected) using backstepping techniques. The Lyapunov function derived is used to analyse the closed‐loop performance of the full system. A theorem is proved that provides a priori bounds on initial error and the trajectory parameters (linear acceleration and its derivatives) that guarantees acceptable tracking performance of the system. The analysis is expected to be of use in verification of trajectory planning procedures. Copyright © 2004 John Wiley & Sons, Ltd.     

输入输出受限船舶的轨迹跟踪自适应递归滑模控制

针对输入输出受限,模型部分不确定和受到未知海洋干扰的全驱动船舶的轨迹跟踪问题,提出一种基于时变非对称障碍李雅普诺夫函数的最小参数自适应递归滑模控制策略.该策略首先设计障碍李雅普诺夫函数约束船舶轨迹在有限区域内,利用最小参数法神经网络逼近模型不确定项,降低系统的计算复杂度,然后采用指令滤波器对输入信号进行幅值约束,同时避免对因反步法导致的微分爆炸问题,综合考虑船舶位置以及速度误差间的关系设计递归滑模控制律,提高系统的鲁棒性,采用双曲正切函数和Nussbaum函数补偿由输入饱和引起的非线性项,提高系统稳定性.最后通过Lyapunov理论分析证明了全驱动船舶闭环系统中所有信号是一致最终有界的.仿真结果表明,本文所设计的船舶轨迹跟踪控制方案能有效处理船舶模型不确定部分以及未知外界干扰的问题,能够实现船舶在输入受限的情况下在有限区域内航行并准确的跟踪期望轨迹,具有较强的鲁棒性.     

高精度轨迹跟踪的6-PRRS并联机器人自抗扰控制研究

针对6-PRRS并联机器人控制系统的非线性、耦合等特性,采用分散控制策略。在关节空间设计强鲁棒性的自抗扰控制器对其进行控制．该自抗扰控制器由非线性跟踪微分器、扩张状态观测器、非线性PD和扰动补偿4部分组成．具有模型补偿功能的扩张状态观测器可以获得系统的状态估计和未知外扰的实时作用量,使系统性能得到有效补偿．该控制器以离散的形式进行设计,易于工程实现．仿真结果证明了所提出的控制策略具有强鲁棒性,跟踪性能良好．     

Logarithmic control,trajectory tracking,and formation for nonholonomic vehicles on Lie group SE(2)

This paper studies the problem of set-point stabilisation, trajectory tracking, and formation tracking for unicycle-type vehicles by taking advantage of the exponential coordinates and the other mathematical tools provided by the Lie group setting of the special Euclidean group SE(2). Motivated by recent developments in geometric control approaches for holonomic systems, we first study the stabilisation problem for nonholonomic constrained kinematic systems by improving the logarithmic stabilising control laws in such a way that they can satisfy nonholonomic constraints too. We then extend the control design to the problem of trajectory tracking by proposing auxiliary systems and investigating the conditions for which the adjoint map in the Lie algebra preserves the velocity constraint. This leads to a global control law which is valid for general time-varying as well as non-smooth trajectories. The tracking control law is also applied to the problem of leader-follower formation tracking by constructing nonholonomic virtual leaders in the desired formation. Finally, the kinematic control law is translated to a differential drive robot using the backstepping technique. To demonstrate the effectiveness of the controllers, the numerical results are presented and the performances are compared with the other three controllers in the literature.     

基于模型预测的自动导引车区间轨迹跟踪控制

针对自动导引车(AGV)轨迹跟踪问题,在确定其可行驶区域的基础上,考虑自动导引车的大小和形状,本文设计了一种基于模型预测控制理论的轨迹跟踪控制方法.首先,将车辆运动学模型进行线性化处理,得到车辆动力学线性模型;其次,运用模型预测控制方法,利用预测路径与期望路径之间的误差,通过优化得到使性能指标最优的控制序列;最后,在MATLAB软件上对轨迹跟踪控制器进行仿真.实验结果表明,AGV可以稳定地跟踪参考轨迹,且距离偏差和角度偏差都在给定的可行范围内,证明了提出的基于模型预测控制的轨迹跟踪算法具有良好的跟踪性能.     

Zero-phase velocity tracking of vibratory systems with actuation constraints

In this paper, a novel filter for precise tracking of constant velocity signals is presented, which allows the reduction of residual vibrations along with the compliance with kinematic constraints that affect the actuation system. A technique achieving both these two objectives at the same time is the main contribution of the work. The filter is based on a cascade of smoothers, i.e. dynamic filters that act on the input signal by increasing its continuity level. Unfortunately, when applied to a generic input composed by ramp (and step) functions, the filter introduces a phase delay not acceptable in many applications where moving parts have to be mated, such as high-speed automatic machines. In order to guarantee a perfect synchronization between the original and the filtered reference signal, once the transient is terminated, a proper compensation scheme has been designed. Moreover, the expressions of the smoothers parameters which assure vibration cancellation at specific frequencies and compliance with given bounds on velocity and acceleration have been analytically deduced. By means of an extensive experimental activity, the effectiveness of the proposed approach has been demonstrated, by comparing its performances with the results of well established approaches for vibrations suppression or signal derivatives limitation.     

Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems

This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then be used to construct explicit trajectories to drive the system between any two points. A kinematic model of a rolling penny is used to illustrate this approach. The methods presented here extend previous work using the chained form and cast that work into a coordinate-free setting.This research was supported in part by a grant from the Powell Foundation.     

A robust trajectory tracking control of a polishing robot system based on CAM data

Polishing a die that has free-form surfaces is a time-consuming and tedious job, and requires a considerable amount of high-precision skill. In order to reduce the polishing time and cope with the shortage of skilled workers, a user-friendly automatic polishing system was developed in this research. The polishing system is composed of two subsystems, a three-axis machining center and a two-axis polishing robot. The developed polishing system with five degrees of freedom is able to keep the polishing tool normal to the die surface during operation. A sliding mode control algorithm with velocity compensation is proposed to reduce tracking errors. Trajectory tracking experiments showed that the effect of reducing the tracking error by the proposed sliding mode control is superior to that by the proportional derivative control. The polishing data is generated from computer-aided design (CAD) data or from teaching data by PolyCAM, a computer-aided manufacturing (CAM) system consisting of 4 modules: a geometric modeller, a CAD data exchange module, a polishing data generation module, and a graphic simulator. To evaluate the performance of the polishing robot system, some polishing experiments on a shadow-mask die were performed.     

四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性集总未知非线性的四旋翼飞行器,提出了一种采用自适应不确定性补偿器的自适应动态面轨迹跟踪方法.通过将四旋翼飞行器系统分解为位置、欧拉角和角速率3个动态子系统,使各子系统虚拟控制器设计能充分考虑欠驱动约束;结合动态面控制技术,通过采用一阶低通滤波器,避免对虚拟控制信号求导;进而设计自适应不确定性补偿器,处理未知外界扰动和系统不确定性,最终确保闭环控制系统的稳定性、跟踪误差一致最终有界和系统所有状态信号有界.仿真研究和实验结果验证了本文提出控制方法的有效性和优越性.     

PD with sliding mode control for trajectory tracking of robotic system

Good tracking performance is very important for trajectory tracking control of robotic systems. In this paper, a new model-free control law, called PD with sliding mode control law or PD–SMC in short, is proposed for trajectory tracking control of multi-degree-of-freedom linear translational robotic systems. The new control law takes the advantages of the simplicity and easy design of PD control and the robustness of SMC to model uncertainty and parameter fluctuation, and avoid the requirements for known knowledge of the system dynamics associated with SMC. The proposed control has the features of linear control provided by PD control and nonlinear control contributed by SMC. In the proposed PD–SMC, PD control is used to stabilize the controlled system, while SMC is used to compensate the disturbance and uncertainty and reduce tracking errors dramatically. The stability analysis is conducted for the proposed PD–SMC law, and some guidelines for the selection of control parameters for PD–SMC are provided. Simulation results prove the effectiveness and robustness of the proposed PD–SMC. It is also shown that PD–SMC can achieve very good tracking performances compared to PD control under the uncertainties and varying load conditions.     

Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.     

The effect of a lower extremity kinematic constraint on lifting biomechanics

Leaning against a stationary barrier during manual materials handling tasks is observed in many industrial environments, but the effects of this kinematic constraint on low back mechanics are unknown. Thirteen participants performed two-handed lifting tasks using both a leaning posture and no leaning posture while trunk kinematics, muscle activity and ground reaction force were monitored. Results revealed that lifting with the leaning posture required significantly less activity in erector spinae (26% vs. 36% MVC) and latissimus dorsi (8% vs. 14% MVC), and less passive tissue moment compared with the no leaning posture. Peak sagittal accelerations were lower when leaning, but the leaning posture also had significantly higher slip potential as measured by required coefficient of friction (0.05 vs. 0.36). The results suggested that the leaning lifting strategy provides reduced low back stress, but does so at the cost of increased slip potential.