A New Nonlinear Controller for Trajectory Tracking of the Longitudinal Dynamics of a Small Scale Helicopter

A nonlinear control scheme is proposed for the trajectory tracking problem of a small scale helicopter’s longitudinal dynamics. The control scheme is based on a control design procedure that constructs static feedback regulators for nonlinear systems which are linearizable by dynamic feedback. Besides, the flatness characteristics of the helicopter’s longitudinal dynamics are used to design the desired trajectory. The controller proposed is based on the longitudinal model of the small scale helicopter including the main rotor and stabilizer bar dynamics. Sufficient conditions are given to guarantee asymptotic convergence to zero of the tracking error and to keep the main rotor thrust always negative assuming that all the helicopter’s parameters are known and that all helicopter’s states are measured. Numerical simulations are given to show the performance of the controller in the presence of the main rotor and stabilizer bar dynamics.     

Constrained dynamical systems,robust model reference adaptive control,and unreliable reference signals

ABSTRACT

In this paper, we address the robust control design problem for nonlinear dynamical systems tracking unreliable reference signals. Specifically, we present robust model reference adaptive control laws that guarantee uniform ultimate boundedness of the trajectory tracking error for nonlinear plants that are affected by matched, unmatched, and parametric uncertainties, and are subject to constraints on the state space and the measured output. These control laws guarantee satisfactory results even in case the reference trajectory or the reference output signal do not verify the given constraints and hence, may draw the plant's trajectory or measured output outside their constraint sets. A numerical example involving the attitude control of a spacecraft illustrates the feasibility of the theoretical results presented.     

Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator

This paper is concerned with the design of an asymptotically stabilizing tracking controller for an undamped wave equation modeling a piezoelectric stack actuator. For this, flatness‐based methods for trajectory planning and feedforward control are combined with dynamic feedback control involving a Luenberger‐type observer within the two degrees‐of‐freedom control concept. The asymptotic stability of the closed‐loop system is verified using Lyapunov's stability theory and LaSalle's invariance principle. Thereby, a separation theorem is introduced for bounded perturbations of infinitesimal generators of asymptotically stable C₀‐semigroups. Finally, the tracking performance is illustrated in simulation scenarios. Copyright © 2010 John Wiley & Sons, Ltd.     

On Trajectory Tracking Model Predictive Control of an Unmanned Quadrotor Helicopter Subject to Aerodynamic Disturbances

In this article a model predictive control (MPC) strategy for the trajectory tracking of an unmanned quadrotor is presented. The quadrotor's dynamics are modeled using a hybrid systems approach and, specifically, a set of piecewise affine (PWA) systems around different operating points of the translational and rotational motions. The proposed control scheme is dual and consists of an integral MPC for the translational motions, followed by an MPC scheme for the tracking of the quadrotor's attitude motions. By the utilization of PWA representations, the controller is computed for a larger part of the quadrotor's flight envelope, which provides more control authority for aggressive maneuvering. The proposed dual control scheme is able to calculate optimal control actions with robustness against atmospheric disturbances (e.g. wind gusts) and with respect to the physical constraints of the quadrotor (e.g. maximum lifting forces or fixed thrust limitations in order to extend flight endurance). Extended simulation studies indicate the efficiency of the MPC scheme, both in trajectory tracking and aerodynamic disturbance attenuation.     

Visual Servoing Path Planning for Cameras Obeying the Unified Model

Abstract

This paper proposes a path planning visual servoing strategy for a class of cameras that includes conventional perspective cameras, fisheye cameras and catadioptric cameras as special cases. Specifically, these cameras are modeled by adopting a unified model recently proposed in the literature and the strategy consists of designing image trajectories for eye-in-hand robotic systems that allow the robot to reach a desired location while satisfying typical visual servoing constraints. To this end, the proposed strategy introduces the projection of the available image features onto a virtual plane and the computation of a feasible image trajectory through polynomial programming. Then, the computed image trajectory is tracked by using an image-based visual servoing controller. Experimental results with a fisheye camera mounted on a 6-d.o.f. robot arm are presented in order to illustrate the proposed strategy.     

主旋翼升力和机身姿态受限的模型直升机非线性控制（英文）

A nonlinear control is proposed for trajectory tracking of a 6-DOF model-scaled helicopter with constraints on main rotor thrust and fuselage attitude. In the procedure of control design, the mathematical model of helicopter is simplified into three subsystems: altitude subsystem, longitudinal-lateral subsystem and attitude subsystem. The proposed control is developed by combining the sub-controls for the corresponding subsystems. The sub-controls for altitude subsystem and longitudinal-lateral subsystem are designed with hyperbolic tangent functions to satisfy the constraints; the sub-control for attitude subsystem is based on backstepping technique such that fuselage attitude tracks the virtual control for longitudinallateral subsystem. It is proved theoretically that tracking errors are ultimately bounded, and control constraints are satisfied.Performances of the proposed controller are demonstrated by simulation results.     

主旋翼升力和机身姿态受限的模型直升机非线性控制

针对主旋翼升力和机身姿态受限的6自由度模型无人直升机的轨迹跟踪控制问题设计了一种非线性控制器.在控制器设计过程中,直升机的数学模型被简化为三个子系统: 姿态子系统,纵-侧向子系统和高度子系统,所设计的控制器由针对这三个子系统的子控制器组成.纵-侧向和高度子控制器基于双曲正切函数进行设计,以保证满足受限条件; 姿态子控制器利用反步法设计,使得机身姿态能够跟踪纵-侧向和高度子系统的虚拟控制.本文在理论上证明了闭环系统跟踪误差最终有界,并且控制器满足受限条件.仿真结果证实了所设计控制器的性能.     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Trajectory planning and tracking for autonomous overtaking: State-of-the-art and future prospects

Trajectory planning and trajectory tracking constitute two important functions of an autonomous overtaking system and a variety of strategies have been proposed in the literature for both functionalities. However, uncertainties in environment perception using the current generation of sensors has resulted in most proposed methods being applicable only during low-speed overtaking. In this paper, trajectory planning and trajectory tracking approaches for autonomous overtaking systems are reviewed. The trajectory planning techniques are compared based on aspects such as real-time implementation, computational requirements, and feasibility in real-world scenarios. This review shows that two important aspects of trajectory planning for high-speed overtaking are: (i) inclusion of vehicle dynamics and environmental constraints and (ii) accurate knowledge of the environment and surrounding obstacles. The review of trajectory tracking controllers for high-speed driving is based on different categories of control algorithms where their respective advantages and disadvantages are analysed. This study shows that while advanced control methods improve tracking performance, in most cases the results are valid only within well-regulated conditions. Therefore, existing autonomous overtaking solutions assume precise knowledge of surrounding environment which is not representative of real-world driving. The paper also discusses how in a connected driving environment, vehicles can access additional information that can expand their perception. Hence, the potential of cooperative information sharing for aiding autonomous high-speed overtaking manoeuvre is identified as a possible solution.     

基于微分平坦与MPC的智能车换道控制算法

为了提高智能车换道的安全性,提出了一种基于微分平坦理论与模型预测控制(MPC)算法相结合的智能车换道轨迹规划与跟踪算法。该算法利用约束求解得到基于sigmoid函数的优化路径;将其与多项式参数化时间函数作为平坦输出,利用微分平坦理论构造一个非线性性能指标函数并对其进行优化求解完成车速规划;从而实现对智能车辆路径-速度分解式的轨迹规划。利用动力学模型预测控制算法线上控制的优点,对智能车的车轮转向进行实时控制,使得车辆按照规划好的轨迹行驶完成换道。通过CarSim与MATLAB/Simulink的联合仿真,将提出的轨迹规划算法应用于车辆系统仿真软件中进行验证,结果表明该算法能够实现对智能车进行轨迹规划和跟踪控制,使其安全高效地换至目标车道。     

Unified nonsingular tracking and stabilization controller design for unicycle-type wheeled mobile robots

A unified, singularity-avoidant controller which enables simultaneous trajectory tracking and posture stabilization of unicycle-type wheeled mobile robots is proposed. The design scheme is based on phase portrait analysis, dynamic feedback linearization and sliding mode control. Path planning via phase portrait analysis plays a key role in choosing the control parameters and the initial value of the extended state in avoiding any singularity. Simulation results on posture stabilization as well as an eight-shaped trajectory tracking are presented to demonstrate the performance of the proposed controller.     

A novel trajectory planning strategy for aircraft emergency landing using Gauss pseudospectral method

To improve the survivability during an emergency situation, an algorithm for aircraft forced landing trajectory planning is proposed. The method integrates damaged aircraft modelling and trajectory planning into an optimal control framework, in order to deal with the complex aircraft flight dynamics, a solving strategy based on Gauss pseudospetral method （GPM） is presented. A 3-DOF nonlinear mass-point model taking into account the wind is developed to approximate the aircraft flight dynamics after loss of thrust. The solution minimizes the forced landing duration, with respect to the constraints that translate the changed dynamics, flight envelope limitation and operational safety requirements. The GPM is used to convert the trajectory planning problem to a nonlinear programming problem （NLP）, which is solved by sequential quadratic programming algorithm. Simulation results show that the proposed algorithm can generate the minimum-time forced landing trajectory in event of engine-out with high efficiency and precision.     

Robust path tracking using flatness for fractional linear MIMO systems: A thermal application

This paper deals with robust path tracking using flatness principles extended to fractional linear MIMO systems. As soon as the path has been obtained by means of the fractional flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for fractional linear SISO systems using a transfer function approach. For fractional systems, especially in MIMO, developments are still to be made. Throughout this paper, flatness principles are applied using polynomial matrices for fractional linear MIMO systems. To illustrate the robustness performances, a third-generation multi-scalar CRONE controller is compared to a PID one.     

On the computation of reference signal constraints for guaranteed tracking performance

This paper concerns the problem of determining constraints on reference signals for tracking systems such that the tracking performance can be guaranteed within a specified tolerance for any reference signal satisfying the constraints. We first consider the problem of computing derivative constraints, which are linear constraints on the (vector-valued) reference signal and its time derivatives, and present an off-line algorithm for computing inner approximations to supremal derivative constraint sets based on the hyperplane method for generating inner and outer approximations to the reachable set of states for the controlled system. No simulation is required. We then consider planning problems in which a finite number of parameters are selected to generate the reference signal. The derivative constraints are mapped into this parameter space. The simplicial approximation method is proposed as a method for computing an approximation to the set of admissible parameters. The resulting (linear) parameter constraints characterize a class of reference signals which can be successfully executed by the tracking system, thereby permitting supervisory planning and control to be carried out in the reference signal parameter space without simulating detailed models of the underlying system dynamics. We illustrate the computational algorithm and the application of derivative and parameter constraints for the problem of generating trajectories for a two-axis computer numerical control (CNC) cutting tool.     

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

In this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.     

Chaos-PSO-based Motion Planning and Accurate Tracking for Position-posture Control of a Planar Underactuated Manipulator with Disturbance

Unlike a fully-actuated manipulator, the position-posture control of a planar underactuated manipulator (PUM) is more difficult, but the research on it is significant due to the wide practical applications. The existing control methods consider no external disturbance and are involved in the staged control idea, bringing the problems of nonsmooth control torque and time-consuming. A novel one-stage control approach is proposed in this paper for the position-posture control of a three-link PUM with the first free joint under the external disturbance. By analyzing the coupling relationship between its active joints and free joint, the position-posture control is transformed into the trajectory tracking control. Unlike the general trajectory planning, the trajectories of the active joints are planned to include several parameters. Meanwhile, the parameters are solved using a chaos particle swarm optimization algorithm to guarantee that all joint angles can reach to their desired angles. Then, to obtain the high trajectory tracking accuracy at every moment under the external disturbance, the nonlinear disturbance observer is constructed and a nonlinear fast terminal sliding mode tracking controller is designed. Finally, the feasibility and superiority of this strategy are verified via two simulations.

     

Stochastic adaptive tracking for a rehabilitative training walker with control constraints considering the omniwheel touchdown characteristic

ABSTRACT

This article investigates the improvement of trajectory tracking on an omnidirectional rehabilitative training walker (ORTW) with random shifts in the centre of gravity, control constraints, and touchdown characteristics of omniwheels. Analysis of the touchdown characteristic improved the accuracy of the dynamic ORTW model. The control constraints guarantee the safety of the omniwheels and the ORTW training process. After describing the random centre-of-gravity shifts using Wiener process, an improved stochastic dynamic model was constructed. Under trajectory tracking control with adaptive technology, the ORTW followed the trajectory designed by the rehabilitation therapist. The exponentially practical stability in mean absolute of the tracking-error system was derived from stochastic theory and Markov's inequality. The effectiveness of the proposed methods was confirmed in simulations.     

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。     

Formation Planning and Control of UGVs with Trailers

This paper provides a framework for planning and control of formations of multiple unmanned ground vehicles with trailers to traverse between goal points in an idealized, disturbance-free environment. This framework allows on-line planning of the formations using the A* search algorithm based on current sensor data. The formation is allowed to dynamically change in order to avoid obstacles in the environment while minimizing a cost function aimed at obtaining collision-free and deadlock-free paths. Based on a feasible path for a leader of the group and the differential flatness property of a truck-tractor-trailer system, the trajectory planner satisfies the kinematic constraints of the individual vehicles while accounting for inter-vehicle collisions and path constraints. Also, optimization techniques are used to on-line change the path of the truck-tractor-trailer system. Illustrative simulations with simplified models of John Deere vehicles with trailers in formations are presented. Laboratory experiments are also performed on a 2-wheel differential drive mobile vehicle attached with a trailer cart on a flat, smooth floor using overhead cameras for precise references. The concluding section of the paper discusses some of the additional work needed to make the results applicable in a real-world environment. Yongxing Hao received the Ph.D. degree in Mechanical Engineering with specialty in Automatic Control and Robotics from the University of Delaware, Newark, DE, in 2004. Prior to joining Hurco Companies, Inc. in 2005, he was a Research Assistant Professor of Electrical and Computer Engineering at West Virginia University Institute of Technology. He received his M.S. and B.S. in Electrical Engineering from Beijing University of Technology and North China University of Technology in 1998 and 1995, respectively.He is a member of IEEE. His research interests include motion planning, controls, robotics, optimization, multi-agent systems and their applications in planning and control of UGVs, UAVs and CNC machines. Sunil K. Agrawal received the Ph.D. degree in Mechanical Engineering from Stanford University, Stanford, CA, in 1990. He has worked in universities, government laboratories, and industries throughout the world. He is currently a Professor of Mechanical Engineering at the University of Delaware, Newark. His research has made contributions in robotics and control, including novel designs of robots and autonomous systems, computational algorithms for planning and optimization of dynamic systems. His work has yielded over 140 technical publications and two books. Dr. Agrawal received the National Science Foundation Presidential Faculty Fellowship from the White House and a Freidrich Wilheim Bessel prize from Alexander von Humboldt Foundation in Germany. He was elected to be a Fellow of American Society of Mechanical Engineers in February 2004.     

Tracking control design for nonholonomic mechanical systems with affine constraints

The trajectory tracking control is considered for nonholonomic mechanical systems with affine constraints and dynamic friction. A new state transformation is proposed to deal with affine constraints, and then an integral feedback compensation strategy is used to identify the dynamic friction. The proposed controller ensures that the output tracking errors converge to zero as t →∞.As an application, a detailed example is presented to illustrate the effectiveness of the control scheme.