An extended divide-and-conquer algorithm for a generalized class of multibody constraints

An extension to the divide-and-conquer algorithm (DCA) is presented in this paper to model constrained multibody systems. The constraints of interest are those applied to the system due to the inverse dynamics or control laws rather than the kinematically closed loops which have been studied in the literature. These imposed constraints are often expressed in terms of the generalized coordinates and speeds. A set of unknown generalized constraint forces must be considered in the equations of motion to enforce these algebraic constraints. In this paper dynamics of this class of multibody constrained systems is formulated using a Generalized-DCA. In this scheme, introducing dynamically equivalent forcing systems, each generalized constraint force is replaced by its dynamically equivalent spatial constraint force applied from the appropriate parent body to the associated child body at the connecting joint without violating the dynamics of the original system. The handle equations of motion are then formulated considering these dynamically equivalent spatial constraint forces. These equations in the GDCA scheme are used in the assembly and disassembly processes to solve for the states of the system, as well as the generalized constraint forces and/or Lagrange multipliers.     

Contouring control of a 3-[P2(US)] parallel manipulator

A three-translational degree of freedom parallel mechanism is introduced in this research. Kinematic and dynamic modelling of the parallel mechanism is investigated and equations of motion are derived via Lagrange formulation. Reduced dynamic equations of the robot are represented as a matrix form for implementation in inverse dynamics control of the constrained system. Equivalent contouring errors are represented in moving tangent-normal coordinates system in joint space. Contouring control of the robot is applied to the system using inverse-dynamics-based feedback linearization technique and application of the control technique is represented through two proposed manoeuvres for robot motion. Trajectory planning of the end-effector path is performed by specification of some accuracy points and cubic spline interpolation through them. Response performance in contour following of the control system is improved by appropriate choice of control parameters and by decoupling of error dynamics via assigning suitable structures for control matrices. The results of practical implementation of the control technique show proper accuracy of the control system in following two desired trajectories and acceptable errors are created with respect to the desired contours.     

基于高阶观测器和干扰补偿控制的模型预测控制方法

针对状态不可测、外部干扰未知, 并且状态和输入受限的离散时间线性系统, 将高阶观测器、干扰补偿控制与标准模型预测控制(Model predictive control, MPC)相结合, 提出了一种新的MPC方法. 首先利用高阶观测器同步观测未知状态和干扰, 使得观测误差一致有界收敛;然后基于该干扰估计值设计新的干扰补偿控制方法, 并将该方法与基于状态估计的标准MPC相结合, 实现上述系统的优化控制. 所提出的MPC方法克服了利用现有MPC方法求解具有外部干扰和状态约束的优化控制问题时存在无可行解的局限, 能够保证系统状态在每一时刻都满足约束条件, 并且使系统的输出响应接近采用标准MPC方法控制线性标称系统时得到的输出响应. 最后, 将所提控制方法应用到船舶航向控制系统中, 仿真结果表明了所提方法的有效性和优越性.     

A symplectic local pseudospectral method for solving nonlinear state‐delayed optimal control problems with inequality constraints

In this paper, a symplectic local pseudospectral (PS) method for solving nonlinear state‐delayed optimal control problems with inequality constraints is proposed. We first convert the original nonlinear problem into a sequence of linear quadratic optimal control problems using quasi‐linearization techniques. Then, based on local Legendre‐Gauss‐Lobatto PS methods and the dual variational principle, a PS method to solve these converted linear quadratic constrained optimal control problems is developed. The developed method transforms the converted problems into a coupling of a system of linear algebraic equations and a linear complementarity problem. The coefficient matrix involved is sparse and symmetric due to the benefit of the dual variational principle. Converged solutions can be obtained with few iterations because of the local PS method and quasi‐linearization techniques are used. The proposed method can be applied to problems with fixed terminal states or free terminal states, and the boundary conditions and constraints are strictly satisfied. Numerical simulations show that the developed method is highly efficient and accurate.     

Saturated Adaptive Output-Constrained Control of Cooperative Spacecraft Rendezvous and Docking

This paper investigates the robust relative pose control for spacecraft rendezvous and docking with constrained relative pose and saturated control inputs. A barrier Lyapunov function is used to ensure the constraints of states, so that the computational singularity of the inverse matrix in control command can be avoided, while a linear auxiliary system is introduced to handle with the adverse effect of actuator saturation. The tuning rules for designing parameters in control command and auxiliary system are derived based on the stability analysis of the closed-loop system. It is proved that all closed-loop signals always keep bounded, the prescribed constraints of relative pose tracking errors are never violated, and the pose tracking errors ultimately converge to small neighborhoods of zero. Simulation experiments validate the performance of the proposed robust saturated control strategy.      

基于几何方法的约束线性系统控制快速算法

针对存在状态量和控制量约束的线性系统控制问题, 提出了新快速算法. 已有的处理上述约束系统控制问题的多面体方法和椭球方法在实际应用过程中分别存在计算繁琐和计算保守的问题. 在数学分析的基础上, 通过对上述算法的水平集计算过程的优化, 提出了一种计算简单的约束控制算法. 仿真结果表明, 这种算法计算简单, 且可以满足系统控制的要求.     

Modeling and control of two constrained manipulators

The coordinated control of two manipulators in the presence of environment constraints is studied in this paper. Such a control method is needed in applications in which the two manipulators grasp a common object whose motion is constrained by environments. The two manipulators are not only constrained with each other, but also constrained by the environment in their workspace. It is realized that the motion and constraint equations obtained directly from mechanics are not suitable for the control purpose. A set of equivalent equations are derived, which are in the standard form of the nonlinear system representation with clear state equations and output equations. A nonlinear feedback is found which exactly linearizes and decouples the dynamic nonlinear system of the two constrained manipulators. The coordinated controller design is then carried out based on the linearized system by using linear system theory.     

Adaptive neural output feedback finite-time command filtered backstepping control for nonlinear systems with full-state constraints

In this paper, an adaptive neural finite-time control method via barrier Lyapunov function, command filtered backstepping, and output feedback is proposed to solve the tracking problem of uncertain high-order nonlinear systems with full-state constraints and input saturation. By utilizing the neural network (NN) to approximate unknown nonlinear functions, the finite-time command filters are used to filtering the virtual control signals and get the intermediate control signals in a finite time in the backstepping process. Because there are errors between the output of finite-time command filters and the virtual control signals, the error compensation signals are added to eliminate the influence of filtering errors. Based on the proposed control scheme, the states of the system can be constrained in the predetermined region, all signals in the system are bounded in finite time, and the tracking error can converge to the desired region in finite time. At last, a simulation example is given to show the effectiveness of the proposed control method.     

The leader-follower formation control of nonholonomic mobile robots

In this paper, the leader-waypoint-follower formation is constructed based on relative motion states of nonholonomic mobile robots. Since the robots’ velocities are constrained, we proposed a geometrical waypoint in cone method so that the follower robots move to their desired waypoints effectively. In order to form and maintain the formation of multi-robots, we combine stable tracking control method with receding horizon (RH) tracking control method. The stable tracking control method aims to make the robot’s state errors stable and the RH tracking control method guarantees that the convergence of the state errors tends toward zero efficiently. Based on the methods mentioned above, the mobile robots formation can be maintained in any trajectory such as a straight line, a circle or a sinusoid. The simulation results based on the proposed approaches show each follower robot can move to its waypoint efficiently. To validate the proposed methods, we do the experiments with nonholonomic robots using only limited on-board sensor information.     

Robust adaptive control for a class of semi‐strict feedback systems with state and input constraints

This paper proposes a dynamic surface control (DSC)–based robust adaptive control scheme for a class of semi‐strict feedback systems with full‐state and input constraints. In the control scheme, a constraint transformation method is employed to prevent the transgression of the full‐state constraints. Specifically, the state constraints are firstly represented as the surface error constraints, then, an error transformation is introduced to convert the constrained surface errors into new equivalent variables without constraints. By ensuring the boundedness of the transformed variables, the violation of the state constraints can be prevented. Moreover, in order to obtain magnitude limited virtual control signal for the recursive design, the saturations are incorporated into the control law. The auxiliary design systems are constructed to analyze the effects of the introduced saturations and the input constraints. Rigorous theoretical analysis demonstrates that the proposed control law can guarantee all the closed‐loop signals are uniformly ultimately bounded, the tracking error converges to a small neighborhood of origin, and the full‐state constraints are not violated. Compared with the existing results, the key advantages of the proposed control scheme include: (i) the utilization of the constraint transformation can handle both time‐varying symmetric and asymmetric state constraints and static ones in a unified framework; (ii) the incorporation of the saturations permits the removal of a feasibility analysis step and avoids solving the constrained optimization problem; and (iii) the “explosion of complexity” in traditional backstepping design is avoided by using the DSC technique. Simulations are finally given to confirm the effectiveness of the proposed approach.     

Design of an Optimal Unknown Input Observer for Load Compensation in Motion Systems

Recently, several model‐based control designs have been proposed for motion systems and computerized numerical control (CNC) machines to improve motion accuracy. However, in real applications, their performance is seriously degraded when significant disturbances or cutting forces are applied. In this paper, we derive straightforward design procedures for a general‐structured unknown input observer (UIO) which perfectly decouples the effect of the external disturbance from the state estimation. Furthermore, we derive the optimal UIO by minimizing the estimation errors for both the state and the disturbance via the Riccati equation. Experimental results show that the performance of alladvanced motion controllers suffers when external loads are applied. By compensating for the disturbance of a servo motor using the proposed optimal‐UIO, the original contouring accuracy, which is degraded by the external loading, can be successfully recovered.     

Quasi-min-max output-feedback model predictive control for LPV systems with input saturation

In the research field of model predictive control (MPC), an output-feedback-type MPC method is consistently required for controlling a wide range of constrained systems. In this paper, we propose a two-stage control strategy for polytopic linear parameter varying (LPV) systems subject to input constraints. This strategy consists of a modified quasi-min-max output-feedback MPC method and a novel terminal output-feedback robust control technique. The proposed control mechanism involves the system states to be first controlled via the MPC method to be driven into a prescribed neighborhood of the origin, and then, the terminal output-feedback robust control method guaranteeing the input constraints is applied to make such states converge to the origin. It is also verified that our control method guarantees the closed-loop stability and feasibility in the presence of model uncertainties and input constraints. Finally, a numerical example is given to demonstrate its effectiveness.     

Distributed consensus of second‐order multiagent systems with nonconvex input constraints

This paper addresses the input constrained consensus of second‐order multiagent systems with nonconvex constraints. A new update law is proposed to make the position states of all agents converge to a common point and the velocities converge to zero, while the input of each agent stays in a certain constraint set. The closed‐loop system is first converted to an equivalent system by taking a novel coordinate transformation. Then, it is proved that the input constrained consensus can be achieved if the graphs jointly have directed spanning trees by using the Metzler matrix theory. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithm.     

航天器全状态约束输出反馈控制

针对无角速度测量的刚性航天器姿态跟踪问题,提出一种全状态约束输出反馈控制方法.建立修正罗德里格参数描述的系统模型,提出能够适用于约束与非约束情况的改进型障碍李雅普诺夫函数(MBLF),拓展传统对数型障碍李雅普诺夫函数的适用范围.构造二阶辅助系统,将控制输入和饱和输入之间的差作为构造系统的输入,进而产生信号以补偿饱和的影响.设计状态观测器估计未知状态量,并结合反步法设计输出反馈控制律,保证系统全状态约束性能和姿态跟踪精度.通过李雅普诺夫稳定性分析证明姿态观测误差和跟踪误差能够达到一致最终有界.仿真结果验证所提方法的有效性.     

六自由度机械臂约束预测控制系统的设计

本文提出了一种基于约束预测控制的机械臂实时运动控制方法.该控制方法分为两层,分别设计了约束预测控制器和跟踪控制器.其中,约束预测控制器在考虑系统物理约束的条件下,在线为跟踪控制器生成参考轨迹;跟踪控制器采用最优反馈控制律,使机械臂沿参考轨迹运动.为了简化控制器的设计和在线求解,本文采用输入输出线性化的方式简化机械臂动力学模型.同时,为了克服扰动,在约束预测控制器中引入前馈策略,提出了带前馈一反馈控制结构的预测控制设计.因此,本文设计的控制器可以使机械臂在满足物理约束的条件下快速稳定地跟踪到目标位置.通过在PUMA560机理模型上进行仿真实验,验证了预测控制算法的可行性和有效性.     

A boundary control for motion synchronization of a two-manipulator system with a flexible beam

A novel synchronization motion control method is proposed in this paper for the system in which two manipulators are constrained by a flexible beam. Different from the general synchronization control method, the coupling dynamics among various actuators is considered as the shear force, which results from the synchronization errors. Then a simple boundary control is introduced to realize the synchronization motion of actuators by suppressing the shear force. In order to avoid the drawbacks of assumed modes model, the dynamic model of flexible beam is described by a distributed parameter model in this paper. A Riesz basis method is used to prove that the proposed control law can guarantee the synchronization system to be exponential stability. Simulation results demonstrate that the proposed method can effectively improve the performance of synchronization motion compared with other methods.     

Control of VTOL aircraft with position state constraints using the Barrier Lyapunov Function

A Barrier Lyapunov Function (BLF) controller algorithm is proposed for position tracking control of vertical take‐off and landing (VTOL) aircraft with position state constraints. When VTOL performs missisons in a narrow space, the VTOL position states have to be restricted within the constrained region. To deal with the above problem, BLFs are employed to prevent position states from violating the constraints. The dynamic surface control method is applied to reduce the “explosion of terms” problem of the back‐stepping method. The stability analysis and simulation results illustrate the effectiveness of the proposed controller.     

Robust observer-based controller design for state constrained uncertain systems: attractive ellipsoid method

ABSTRACT

This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers.     

Equations of Motion of Planar Serial Chains of Rigid Bodies

In the present study, the equations of motion of planar serialchains that consist of a system of rigid bodies with all commontypes of kinematic joints are presented. The system of rigid bodiesis replaced by a dynamically equivalent constrained system ofparticles. The concepts of linear and angular momentums are used togenerate the equations of motion for the resulting equivalentconstrained system of particles without either introducing anyrotational coordinates or distributing the external forces and forcecouples over the particles. The method can be applied for open orclosed chains. An example of a closed chain is chosen to demonstratethe generality and simplicity of the proposed method.     

控制增益未知的多变量极值搜索系统神经网络自适应协同控制

针对一类控制增益未知的多变量极值搜索系统,提出了一种神经网络自适应协同控制方法.该方法利用协同控制实现状态变量之间的协同收敛,并确保对系统内部参数扰动和外界干扰具有不变性;以极值搜索控制方法得到的搜寻变量作为输入量,设计多层神经网络逼近状态变量的极值变化率和未知的变量与函数;采用Nussbaum函数解决系统控制增益未知的问题;同时运用自适应参数抵消神经网络逼近误差的影响.稳定性分析证明了系统的状态跟踪误差、输出量与其极值之间的误差、极值搜索变量的跟踪误差以及神经网络各参数的估计误差均指数收敛至原点的一个有界邻域.理论分析与仿真结果验证了该方法的有效性.