考虑时域约束的线性系统非脆弱H∞控制

针对带有时域约束(包含控制输入约束、状态约束或两者的混合约束)的线性系统,在线性矩阵不等式(LMI)优化框架下,提出了一种非脆弱H∞状态反馈控制器设计方法。首先通过初始条件和外部干扰能量的假设确定一个能包含系统所有可能状态的固定椭圆域,然后得到控制器增益在一定范围内摄动情况下确保闭环系统满足时域约束的充分条件,进而转化为相应的矩阵不等式,详细地给出了推导过程。最终时域约束线性系统的非脆弱H∞控制问题可转化为求解多目标的LMI优化问题。将该方法用于质量-弹簧-阻尼系统的干扰抑制控制。仿真实验结果表明：利用该方法设计的控制器能够在满足时域约束的条件下,提高闭环系统对控制器增益摄动的鲁棒性。     

Periodic motion planning and control for underactuated mechanical systems

We consider the problem of periodic motion planning and of designing stabilising feedback control laws for such motions in underactuated mechanical systems. A novel periodic motion planning method is proposed. Each state is parametrised by a truncated Fourier series. Then we use numerical optimisation to search for the parameters of the trigonometric polynomial exploiting the measure of discrepancy in satisfying the passive dynamics equations as a performance index. Thus an almost feasible periodic motion is found. Then a linear controller is designed and stability analysis is given to verify that solutions of the closed-loop system stay inside a tube around the planned approximately feasible periodic trajectory. Experimental results for a double rotary pendulum are shown, while numerical simulations are given for models of a spacecraft with liquid sloshing and of a chain of mass spring system.     

基于受控拉格朗日函数的垂直起降飞机控制器设计

本文将单欠驱动度力学系统基于受控拉格朗日函数(CL)的控制器设计技术应用到具有输入耦合的垂直起降(PVTOL)飞机的控制问题中. 在显式陀螺力的匹配条件下, 得到的光滑反馈控制律保证了系统几乎全局渐近稳定. 与现有同类方法所得到的结果相比, 该匹配控制器形式更简单而收敛性能得到保持.     

仿昆扑翼飞行器全解耦控制

针对仿昆扑翼飞行器飞行控制所面临的欠驱动问题,基于平均理论,提出采用周期时变反馈策略控制仿昆扑翼飞行器的策略,并给出了设计周期时变反馈控制器的输入参数化设计方法．该方法对飞行昆虫的扑翼运动进行仿生模拟,通过调整根翅运动参数,实现了对6个方向气动力和力矩的独立控制．本质上就是用参数表示欠驱动系统的输入,并以此构造周期时变反馈函数;从而在原系统中引入更多数目的独立控制量,将原系统转化为完全能控系统．然后,将此可控系统线性化,并利用线性反馈控制器设计工具设计其反馈控制律．仿真结果表明,基于该策略设计的控制器具有响应速度快、稳定误差小、鲁棒性强等特点．     

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control

This work considers the problem of stabilization of nonlinear systems subject to state and control constraints, for cases where the state constraints need to be enforced at all times (hard constraints) and where they can be relaxed for some time (soft constraints). We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time during which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.     

Gait generation and control for biped robots with underactuation degree one

The paper develops a unified feedback control law for n degree-of-freedom biped robots with one degree of underactuation so as to generate periodic orbits on different slopes. The periodic orbits on different slopes are produced from an original periodic orbit, which is either a natural passive limit cycle on a specific slope or a stable periodic walking gait on level ground generated with active control. First, inspired by the controlled symmetries approach, a general result on gait generation on different slopes based on a periodic orbit on a specific slope is obtained. Second, the time-scaling control approach is integrated to reproduce geometrically same periodic orbits for biped robots with one degree of underactuation. The degree of underactuation is compensated by one degree-of-freedom in the temporal evolution that scales the original periodic orbit. Necessary and sufficient conditions are investigated for the existence and stability properties of periodic orbits on different slopes with the proposed control law. Finally, the proposed approach is illustrated by two kinds of underactuated biped robots: one has a passive gait on a specific ground slope and the other does not have a natural passive gait.     

Polynomial joint angle arm robot motion planning in complex geometrical obstacles

This paper addresses a point-to-point of an arm robot motion planning in complex geometrical obstacle. It will govern a two-layer optimization strategy utilizing sixth degree polynomial as joint angle path. At the beginning of the motion planning process, the path planning starts with the optimization objective to minimize the joint angle travelling distance under collision detection rules as constraint. After the best path has been met, the associated time will be searched with the optimization objective to minimize the total travelling time and the torque under the maximum velocity, the maximum acceleration, the maximum jerk, and the maximum torque constraints. The performance of a Genetic Algorithm (GA) and a Particle Swarm Optimization (PSO) will be investigated in searching the feasible sixth degree polynomial joint angle path and the total travelling time that gives the optimal trajectories under kinodynamic constraints. A 3-Degree-Of-Freedom (3-DOF) planar robot will be utilized to simulate the proposed scenario.     

Solution of a non-convex optimization arising in PI/PID control design

As shown by Åström et al. (Automatica 34(5) (1998) 585), the problem of designing a stabilizing PI controller based on minimizing integral of error associated with step load disturbance while subjecting to constraints on maximum sensitivity and/or complementary sensitivity amounts to that of finding the maximum allowable integral gain. The latter problem is a non-convex optimization problem whose true solution cannot be obtained with a guarantee by a gradient-based search algorithm. In this paper, we present a novel and effective approach to solve such a non-convex optimization problem. Our approach is based on regarding an equality constraint set on controller gain parameters as a two-dimensional value set in the complex plane and using the notion of principal points to characterize its boundary. With this treatment, we are able to derive analytical expressions for describing the boundary of an equality constraint set in the controller gain plane. These expressions allow one to trace the boundaries of equality constraint sets using an existing path-following algorithm. Hence, by constructing the boundary of the feasible domain in the controller gain space, the maximum allowable integral gain can be obtained. In addition to having the ability to obtain global optimal solution, our approach can handle sensitivity and complementary sensitivity constraints simultaneously without using an iterative procedure.     

带有状态约束的双摆效应吊车轨迹规划

对于欠驱动吊车而言,已有方法大都将负载摆动视为单摆进行处理.然而当吊钩质量相比负载质量不可忽略或负载体积较大时,负载会绕吊钩产生第二级摆动,出现双摆效应,使系统的摆动特性更为复杂,欠驱动度更高,其控制更具挑战性;此外,现有方法均无法保证系统的暂态控制性能.针对这些问题,本文提出了一种基于轨迹规划的消摆定位控制方法.具体而言,本方法所规划的台车轨迹具有解析表达式,且充分考虑系统安全性(摆动幅值)及台车运动的物理约束;通过构造新颖的平坦输出信号,将施加在台车运动和两级摆动上的约束/指标转化为对平坦输出的约束,从而将轨迹规划转化为凸优化问题.该方法能够保证整个过程中系统两级摆动的角度、角速度,台车的速度、加速度、加加速度均保持在设定范围内.通过与已有方法进行仿真对比,可见本方法不仅简单易行,且在工作效率与摆动抑制方面均具有更为良好的控制性能.     

Time-optimal tool motion planning with tool-tip kinematic constraints for robotic machining of sculptured surfaces

A time-optimal motion planning method for robotic machining of sculptured surfaces is reported in this paper. Compared with the general time-optimal robot motion planning, a surface machining process provides extra constraints such as tool-tip kinematic limits and complexity of the curved tool path that also need to be taken into account. In the proposed method, joint space and tool-tip kinematic constraints are considered. As there are high requirements for tool path following accuracy, an efficient numerical integration method based on the Pontryagin maximum principle is adopted as the solver for the time-optimal tool motion planning problem in robotic machining. Nonetheless, coupled and multi-dimensional constraints make it difficult to solve the problem by numerical integration directly. Therefore, a new method is provided to simplify the constraints in this work. The algorithm is implemented on the ROS (robot operating system) platform. The geometry tool path is generated by the CAM software firstly. And then the whole machine moving process, i.e. the feedrate of machining process, is scheduled by the proposed method. As a case study, a sculptured surface is machined by the developed method with a 6-DOF robot driven by the ROS controller. The experimental results validate the developed algorithm and reveal its advantages over other conventional motion planning algorithms for robotic machining.     

Optimization process planning using hybrid genetic algorithm and intelligent search for job shop machining

Optimization of process planning is considered as the key technology for computer-aided process planning which is a rather complex and difficult procedure. A good process plan of a part is built up based on two elements: (1) the optimized sequence of the operations of the part; and (2) the optimized selection of the machine, cutting tool and Tool Access Direction (TAD) for each operation. In the present work, the process planning is divided into preliminary planning, and secondary/detailed planning. In the preliminary stage, based on the analysis of order and clustering constraints as a compulsive constraint aggregation in operation sequencing and using an intelligent searching strategy, the feasible sequences are generated. Then, in the detailed planning stage, using the genetic algorithm which prunes the initial feasible sequences, the optimized operation sequence and the optimized selection of the machine, cutting tool and TAD for each operation based on optimization constraints as an additive constraint aggregation are obtained. The main contribution of this work is the optimization of sequence of the operations of the part, and optimization of machine selection, cutting tool and TAD for each operation using the intelligent search and genetic algorithm simultaneously.     

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.     

Visual Servoing Path Planning via Homogeneous Forms and LMI Optimizations

Path planning is a useful technique for visual servoing as it allows one to take into account system constraints and achieve desired performances during the camera motion. In this paper, we propose a new framework for path planning based on the use of homogeneous forms and linear matrix inequalities (LMIs). Specifically, we introduce a general parametrization of the trajectories from the initial to the desired location based on homogeneous forms and a parameter-dependent version of the Rodrigues formula. This allows us to impose typical constraints (field of view, workspace, joint, avoidance of collision, and occlusion) via positivity conditions on suitable homogeneous forms. Then, we reformulate the problem of finding a trajectory in the 3-D space satisfying all these constraints as an LMI optimization that can handle the maximization of typical performances (e.g., visibility margin, similarity to a straight line). The planned camera path is tracked by using an image-based controller. The proposed approach is illustrated and validated through simulations and experiments.     

基于收缩约束模型预测控制的无人车辆路径跟踪

针对存在有界扰动的非线性无人驾驶车辆避障过程中最优路径规划跟踪问题,提出一种基于预测时域内系统输入输出收缩约束(PIOCC)的模型预测控制(MPC)方法.首先在构建目标函数时,为扩大可行性解的范围引入软约束思想,将最优规划路径的跟随问题转化为对模型预测控制优化问题的求解;其次为避免短预测时域造成闭环系统发散而导致在约束条件限定下出现无可行性解的情况,采用预测时域内系统输入输出收缩约束的方法,设计模型预测控制器;再次基于Lyapunov稳定性理论证明所设计的模型预测闭环控制系统是渐近稳定的;最后通过仿真实例验证了所提出基于PIOCC的控制策略在解决扩大可行解范围和避免闭环系统发散问题时的有效性,实现了无人驾驶车辆在路径跟踪时具有良好的快速性和稳定性.     

Transverse Linearization for Impulsive Mechanical Systems With One Passive Link

A general method for planning and orbitally stabilizing periodic motions for impulsive mechanical systems with underactuation one is proposed. For each such trajectory, we suggest a constructive procedure for defining a sufficient number of nontrivial quantities that vanish on the orbit. After that, we prove that these quantities constitute a possible set of transverse coordinates. Finally, we present analytical steps for computing linearization of dynamics of these coordinates along the motion. As a result, for each such planned periodic trajectory, a hybrid transverse linearization for dynamics of the system is computed in closed form. The derived impulsive linear system can be used for stability analysis and for design of exponentially orbitally stabilizing feedback controllers. A geometrical interpretation of the method is given in terms of a novel concept of a moving PoincarÉ section. The technique is illustrated on a devil stick example.      

Decentralized control and state estimation of linear time-periodic systems

The main contributions of this article are the design of a decentralized controller and state estimator for linear time-periodic systems with fixed network topologies. The proposed method to tackle both problems consists of reformulating the linear periodic dynamics as a linear time-invariant system by applying a time-lifting technique and designing a discrete-time decentralized controller and state estimator for the time-lifted formulation. The problem of designing the decentralized estimator is formulated as a discrete-time Kalman filter subject to sparsity constraints on the gains. Two different algorithms for the computation of steady-state observer gains are tested and compared. The control problem is posed as a state feedback gain optimization problem over an infinite-horizon quadratic cost, subject to a sparsity constraint on the gains. An equivalent formulation that consists in the optimization of the steady-state solution of a matrix difference equation is presented and an algorithm for the computation of the decentralized gain is detailed. Simulation results for the practical cases of the quadruple-tank process and an extended 40-tank process are presented that illustrate the performance of the proposed solutions, complemented with numerical simulations using the Monte Carlo method.     

基于ARM处理器的运动控制器的设计与实现

针对传统的运动控制器二次开发难、成本高、功能单一等缺点,设计了基于网络接口的运动控制器,该运动控制器集灯源、光栅尺计数和运动控制于一体,采用ARM+ FPGA的结构,FPGA对光栅尺信号进行处理及完成运动控制规划,ARM上运行Linux操作系统,实现对灯源的控制,负责与FPGA的总线通信以及与PC的网络通信.该控制器适合二次开发,且大大降低了成本.该运动控制器主要应用于影像测量系统中,实验已经证明该设计的可行性.     

基于集成约束无人机两步制航迹规划方法

无人机航迹规划是一个富含地形威胁、雷达威胁和自身可飞性等多约束的优化问题.采用两步制的规划框架,提出一种基于集成约束的无人机航迹规划方法.规划第1阶段采用基于多种群策略的差分进化优化方法,规划第2阶段采用海洋捕食者算法的Lévy运动优化;集成约束机制在搜索过程中动态更新约束策略来补偿可行解数量骤减,抑制搜索停滞.与典型算法和约束处理策略进行对比,实验结果表明,所提出无人机航迹规划方法收敛性好、稳定性强,能够有效地求解复杂多约束无人机航迹规划问题.     

Coordinated control of a satellite-mounted manipulator with consideration of payload flexibility

When a space robot performs tasks, disturbances caused by payload motion downgrade the attitude control's accuracy. Thus, the payload should be controlled so as not to generate large disturbances. In this paper, payload motion planning based on angular momentum constraints (AMC) is proposed. In this method, disturbances are reduced by controlling the payload's redundant motions. Remaining disturbances caused by payload flexibility are compensated for by a robust feedback controller consisting of a variable gain and a H_∞ controller. The usefulness of this approach is verified through numerical simulations and hardware experiments.     

面向反馈运动控制器的多目标求解

目的 基于物理模拟的人体运动生成方法由于能够合成符合自然规律的运动片段,可实时响应环境的变化,且生成的物理运动不是机械性的重复,因此是近年来计算机动画和虚拟现实领域中最活跃的研究方向之一。然而人体物理模型具有高维、非线性及关节间强耦合性等特点,求解人体物理运动十分困难。反馈控制器常用于人体物理运动控制,求解时通常需要对多个目标函数加权求和,然而权重的设置需多次试验,烦杂耗时。针对运动控制器求解困难的问题,本文提出了一种面向反馈运动控制器的多目标求解方法。方法 首先,对运动数据进行预处理并提取关键帧求解初始控制器,并设计一种改进的反馈控制机制;在此基础上,种群父代个体变异产生子代,采用禁选区域预筛选策略去除不满足约束的个体,并通过重采样获取新解;然后,通过物理仿真获得多目标适应度值,采用区域密度多层取优选取分布均匀的优秀个体作为下一代父代,并通过基于剪枝的多阶段物理求解算法决定是否进入下一阶段优化;经过多次迭代后获得物理控制器,从而生成具有反馈的人体物理运动。结果 针对提出的方法,本文针对多个测试函数和物理运动分别进行实验：在测试函数实验中,本文分别采用经典的测试函数进行实验对比,在相同的迭代次数下,相比之前算法,本文算法中满足约束的优秀个体命中率更高,反转世距离更小,且最优解集的分布更加均匀;物理运动生成实验中,分别针对走路、跑步和翻滚等运动进行物理运动生成,与之前算法进行对比,本文算法可以更早地完成收敛,同时目标函数值更小,表明生成的运动效果更好。结论 本文提出的进化求解方法可以生成不同运动的控制器,该控制器不仅可以生成物理运动,而且还具备外力干扰下保持平衡的能力,解决了运动控制器求解中多目标权重设置困难、优化时间长的问题;除此之外,本文算法还对具有约束的多目标问题具有较好的求解效果。