Robust output maneuvering for a class of nonlinear systems

The output maneuvering problem involves two tasks. The first, called the geometric task, is to force the system output to converge to a desired path parametrized by a continuous scalar variable θ. The second task, called the dynamic task, is to satisfy a desired dynamic behavior along the path. This dynamic behavior is further specified via a time, speed, or acceleration assignment. While the main concern is to satisfy the geometric task, the dynamic task ensures that the system output follows the path with the desired speed. A robust recursive design technique is developed for uncertain nonlinear plants in vectorial strict feedback form. First the geometric part of the problem is solved. Then an update law is constructed that bridges the geometric design with the speed assignment. The design procedure is illustrated through several examples.     

Path-following for linear systems with unstable zero dynamics

A constructive solution to the path-following problem for MIMO linear systems with unstable zero dynamics is developed. While the original control variable steers the system output along the path, the path parameter θ is used as an additional control to stabilize zero dynamics with a feedback law which is nonlinear due to the path constraint. A sufficient condition for solvability of the path-following problem is given in terms of the geometric properties of the path. When this condition is satisfied, an arbitrary small L₂ norm of path-following error can be achieved, thus avoiding performance limitations of the standard reference tracking problem imposed by unstable zero dynamics.     

A constraint-based dynamic geometry system

Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. The main problem in dynamic geometry systems is the ambiguity that arises from operations that lead to more than one possible solution. Most dynamic geometry systems deal with this problem in such a way that the solution selection method leads to a fixed dynamic behavior of the system. This is specially annoying when the behavior observed is not the one the user intended.In this work we propose a modular architecture for dynamic geometry systems built upon a set of functional units which will allow us to apply some well-known results from the Geometric Constraint Solving field. A functional unit called filter will provide the user with tools to unambiguously capture the expected dynamic behavior of a given geometric problem.     

一类非线性系统的加速度规划输出跟踪动态控制

针对一类严格反馈形式的非线性二阶多输入多输出系统,提出一种带有加速度规划的输出跟踪动态控制策略.引入一个代替时间变量的路径参数用以规划路径跟踪时的加速度,回避了设计内环加速度控制回路的常规方法,简化了控制器的设计过程.对二阶系统的控制项求导进行系统扩维,基于新的增广系统,设计了使系统输出收敛于期望路径的反馈线性化动态控制律.再对加速度跟踪误差基于梯度法设计更新律使其渐近收敛于零,最后通过调节期望加速度实现定常速度控制.理论分析表明,误差闭环系统一致渐近稳定,速度误差有界.动力定位船舶循迹控制仿真结果表明了所提出控制器的有效性.     

Globally Stable Adaptive Dynamic Surface Control for Cooperative Path Following of Multiple Underactuated Autonomous Underwater Vehicles

The cooperative path following problem of multiple underactuated autonomous underwater vehicles (AUVs) involves two tasks. The first one is to force each AUV to converge to the desired parameterized path. The second one is to satisfy the requirement of a cooperative behavior along the paths. In this paper, both of the tasks have been further studied. For the first one, a simplified path following controller is proposed by incorporating the dynamic surface control (DSC) technique to avoid the calculation of derivatives of virtual control signals. Besides, in order to handle the uncertain dynamics, a new type of neural network (NN) adaptive controller is derived, and then an NN based energy‐efficient path following controller is firstly proposed, which consists of an adaptive neural controller dominating in the neural active region and an extra robust controller working outside the neural active region. For the second one, in order to reduce the amount of communications between multiple AUVs, a distributed estimator for the reference common speed is firstly proposed as determined by the communications topology adopted, which means the global knowledge of the reference speed is relaxed for the problem of cooperative path following. The overall algorithm ensures that all the signals in the closed‐loop system are globally uniformly ultimately bounded (GUUB) and the output of the system converges to a small neighborhood of the reference trajectory by properly choosing the design parameters. Simulation results validate the performance and robustness of the proposed strategy.     

Performance limitations in reference tracking and path following for nonlinear systems

We investigate limits of performance in reference tracking and path following and highlight an essential difference between them. For a class of nonlinear systems, we show that in reference tracking, the smallest achievable L₂ norm of the tracking error is equal to the least amount of control energy needed to stabilize the zero dynamics of the error system. We then show that this fundamental performance limitation does not exist when the control objective is to force the output to follow a geometric path without a timing law assigned to it. This is true even when an additional desired speed assignment is required to be satisfied asymptotically or in finite time.     

Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.     

Parametric studies of exhaust smoke-superstructure interaction on a naval ship using CFD

The prediction of flow path of exhaust plume from the ship funnels is extremely complicated since the phenomenon is affected by a large number of parameters like wind velocity and direction, level of turbulence, geometry of the structures on ship’s deck, efflux velocity of smoke etc. To complicate the matters, the entire turbulent flow field is subject to abrupt changes as the yaw angle changes. In order to understand how the smoke is brought down to ship’s deck, it is necessary to have a knowledge of the funnel exhaust behavior very early in the design spiral of the ship by undertaking parametric investigation of the interaction effect between exhaust smoke and the ship superstructure. This paper presents such a parametric investigation on representative topside configurations of a generic frigate using computational fluid dynamics (CFD). The results presented have been analysed for a total of 112 different cases by varying velocity ratios and onset wind direction for four superstructure configurations. Use of both experimental and computational approaches has been made so that they become complementary to each other. The CFD simulation has been done using the computational code FLUENT version 6.0. Closure was achieved by using the standard k-ε turbulence model. The parametric study has demonstrated that CFD is a powerful tool to study the problem of exhaust smoke-superstructure interaction on ships and is capable of providing a means of visualising the path of the exhaust under different operating conditions very early in the design spiral of a ship.     

Calculation of coordinates from molecular geometric parameters and the concept of a geometric calculator

Three different geometric parameters, distance r(i,j), angle θ(i,j, k), and dihedral (or torsion) angle φ(i,j, k, l), are commonly used to specify the shape of a molecule. Given Cartesian coordinates it is simple to calculate such parameters. The, non-trivial, inverse problem of finding coordinates when given such parameters is considered here. When a triple of such geometric parameters is given to specify the position of an atom, n, relative to reference atoms i,j, k,…, with known positions, five qualitatively different cases arise: r(n, i), θ(n, i,j), φ(n, i,j, k), θ(j, n, i) and φ(k, n, i,j). Each such geometric coordinate specifies n to lie on a certain type of surface. To calculate its position one must find the point of intersection of three such surfaces. A program, Evclid, that can perform these calculations is integrated with an interactive set of routines that constitute a geometric calculator and editor. It works on (three-dimensional) points and has a number of input, display and output options. It can translate, rotate, reflect, invert and scale as well as edit the point set or subsets.     

A geometric approach to multivariable control system design of a distillation column

A multivariable control problem of a distillation column is considered, where the object is to maintain two output variables, the compositions of the distillate and the bottom product at some desired values by manipulating the reflux flow rate and the boil-up rate.Based on a linearized model, a geometric approach is applied to the design problem of disturbance rejection control. In other words, a feedback control strategy is desired which enables the complete rejection of the effect of disturbances on both output variables.In obtaining the feedback control, the problem of how many and what state variables are to be measured and fed back has been made clear. In this control strategy, only five state variables are fed back. Thus, only five columns of the feedback gain matrix have non-zero values. Furthermore, two out of these five columns are uniquely determined, and the other three columns can be assigned arbitrary values and used for pole assignment of the controlled system.For the disturbances in composition and flow rate of the feed stream, Δx_F and ΔL_F, the effect of the disturbance Δx_F is completely rejected by the feedback controller, but the effect of the disturbance ΔL_F can only be eliminated from the output Δx_D.A digital simulation of a distillation column composed of nine plates, a condenser and a reboiler was carried out to confirm these results and to show that the linearized model used in this paper is valid for fairly large step changes.     

Optimal input design for parameter estimation in a single and double tank system through direct control of parametric output sensitivities

In this paper the traditional and well-known problem of optimal input design for parameter estimation is considered. In particular, the focus is on input design for the estimation of the flow exponent present in Bernoulli's law. The theory will be applied to a water tank system with a controlled inflow and free outflow. The problem is formulated as follows: Given the model structure (f, g), which is assumed to be affine in the input, and the specific parameter of interest (θ), find a feedback law that maximizes the sensitivity of the model output to the parameter under different flow conditions in the water tank. The input design problem is solved analytically. The solution to this problem is used to estimate the parameter of interest with a minimal variance. Real-world experimental results are presented and compared with theoretical solutions.     

A passive mechanism that improves robotic positioning through compliance and constraint

This paper presents the design of a passive robotic wrist that is capable of establishing and maintaining an accurate position relative to a workpart edge through compliance and constraint (force guidance).In previous work, we have shown that, through proper selection of a manipulator's impedance, a manipulator's end-effector can be guided to its desired relative position despite errors in its commanded position. The selected proper impedance is attained here through the design of a passive micromanipulator that is mounted on the end-effector of a conventional manipulator. The micromanipulator consists of three linkages connected by revolute joints and torsional springs. The outermost linkage contacts the workpart at multiple locations providing multidirectional unilateral kinematic constraint. This kinematic constraint in conjunction with the compliance provided by the torsional springs causes the linkage to be re-positioned so that any existing misalignment (that inevitably occurs) is eliminated and a unique planar position/orientation with respect to the workpart edge is attained.Here, we present the procedure used in the parametric design of this mechanism. The desired compliant properties identified in task space (using Cartesian variables (x, y, and θ) for force and motion) are extended here to joint space (using joint variables (θ₁, θ₂), and θ₃) for torque and motion). The appropriate micromanipulator link lengths, initial linkage angles, and the appropriate torsional spring constants are selected using an optimization procedure. Computer simulation of the constrained manipulator/workpart interaction demonstrates that the desired force guidance behavior is attained.     

Large-scale DES computations of the forward speed diffraction and pitch and heave problems for a surface combatant

This paper aims at presenting the most resolved solutions to date for the ship forward speed diffraction and pitch and heave problems, and discuss the method that enables these computations. Large-scale DES computations (60-115 million grid points, 276-500 processors) of ship hydrodynamics problems are presented for the DTMB model 5512 surface combatant. The forward speed diffraction problem is studied at Fr = 0.28 with waves of amplitude a = 0.006 and wavelength λ=1.5, with the ship static allowing the overset assembly to be a pre-processing step. In the pitch and heave problem the ship faces head waves at Fr = 0.41 with waves of amplitude a = 0.006 and wavelength λ=1.5, with the ship is allowed to pitch and heave, thus requiring dynamic overset grid processing. The code CFDShip-Iowa version 4 and the overset assembly code Suggar were modified to carry out some large scale simulations of free surface ship hydrodynamics. These modifications were focused on reducing the memory requirement and optimizing the per-processor and parallel performance at the implementation and algorithmic levels, plus the addition of a lagged mode for the overset domain connectivity computation. The simulation results show very significant improvements in the local flow and free surface results, but minor in forces and moments when compared with previous URANS computations performed with grids with about three million points.     

基于MCPDDPG的智能车辆路径规划方法及应用

针对智能车路径规划过程中常存在动态环境感知预估不足的问题,使用基于蒙特卡罗深度策略梯度学习(Monte Carlo prediction deep deterministic policy gradient, MCPDDPG)的智能车辆路径规划方法,设计一种基于环境感知预测、行为决策和控制序列生成的框架,实现实时的决策...     

基于高增益观测器的船舶动力定位系统的输出反馈控制

针对动力定位船舶的速度向量不可测的问题, 考虑外部环境扰动, 将高增益观测器、动态面控制技术和矢量backstepping方法相结合, 设计仅依赖于船舶位置和艏摇角测量值的船舶动力定位系统输出反馈控制律. 动态面控制技术的引入, 使控制律结构简单, 易于工程实现. 应用Lyapunov函数证明了所设计的控制律能迫使船舶的位置和艏摇角收敛于期望值, 并保证船舶动力定位输出反馈闭环系统所有信号均一致最终有界. 基于一艘供给船的仿真研究验证了所设计的基于高增益观测器的船舶动力定位输出反馈控制律的有效性.     

Holistic ship design optimization

Ship design is a complex endeavor requiring the successful coordination of many disciplines, of both technical and non-technical nature, and of individual experts to arrive at valuable design solutions. Inherently coupled with the design process is design optimization, namely the selection of the best solution out of many feasible ones on the basis of a criterion, or rather a set of criteria. A systemic approach to ship design may consider the ship as a complex system integrating a variety of subsystems and their components, for example, subsystems for cargo storage and handling, energy/power generation and ship propulsion, accommodation of crew/passengers and ship navigation. Independently, considering that ship design should actually address the whole ship’s life-cycle, it may be split into various stages that are traditionally composed of the concept/preliminary design, the contractual and detailed design, the ship construction/fabrication process, ship operation for an economic life and scrapping/recycling. It is evident that an optimal ship is the outcome of a holistic optimization of the entire, above-defined ship system over her whole life-cycle. But even the simplest component of the above-defined optimization problem, namely the first phase (conceptual/preliminary design), is complex enough to require to be simplified (reduced) in practice. Inherent to ship design optimization are also the conflicting requirements resulting from the design constraints and optimization criteria (merit or objective functions), reflecting the interests of the various ship design stake holders.The present paper provides a brief introduction to the holistic approach to ship design optimization, defines the generic ship design optimization problem and demonstrates its solution by use of advanced optimization techniques for the computer-aided generation, exploration and selection of optimal designs. It discusses proposed methods on the basis of some typical ship design optimization problems with multiple objectives, leading to improved and partly innovative designs with increased cargo carrying capacity, increased safety and survivability, reduced required powering and improved environmental protection. The application of the proposed methods to the integrated ship system for life-cycle optimization problem remains a challenging but straightforward task for the years to come.     

Classifying the multi robot path finding problem into a quadratic competitive complexity class

We explore two motion planning problems where a group of mobile robots has to reach a target located in an a priori unknown environment while on-line planning the next step. In the first problem the target position is unknown and should be found by the robots, while in the second problem the target position is known and only a path to it should be found. We focus on optimizing the cost of the task in terms of motion time, which, under the assumption of uniform velocity of all the robots, correlates to the path length passed by the robot which reaches the target. The performance of an on-line algorithm is usually expressed in terms of Competitiveness, the constant ratio between the on-line and the optimal off-line solutions. Specifically, the ratio between the lengths of the actual path made by the robot which reached the target to the shortest path to the target. We use generalized competitiveness, i.e., the ratio is not necessarily constant, but could be any function. Classification of a motion planning task in the sense of performance is done by finding an upper and a lower bounds on the competitiveness of all algorithms solving that task. If the two bounds belong to the same functional class this is the Competitive Complexity Class of the task. We find the two bounds for the aforementioned common on-line motion planning problems, and classify them into competitive classes. It is shown that in general any on-line motion planning algorithm that tries to solve these problems must have at least a quadratic competitive performance. This is a lower bound of the problems. This paper describes two new on-line navigation algorithm which solve the problems under discussion. The first is called MRSAM, short for Multi-Robot Search Area Multiplication, and the second is called MRBUG, short for Multi-Robot BUG which extends Lumelsky famous BUG algorithm. Both algorithms have quadratic upper bounds, which prove that the problems they solve have quadratic upper bounds. Thus it is shown that navigation in an unknown environment by a group of robots belongs to a quadratic competitive class. MRSAM and MRBUG have a quadratic competitive performance and thus have optimal competitiveness. The algorithms’ performance is simulated in office-like environments.     

An empirical, path-oriented approach to software analysis and testing

Error flow analysis and testing techniques focus on the introduction of errors through code faults into data states of an executing program, and their subsequent cancellation or propagation to output. The goals and limitations of several error flow techniques are discussed, including mutation analysis, fault-based testing, PIE analysis, and dynamic impact analysis. The attributes desired of a good error flow technique are proposed, and a model called dynamic error flow analysis (DEFA) is described that embodies many of these attributes. A testing strategy is proposed that uses DEFA information to select an optimal set of test paths and to quantify the results of successful testing. An experiment is presented that illustrates this testing strategy. In this experiment, the proposed testing strategy outperforms mutation testing in catching arbitrary data state errors.     

Algorithms for computing diffuse reflection paths in polygons

Let s be a point source of light inside a polygon P of n vertices. A polygonal path from s to some point t inside P is called a diffuse reflection path if the turning points of the path lie on edges of?P. A?diffuse reflection path is said to be optimal if it has the minimum number of reflections on the path. The problem of computing a diffuse reflection path from s to t inside P has not been considered explicitly in the past. We present three different algorithms for this problem which produce suboptimal paths. For constructing such a path, the first algorithm uses a greedy method, the second algorithm uses a transformation of a minimum link path, and the third algorithm uses the edge–edge visibility graph of?P. The first two algorithms are for polygons without holes, and they run in O(n+klogn) time, where k denotes the number of reflections in the constructed path. The third algorithm is for polygons with or without holes, and it runs in O(n ²) time. The number of reflections in the path produced by this third algorithm can be at most three times that of an optimal diffuse reflection path. Though the combinatorial approach used in the third algorithm gives a better bound on the number of reflections on the path, the first and the second algorithms stand on the merit of their elegant geometric approaches based on local geometric information.     

Hierarchical A1 based path planning — a case study

Usually it is impossible to know in advance how coarsely robot movements can be discretized in order to find a collision-free path from an initial robot position to a desired goal position in a presence of obstacles. Our solution to the problem is to introduce a new method of constructing hierarchical path planning algorithms. It is based on a novel application of the A¹ control strategy, called here Meta A¹.We test four hierarchical path planning algorithms, two of which are based on Meta A¹, using five simulated robot workcells. The simulations suggest that the Meta A¹ based planners, on average, find paths faster and consume less memory than the other two algorithms.