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On the methods of analytical mechanics for mathematical modeling of the dynamics of non-free systems and some variants of their application to the dynamics of parallel manipulators 非自由系统动力学数学建模的分析力学方法及其在并联机械臂动力学中的应用
Pub Date : 2022-02-14 DOI: 10.15406/iratj.2023.09.00256
A. Krasinskiy
The level of development of actuator technology and the element base and software of control loops of modern automatic devices makes it possible to use in technical practice complex control algorithms based on the results of mathematical control theory, including with incomplete information about the state. The effectiveness of such algorithms is determined by the presence of an adequate mathematical model of the device under study. For such a widespread class of automatic devices as manipulators with parallel kinematics, the problem of developing methods for creating mathematical models that allow taking into account nonlinear effects, despite the efforts of numerous researchers, remains relevant. To a large extent, the complexity of modeling the dynamics of this class of automatic devices is associated with the presence of parallel kinematic chains, which leads to the need to apply the results of analytical mechanics of non-free systems. In this section of theoretical mechanics, several rigorous methods have been developed, as a result of which mathematical models of different dimensions are obtained with different levels of complexity of the algorithms for their derivation and study. This leads to the need for a critical analysis of both the methods themselves and their possible application in technical practice. In this paper, the main algorithms for obtaining mathematical models of the dynamics of systems with geometric constraints are presented in detail and some comparative analysis of their application to modeling the dynamics of manipulators with parallel kinematics is carried out.
执行器技术的发展水平以及现代自动装置控制回路的元件基础和软件,使得在技术实践中使用基于数学控制理论结果的复杂控制算法,包括不完全状态信息的控制算法成为可能。这种算法的有效性取决于所研究设备的适当数学模型的存在。对于具有平行运动学的机械臂这样一类广泛使用的自动装置,尽管许多研究人员做出了努力,但开发方法来创建允许考虑非线性效应的数学模型的问题仍然是相关的。在很大程度上,这类自动装置动力学建模的复杂性与并联运动链的存在有关,这导致需要应用非自由系统的分析力学结果。在理论力学的这一部分中,已经发展了几种严格的方法,从而获得了不同维度的数学模型,其推导和研究的算法具有不同的复杂程度。这导致需要对方法本身及其在技术实践中的可能应用进行批判性分析。本文详细介绍了获取几何约束系统动力学数学模型的主要算法,并对其在并联机械臂动力学建模中的应用进行了比较分析。
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引用次数: 0
Shortest paths of trefoil knot designs using Rubik’s Snakes 最短路径的三叶草结设计使用魔方蛇
Pub Date : 2022-01-28 DOI: 10.15406/iratj.2022.08.00238
Songming Hou, Jianning Su
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引用次数: 3
Applications of mechatronics opportunities in textiles 机电一体化在纺织品中的应用机会
Pub Date : 2022-01-20 DOI: 10.15406/iratj.2022.08.00237
Elsayed Ahmed Elnashar 
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引用次数: 2
Industrial robots integration based in object location and component inspection in industry 4.0 using vision guided robot (VGR) 基于视觉引导机器人(VGR)的工业4.0中物体定位和部件检测的工业机器人集成
Pub Date : 2022-01-13 DOI: 10.15406/iratj.2022.08.00236
Adas Pereira Vitall, Rogério Clemente, Arnaldo Ortiz, Rosário A, João Maurício
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引用次数: 0
World’s first self-driving amphibious bus 世界上第一辆自动驾驶水陆两栖巴士
Pub Date : 2022-01-09 DOI: 10.15406/iratj.2023.09.00254
D. Watabe, M. Wada, Nobumitu Shimizu, Tastuma Ohkubo
Amphibious buses are extensively used worldwide for transporting people to and from tourist attractions across water and land. Although numerous studies on self-driving technologies have been reported, research on the automatic operation and navigation of an amphibious vehicle has been sparse; moreover, owing to the size of the amphibious vehicles, automatic transport of multiple people is not possible. Therefore, in this study, we attempted to realize unmanned operation of a sightseeing amphibious bus for 45 passengers. The bus was outfitted with a by-wire system. On the vessel side, an actuator, similar to that used in JOY cars, was installed to turn the captain’s steering wheel. We also developed a software for the automatic operation and navigation of the bus. The relationship between the car’s steering-wheel angle and the front-tire angles is linear, whereas that between the captain’s steering-wheel angle and the vessel’s rudder-plate angle is not (and was approximated with a sixth-order polynomial). Furthermore, Autoware—a leading autonomous-driving software utilizing model-based predictive control algorithms to control the steering wheel of automobiles—was employed in this work. These algorithms were altered using Nomoto’s KT vessel model equation to improve the accuracy of vessel-path tracking. To the best of our knowledge, till date, no studies have documented the functioning of self-driving vessels using predictive controls based on Nomoto’s KT vessel model equation. In accordance with the vessel navigation rules based on the Autoware obstacle avoidance logic, LiDAR, cameras, and sonars were employed to detect obstructions and give-way paths. Thus, we successfully demonstrated the working of world's first self-driving amphibious bus, with automated controls for entering/exiting water and during give-way operations.
水陆两栖巴士在世界范围内被广泛用于运输人们往返于水上和陆地的旅游景点。尽管有大量关于自动驾驶技术的研究报道,但对两栖车辆的自动操作和导航的研究却很少;此外,由于水陆两栖车辆的尺寸,自动运输多人是不可能的。因此,在本研究中,我们尝试实现45人观光水陆客车的无人驾驶。这辆公共汽车装有电传系统。在船的一侧,安装了一个驱动器,类似于JOY汽车上使用的驱动器,用来转动船长的方向盘。我们还开发了一款用于公交车自动操作和导航的软件。汽车的方向盘角与前轮胎角之间是线性关系,而船长的方向盘角与船的舵板角之间不是线性关系(并且用六阶多项式近似)。此外,本文还采用了基于模型的预测控制算法来控制汽车方向盘的自动驾驶软件autoware。使用Nomoto的KT血管模型方程对这些算法进行了修改,以提高血管路径跟踪的准确性。据我们所知,到目前为止,还没有研究记录使用基于野本KT船舶模型方程的预测控制的自动驾驶船舶的功能。根据基于Autoware避障逻辑的船舶导航规则,采用激光雷达、摄像头和声纳探测障碍物和让路路径。因此,我们成功地展示了世界上第一辆自动驾驶水陆两栖巴士的工作原理,该巴士具有进出水和让路操作的自动控制。
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引用次数: 0
Optimization of distance between fire stations: effects of fire ignition probabilities, fire engine speed and road limitations, property values and weather conditions 消防站之间距离的优化:着火概率、消防车速度和道路限制、财产价值和天气条件的影响
Pub Date : 2021-12-02 DOI: 10.15406/iratj.2021.07.00235
P. Lohmander
A general spatial fire brigade unit network density optimization problem has been solved. The distance to a particular road, from a fire station, is approximated as a continuous variable. It is proved, via integral convolution, that the probability density function of the total travel time, PDFT, is triangular. The size of the fire, when it stopped, is a function of the time it takes until the fire brigade reaches the fire location. An explicit continuous function for the expected total cost per square kilometer, based on the cost per fire station, the PDFT, the exponential fire cost function parameters, the distance between fire stations, and the speed of fire engines, is derived. It is proved that the optimal distance between fire brigade unit positions, OFD, which minimizes the total expected cost, is unique. Then, the OFDs are replaced by integers, OFDIs, for different parameter assumptions. In this process, also the optimal expected total costs are determined. It is proved that the OFD is a strictly decreasing function of the expected number of fires per area unit, a strictly increasing function of the speed of the fire engines, a strictly decreasing function of the parameters of the exponential fire cost function, and a strictly increasing function of the cost per fire station. These effects of parameter changes are also illustrated via graphs in the numerical section.
解决了一般空间消防队单位网络密度优化问题。从消防站到特定道路的距离近似为连续变量。通过积分卷积证明了总行程时间的概率密度函数PDFT是三角形的。当火灾停止时,火灾的规模是消防队到达火灾地点所需时间的函数。基于每个消防站的成本、PDFT、指数火灾成本函数参数、消防站之间的距离和消防车的速度,导出了每平方公里预期总成本的显式连续函数。证明了使总期望成本最小的消防队单位位置之间的最优距离OFD是唯一的。然后,根据不同的参数假设,将ofd替换为整数ofdi。在此过程中,还确定了最优期望总成本。证明了OFD是单位面积期望火灾数的严格递减函数,是消防车速度的严格递增函数,是指数火灾代价函数参数的严格递减函数,是每个消防站代价的严格递增函数。这些参数变化的影响也在数值部分通过图表加以说明。
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引用次数: 0
A suggested simple design and inverse kinematics for a multi-degrees-of-freedom robot arm 提出了一种多自由度机械臂的简单设计和运动学逆解
Pub Date : 2021-11-19 DOI: 10.15406/iratj.2021.07.00234
K. Pasha
In this paper, architecture for the robot arm and a mathematical model was suggested to simplify the inverse kinematics that describes the movement and orientation of this end-effector. Although this design contains eight degrees of freedom, all the angular displacements and velocities could be formulated as functions of the three coordinates of the end-effecter starting point. These three values are enough to set the end-effector at the desired point in the workspace, and with the desired orientation. The tip of the end-effecter could be equipped with a grabber or any attached manufacturing tool. To check the reliability of the introduced mathematical model, a simple model for the arm was built using aluminum beams. The joints are actuated by stepper motors that are controlled by a microprocessor. The model executed the positioning and orientation of the end-effector with an accuracy of about 93% of any traveled distance. This lack of accuracy may be accounted for by the low resolutions of the used motors. In this study, the positioning and orientation were only considered, and future work is required for the analysis of loads and power capacities
本文提出了机械臂的结构和数学模型,以简化描述该末端执行器的运动和方向的逆运动学。虽然该设计包含八个自由度,但所有角位移和角速度都可以表示为末端执行器起点三个坐标的函数。这三个值足以将末端执行器设置在工作空间中所需的点上,并具有所需的方向。末端执行器的尖端可以配备抓手或任何附加的制造工具。为了验证所引入的数学模型的可靠性,利用铝梁建立了一个简单的机械臂模型。这些关节由由微处理器控制的步进电机驱动。该模型对末端执行器的定位和定向精度约为任意移动距离的93%。这种精度的缺乏可能是由于所用电机的低分辨率造成的。在本研究中,只考虑了定位和方向,未来还需要对负载和功率容量进行分析
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引用次数: 0
Inertial torques acting on a spinning sphere 作用在旋转球体上的惯性力矩
Pub Date : 2021-11-16 DOI: 10.15406/iratj.2021.07.00233
R. Usubamatov, A. Arzybaev
New studies of the dynamics of rotating objects have shown the origin of their gyroscopic effects is more sophisticated than presented in publications. Their rotating mass acting on bodies generates the system of the kinetically interrelated inertial torques. The method for developing mathematical models for inertial torques of the spinning objects shows their dependencies on geometries. The inertial torques generated by the disc, ring, paraboloid, and others have confirmed this statement. The derived analytical method presents a new direction for the dynamics of classical mechanics. The several inertial torqueses acting on any movable spinning objects in space were unknown until recent times. The gyroscopic effects of rotating objects in engineering and a new method for computing their inertial torques are the challenges for researchers. The novelty of this manuscript is the mathematical models for the inertial torques generated by the rotating mass acting on the spinning solid and hollow sphere.
对旋转物体动力学的新研究表明,它们的陀螺仪效应的起源比在出版物中提出的更为复杂。它们的旋转质量作用在物体上,产生了动力学上相互关联的惯性力矩系统。建立旋转物体惯性力矩数学模型的方法表明了惯性力矩对几何形状的依赖性。圆盘、环、抛物面等产生的惯性力矩证实了这一说法。导出的解析方法为经典力学动力学提供了一个新的方向。作用在空间中任何可移动的旋转物体上的几个惯性力矩直到最近才为人所知。工程中旋转物体的陀螺效应及其惯性转矩的计算方法是研究人员面临的挑战。本文的新颖之处在于建立了旋转质量作用于旋转实心球和空心球所产生的惯性力矩的数学模型。
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引用次数: 1
Optimization problem of attitude control of a spacecraft with bounded rotary energy using quaternions 基于四元数的有界旋转能量航天器姿态控制优化问题
Pub Date : 2021-08-26 DOI: 10.15406/iratj.2021.07.00228
M. V. Levskii
The original control problem of optimal reorientation from a state of rest to a state of rest is considered and solved. The control function is torque vector. Problem of optimal control is investigated in detail for statement when control is restricted and the used functional of optimality includes kinematical rotary energy and time of maneuver. For solving and synthesis of the optimal control program, the quaternion method and the Pontryagin’s maximum principle are applied. Analytic solution of the proposed problem is presented basing on the differential equation connecting the angular velocity vector and quaternion of spacecraft attitude. It is shown that a chosen criterion of optimality provides a turn of a spacecraft with rotation energy which does not exceed the required value. This property of proposed control increases safety of flight. The time-optimal problem was solved also. The control law is formulated in the form of an explicit dependence of the control variables on the phase coordinates. All key expressions and equations are written in quaternion form which is convenient for onboard realization and implementation. The analysis of the special control regime of the spacecraft was made. Analytical formulas were written for duration of acceleration and braking. For specific cases of spacecraft configurations (dynamically symmetric spacecraft and spheric-symmetrical spacecraft as particular cases), complete solution of optimal control problem in closed form is given. Numerical example and the results of mathematical simulation for spacecraft motion under optimal control are demonstrated. This data supplements the made theoretical descriptions, and illustrates the practical feasibility of the designed algorithm for controlling the spatial orientation of the spacecraft showing reorientation process in visual form.
考虑并解决了从静止状态到静止状态的最优定向控制问题。控制函数为转矩矢量。详细研究了控制受限情况下的最优控制问题,最优性函数包括运动旋转能量和机动时间。应用四元数法和庞特里亚金极大值原理求解和综合最优控制程序。基于航天器姿态角速度矢量与四元数的微分方程,给出了该问题的解析解。结果表明,所选择的最优准则使航天器的旋转能量不超过要求值。拟议控制的这一特性增加了飞行的安全性。同时还解决了时间最优问题。控制律的形式是控制变量对相位坐标的显式依赖。所有关键表达式和方程均以四元数形式编写,便于板载实现。对航天器的特殊控制方式进行了分析。给出了加速和制动持续时间的解析公式。对于航天器构型的具体情况(以动态对称航天器和球对称航天器为例),给出了最优控制问题的闭形式的完全解。给出了最优控制下航天器运动的数值算例和数学仿真结果。该数据补充了已有的理论描述,说明了所设计的航天器空间定向控制算法的实际可行性,以可视化的形式显示了航天器的重定向过程。
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引用次数: 0
Chance-constrained path planning in narrow spaces for a dubins vehicle 杜宾车在狭窄空间的机会约束路径规划
Pub Date : 2021-07-23 DOI: 10.15406/iratj.2021.07.00277
Rachit Aggarwal, Mrinal Kumar, Rachel E Keil, Anil V. Rao
The problem of optimal path planning through narrow spaces in an unstructured environment is considered. The optimal path planning problem for a Dubins agent is formulated as a chance-constrained optimal control problem (CCOCP), wherein the uncertainty in obstacle boundaries is modelled using standard probability distributions. The chance constraints are transformed to deterministic equivalents using the inverse cumulative distribution function and subsequently incorporated into a deterministic optimal control problem. Due to multiple convex sub-regions introduced by the obstacles, the initial guess provided to optimal control solver is crucial for computation time and optimality of the solution. A constrained Delaunay triangulation mesh based approach is developed that ensures the initial guess to lie in the optimal sub-convex region. Finally, off-the-shelf software is used to transcribe the optimal control problem to a nonlinear program (NLP) using Gaussian quadrature orthogonal collocation and solved to obtain an optimal path that conforms to system dynamics. By varying the upper bound on probability of obstacle collision, a family of solutions is generated, parameterized by the risk associated with each solution. This approach enables discovery of special “keyhole trajectories” that can provide significant cost savings in a tightly-spaced obstacle field. Merits of this approach are illustrated by comparing it with the traditional bounded uncertainty approach.
研究非结构化环境中狭窄空间的最优路径规划问题。将Dubins智能体的最优路径规划问题表述为机会约束最优控制问题(CCOCP),其中障碍物边界的不确定性使用标准概率分布建模。利用逆累积分布函数将机会约束转化为确定性等效约束,并将其纳入确定性最优控制问题。由于障碍物引入了多个凸子区域,因此提供给最优控制求解器的初始猜测对计算时间和解的最优性至关重要。提出了一种基于约束Delaunay三角剖分网格的方法,确保初始猜测位于最优子凸区域。最后,利用现成软件将最优控制问题转化为非线性程序(NLP),采用高斯正交配置法求解,得到符合系统动力学的最优路径。通过改变障碍碰撞概率的上界,生成一组解,并以每个解的风险参数化。这种方法可以发现特殊的“锁眼轨迹”,可以在狭窄的障碍物场中显著节省成本。通过与传统的有界不确定性方法的比较,说明了该方法的优点。
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引用次数: 1
期刊
International Robotics & Automation Journal
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