General Optimal Trajectory Planning:Enabling Autonomous Vehicles with the Principle of Least Action

This study presents a general optimal trajectory planning(GOTP)framework for autonomous vehicles(AVs)that can effectively avoid obstacles and guide AVs to complete driving tasks safely and efficiently.Firstly,we employ the fifth-order Bezier curve to generate and smooth the reference path along the road centerline.Cartesian coordinates are then transformed to achieve the curvature continuity of the generated curve.Considering the road constraints and vehicle dynamics,limited polynomial candidate trajectories are generated and smoothed in a curvilinear coordinate system.Furthermore,in selecting the optimal trajectory,we develop a unified and auto-tune objective function based on the principle of least action by employing AVs to simulate drivers’behavior and summarizing their manipulation characteristics of“seeking benefits and avoiding losses.”Finally,by integrating the idea of receding-horizon optimization,the proposed framework is achieved by considering dynamic multi-performance objectives and selecting trajectories that satisfy feasibility,optimality,and adaptability.Extensive simulations and experiments are performed,and the results demonstrate the framework’s feasibility and effectiveness,which avoids both dynamic and static obstacles and applies to various scenarios with multi-source interactive traffic participants.Moreover,we prove that the proposed method can guarantee real-time planning and safety requirements compared to drivers’manipulation.

THE PRINCIPLES OF LEAST ACTION OF VARIABLE MASS NONHOLONOMIC NONCONSERVATIVE SYSTEM IN NONINERTIAL REFERENCE FRAMES

This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.

On the Fundamental Meaning of the Principle of Least Action and Consequences for a “Dynamic” Quantum Physics

The principle of least action, which has so successfully been applied to diverse fields of physics looks back at three centuries of philosophical and mathematical discussions and controversies. They could not explain why nature is applying the principle and why scalar energy quantities succeed in describing dynamic motion. When the least action integral is subdivided into infinitesimal small sections each one has to maintain the ability to minimize. This however has the mathematical consequence that the Lagrange function at a given point of the trajectory, the dynamic, available energy generating motion, must itself have a fundamental property to minimize. Since a scalar quantity, a pure number, cannot do that, energy must fundamentally be dynamic and time oriented for a consistent understanding. It must have vectorial properties in aiming at a decrease of free energy per state (which would also allow derivation of the second law of thermodynamics). Present physics is ignoring that and applying variation calculus as a formal mathematical tool to impose a minimization of scalar assumed energy quantities for obtaining dynamic motion. When, however, the dynamic property of energy is taken seriously it is fundamental and has also to be applied to quantum processes. A consequence is that particle and wave are not equivalent, but the wave (distributed energy) follows from the first (concentrated energy). Information, provided from the beginning, an information self-image of matter, is additionally needed to recreate the particle from the wave, shaping a “dynamic” particle-wave duality. It is shown that this new concept of a “dynamic” quantum state rationally explains quantization, the double slit experiment and quantum correlation, which has not been possible before. Some more general considerations on the link between quantum processes, gravitation and cosmological phenomena are also advanced.

Optic eikonal, Fermat’s principle and the least action principle

A generalized refractive index in the form of optic eikonal is defined through com- paring frame definitions of left-handed and right-handed sets and indicates the sign of the refractive index covered by the quadratic form of the eikonal equation. Fer- mat’s principle is generalized, and the general refractive law is derived directly. Under this definition, the comparison between Fermat’s principle and the least ac- tion principle is made through employing path integral and analogizing L. de Broglie’s theory.

Generalized principle of least action in electromagnetism and its applications

The generalized principle of least action in electromagnetism is presented, which is effective even though in lossy and nonreciprocal media. It is pointed out that the Maxwell’s equations can be derived from this principle. At last for example of its applications, some useful variational expressions for electromagnetic fields are derived systematically from the principle.

具有一般非线性项的基尔霍夫方程的规范基态解

研究了全空间上带有一般非线性项的基尔霍夫方程规范基态解的存在性问题,利用集中紧性原理证明了极值函数的存在性.另外,根据最小作用解的山路特征,证明了规范基态解与最小作用解是一致的.

热-盐作用下水稳碎石强度变化规律及破坏特征研究

水泥稳定碎石材料在热-盐作用下发生物理和化学侵蚀反应,使得试件强度变化规律和破坏特征发生变化。文章采用无侧限抗压强度试验和数码相机图像采集技术,分析了硫酸钠含量、成型温度、水泥含量对水稳碎石材料强度变化规律和试件破坏特征的影响。结果表明:随着硫酸钠含量增加,无侧限抗压强度先增大后减小,峰值点在2.5%,试件破坏形式由龟裂破坏转变为主裂缝破坏,再转变为多裂缝破坏;无侧限抗压强度随着成型温度、水泥含量的升高逐渐增大,且试件由龟裂破坏转变为主裂缝破坏;当试件强度强化,其破坏形式以主裂缝破坏为主;基于强度变化规律,采用最小二乘法和归一化法,建立了热-盐作用下水稳碎石无侧限抗压强度变化预测模型。

基于局部轮廓曲线的图像配准方法

图像配准是计算机视觉领域的基本问题.提出了一种基于局部轮廓曲线的图像配准方法.首先,利用图像的最小作用曲面提取从角点出发的局部轮廓曲线,并通过MLSD描述符描述轮廓曲线;其次,对曲线的MLSD特征向量进行傅里叶变换以便于使用轮盘匹配方法实现两幅图像中从角点出发的局部轮廓曲线的配准;然后运用最小二乘法迭代求解局部配准参数;最后,统计局部配准参数直方图获取全局配准参数.实验结果表明:此配准方法有较高精度.

路径积分传播子测量的研究进展

传播子在路径积分理论中扮演着核心角色,因此在路径积分理论可使用的多个现代量子物理领域中有重要价值.然而,由于其一直未能在实验中被直接测量,基于路径积分表述研究量子系统的实验进展受到了严重制约.最近,基于波函数直接测量方法,我们提出了传播子测量方案,并利用单光子实验首次成功实现了传播子的实验测量.此外,在这项研究中还首次演示了量子力学的最小作用量原理.该研究成功解决了路径积分实验研究中的技术难题.本文综述了此领域的研究进展,具体为简述波函数直接测量的基本概念和研究进展,并详细介绍传播子测量的理论模型、实验设计和实验结果.最后,介绍了一个重要的应用范例,即通过传播子测量实现最小作用量原理的实验演示.本文综述的传播子测量研究进展,将为今后使用该方法开展相关实验研究提供重要的参考.

二阶扰动Hamilton系统周期解的存在性

本文利用变分法研究了一类二阶扰动Hamilton系统的周期解。首先,给出了周期解存在的一些充分条件;其次,利用极小作用原理证明了周期解的存在性;最后,给出了满足新条件的例子。

基于最小作用量原理的岩石微振动方程及分析

为了研究冲击钻井中钻具冲击频率、岩石固有频率等对破岩效率的影响,基于最小作用量原理,建立了岩石在压头冲击作用下的微振动方程,并以此为基础,分析了岩石的质量和固有频率、压头的冲击力和冲击频率以及时间等因素与岩石振动位移的关系。分析研究发现,岩石振动位移在平衡位置处上下变化,当压头冲击力为30kN、岩石密度为2.39g/cm3时,岩石的振动位移最大,分别为1.3和8mm;固有频率为1 000,1 500和2 000Hz的岩石,分别在1 000,1 500和2 000Hz左右冲击频率下产生16,13和6mm的最大振动位移。研究结果表明:岩石的振动位移曲线类似余弦曲线,振动位移与压头的冲击力成正比,与岩石的密度(质量)成反比;当压头的冲击频率与岩石的固有频率共振时,振动位移最大。

两类Lagrange系统的周期解

用极小作用原理研究了具有次可加位势或具有次线性非线性项的Lagrange系统的周期解 。

集中谐载力作用下三边固定一边自由板的受迫振动

应用混合变量最小作用量原理求解了三边固定一边自由矩形板在任意集中谐载作用下的受迫振动 问题，建立了求解这类问题受迫振动稳态解的新方法．对于结构工程抗震问题中的振动分析给出了一个新 的解决途径．所获得的计算结果，跟现有的文献进行比较证明了其正确性．因此该方法不仅具有重要的理论 价值，而且可以为工程实际直接采用．

极小作用原理在二阶Hamilton系统中的应用

综述了用极小作用原理得到的关于二阶Hamilton系统周期解存在性的有关结果

Towards the Unified Principles for Level 5 Autonomous Vehicles

The rapid advance of autonomous vehicles(AVs)has motivated new perspectives and potential challenges for existing modes of transportation.Currently,driving assistance systems of Level 3 and below have been widely produced,and several applications of Level 4 systems to specific situations have also been gradually developed.By improving the automation level and vehicle intelligence,these systems can be further advanced towards fully autonomous driving.However,general development concepts for Level 5 AVs remain unclear,and the existing methods employed in the development processes of Levels 0-4 have been mainly based on task-driven function development related to specific scenarios.Therefore,it is difficult to identify the problems encountered by high-level AVs.The essential logical and physical mechanisms of vehicles have hindered further progression towards Level 5 systems.By exploring the physical mechanisms behind high-level autonomous driving systems and analyzing the essence of driving,we put forward a coordinated and balanced framework based on the brain-cerebellum-organ concept through reasoning and deduction.Based on a mixed mode relying on the crow inference and parrot imitation approach,we explore the research paradigm of autonomous learning and prior knowledge to realize the characteristics of self-learning,self-adaptation,and self-transcendence for AVs.From a systematic,unified,and balanced point of view and based on least action principles and unified safety field concepts,we aim to provide a novel research concept and develop an effective approach for the research and development of high-level AVs,specifically at Level 5.

一类奇异半线性椭圆方程解的存在性(英文)

运用极小作用原理获得了奇异半线性椭圆Dirichlet边值问题:-Δu=u-γ+g(x,u)x∈Ωu>0x∈Ωu=0x∈Ω的一个存在性结果,其中ΩRn(n≥3)是一个有界区域,γ是正常数.

柔顺五杆三稳态机构的设计方法

以平面柔顺五杆机构为研究对象,提出一种柔顺五杆三稳态机构的设计方法.建立了平面柔顺五杆机构的5R伪刚体模型和势能函数,基于最小作用量原理用约束优化方法确定了单输入柔顺五杆机构的运动位形及势能曲线,提出用势能极小值点数目和位置闭环方程构建优化目标函数,用无约束优化方法来设计柔顺五杆三稳态机构.最后,用两个设计实例证明了该方法可有效用于柔顺五杆三稳态机构的设计.

基于钻柱内外钻井液流速影响的横向振动频率模型

钻柱横向振动危害较大,钻井液流速是影响钻柱横向振动频率的重要因素之一。从理论上分析了钻柱内外钻井液流速对钻柱横向振动频率的影响,为减少钻柱共振发生提供了理论依据。根据最小作用量原理,用欧拉法建立考虑钻柱内钻井液流速影响的钻柱横向振动微分方程。采用力学平衡法,引入附加质量系数,建立考虑钻柱内外钻井液流速影响的钻柱横向振动微分方程。分析了钻柱外钻井液流速对横向振动频率的影响,得出了考虑钻柱内外钻井液流速影响的钻柱横向振动频率数学模型。现场应用表明,模型计算值与现场实测值的平均误差为9.15%,该模型计算结果比较符合现场实际。

基于宏观系统的冲积河流自动调整研究评述

冲积河流自动调整作用体现了河流的自适应特征,是河床演变最基本的规律,这一规律在微观上表现为输沙量与挟沙力的相互趋近,宏观上则显示河道朝一定的平衡形态或水力几何形态发展。传统的牛顿力学方法并不能完全给出河流调整过程的理论解,从宏观河流系统角度出发的研究方法不失为一种有效的解决途径。本文选取热力学中的熵与极值假设、最小作用量原理、速率定律和突变理论为基于宏观系统研究的典型代表,对这些研究方法的概念和应用进行介绍和阐述,从多种角度出发探讨河流自动调整过程中水流能量的分配、输沙效率、系统的调整路径和变化速率等特点。

基于ADAMS的助力型外骨骼特征动作驱动液压缸运动学研究

以助力型外骨骼为研究对象,以建立助力型外骨骼运动学模型以及分析外骨骼运动学特性为研究目标,以运动生物力学为基础,选择单膝下跪-起立动作为特征动作,采用多层次光学捕捉系统采集人体运动数据,采用多波峰(波谷)最小二乘法进行数据拟合,得到人体运动时特征角度的数学模型。助力型外骨骼在完成动作时需要与人体高度偕行,因此将特征角度的数学模型运用到助力型外骨骼中,建立外骨骼三维模型,在ADAMS软件中完成外骨骼特征动作仿真,以此来分析外骨骼运动学特性。