Path Planning for a Point Robot
移动机器人路径规划(共19张PPT)
路径(lùj或由直线段
序列组成 • 路径平滑：依据机器人运动学或动力学约
束形成机器人可跟踪执行的运动轨迹 • 如果(rúguǒ)考虑机器人运动学约束，则路
径轨迹的一阶导数应连续 • 如果(rúguǒ)考虑动力学约束，则路径轨迹
的二阶导数应连续
第五页，共19页。
路径(lùjìng)规划
• 基于地图(dìtú)的全局路径规划 • 环境已知的离线全局路径规划 • 环境未知的在线规划 • 基于进化算法 • 基于广义预测控制 • 基于传感器的局部路径规划 • 增量式构造当前可视区域路径图的规划方
法 • 基于近似单元分解的局部路径规划方法 • 基于微分平坦系统理论的运动规划方法
Brooks R, Robis A. Layered Control System for a Mobile Robot. IEEE Trans on Robotics & Automation. 1986, 2(1):14-23
第二页，共19页。
路径(lùjìng)规划
• 以C表示机器人的位形空间，以F表示无碰 撞的自由位形空间。给定机器人初始位形 qinit和目标位形qgoal，在F中寻找一条连接 这两点的连续曲线，满足某些性能指标， 如路径最短、行走时间最短、工作 (gōngzuò)代价最小等。
• Dijkstra算法：通过枚举求解两点间距离最 短
• A*算法：通过代价评估加快搜索(sōu suǒ)
• 梯度法：由起点到目标点距离下降最大梯 度方向搜索(sōu suǒ)，不能保证全局最短， 可能陷入局部最小点
• 距离变换法：逆向的梯度法，保证全局最 短，但搜索(sōu suǒ)效率随栅格和障碍物
• 衍生算法：退火遗传算法、改进遗传算子等
机器人路径规划
路径规划1.引言1.1.研究目的1.2.文档范围1.3.参考文献2.概述2.1.路径规划的定义2.2.应用领域3.基本概念3.1.3.2.路径规划3.3.环境模型4.路径规划算法4.1.Dijkstra算法4.2.A算法4.3.RRT算法4.4.离散化路径规划算法5.传感器和感知技术5.1.摄像头5.2.激光雷达5.3.超声波传感器6.运动和控制6.1.运动学模型6.2.动力学模型6.3.控制器设计7.路径规划软件工具7.1.ROS (Robot Operating System)7.2.MoveIt!7.3.OMPL (Open Motion Planning Library)8.实验设计和结果分析8.1.实验目的8.2.实验设置8.3.实验结果9.总结与展望附件：- 图表和实验数据- 代码示例法律名词及注释：1.：根据《产品安全规范》定义，是一种可编程、具有感知能力、可以协作工作的自动化机械设备。
2.路径规划：指在给定环境中计算出能够实现指定任务的运动路径的过程。
3.环境模型：在路径规划中，环境模型是对所处环境的描述，包括障碍物、目标位置等。
4.Dijkstra算法：一种基于图论的最短路径算法，用于计算两个节点之间的最短路径。
5.A算法：一种启发式搜索算法，通过估计函数来优化搜索路径，适用于路径规划问题。
6.RRT算法：快速随机树算法是一种基于随机采样的路径规划算法。
7.离散化路径规划算法：将连续的运动空间离散化为网格，然后在网格中搜索路径。
8.ROS：一种操作系统，提供了一系列工具和库，用于开发应用程序。
9.MoveIt!：ROS中的一种功能强大的运动规划和控制软件包。
10.OMPL：一种开源运动规划库，支持多种路径规划算法。
(完整版)机器人路径规划_毕业论文外文翻译_
外文文献：Space Robot Path Planningfor Collision AvoidanceYuya Yanoshita and Shinichi TsudaAbstract —This paper deals with a path planning of space robot which includes a collision avoidance algorithm. For the future space robot operation, autonomous and self-contained path planning is mandatory to capture a target without the aid of ground station. Especially the collision avoidance with target itself must be always considered. Once the location, shape and grasp point of the target are identified, those will be expressed in the configuration space. And in this paper a potential method.Laplace potential function is applied to obtain the path in the configuration space in order to avoid so-called deadlock phenomenon. Improvement on the generation of the path observed by applying path smoothing method, which utilizes the spline function interpolation. This reduces the computational load and generates the smooth path of the space robot. The validity of this approach is shown by a few numerical simulations.Key Words —Space Robot, Path Planning, Collision Avoidance, Potential Function, Spline InterpolationI. INTRODUCTIONIn the future space development, the space robot and its autonomy will be key features of the space technology. The space robot will play roles to construct space structures and perform inspections and maintenance of spacecrafts. These operations are expected to be performed in an autonomous.In the above space robot operations, a basic and important task is to capture free flying targets on orbit by the robotic arm. For the safe capturing operation, it will be required to move the arm from initial posture to final posture without collisions with the target.The configuration space and artificial potential methods are often applied to the operation planning of the usual robot. This enables the robot arm to evade the obstacle and to move toward the target. Khatib proposed a motion planning method, in which between each link of the robot and the obstacle the repulsive potential is defined and between the end-effecter of the robot and the goal the attractive potential is defined and by summing both of the potentials and using the gradient of this potential field the path is generated. This method is advantageous by its simplicity and applicability for real-time operation. However there might be points at which the repulsive force and the attractive force are equal and this will lead to the so-called deadlock.In order to resolve the above issue, a few methods are proposed where the solution of Laplace equation is utilized. This method assures the potential fields without the local minimum, i.e., no deadlock. In this method by numerical computation Laplace equation will be solved and generates potential field. The potential field is divided into small cells andon each node the discrete value of the potential will be specified.In this paper for the elimination of the above defects, spline interpolation technique is proposed. The nodal point which is given as a point of path will be defined to be a part of smoothed spline function. And numerical simulations are conducted for the path planning of the space robot to capture the target, in which the potential by solving the Laplace equation is applied and generates the smooth and continuous path by the spline interpolation from the initial to the final posture.II. ROBOT MODELThe model of space robot is illustrated in Fig.1.The robot is mounted on a spacecraft and -plane motion of the end-effecter. In this case we additional freedom of the spacecraft attitude angle and this will be considered the additional rotary joint. This means that the space robot is three linked with 3 DOF (Degree Of Freedom). The length of each link and the angle of each rotary joint are given byand (i = 1,2,3) , respectively. In order to simplify the discussions a few assumptions are made in this paper:-the motion of the space robot is in-plane,i.e., two dimensional one.-effect of robot arm motion to the spacecraft attitude is negligible.-robot motion is given by the relation of static geometry and not explicitly depending on time.-the target satellite is inertially stabilized.In general in-plane motion and out-of-plane motion will be separately performed. So we are able to assume the above first one without loss of generality. The second assumption derives from the comparison of theratio of mass between the robot arm and the spacecraft body. With respect to the third assumption we focus on generating the path planning of the robot and this is basically given by the static nature of geometry relationship and is therefore not depending on the time explicitly. The last one means the satellite is cooperative.Fig.1 Model of Two-link Space RobotIII. PATH PLANNING GALGORITHMA. Laplace Potential GuidanceThe solution of the Laplace equation (1) is called a Harmonic potential function, and its and minimum values take place only on the boundary. In the robot path generation the boundary means obstacle and goal. Therefore inside the region where the potential is defined, no local minimum takes place except the goal. This eliminates the deadlock phenomenon for path generation.（1）The Laplace equation can be solved numerically. We define two dimensional Laplace equation as below:（2）And this will be converted into the difference equation and then solved by Gauss -Seidel method. In equation (2) if we take the central difference formula for second derivatives, the following equation will be obtained:2222220x y(x x,y )2(x,y )(x x,y )x(x,y y )2(x,y )(x,y y )y ∆∆∂∅∂∅+=∂∂∅+∆-∅+∅-∆⇒∅+∆-∅+∅-∆+ （3） where ， are the step (cell) sizes between adjacent nodes for each x , y direction. If the step size is assumed equal and the following notation is used:Then equation (3) is expressed in the following manner:1,1,,1,1,0i j i j i j i j i j +-+-∅+∅+∅+∅-4∅= （4）And as a result, two dimensional Laplace equation will be converted into the equation (5) as below:i,j i 1,j i 1,j i,j 1i,j 114+-+-∅=(∅+∅+∅+∅) （5） In the same manner as in the three dimensional case, the difference equation for the three dimensional Laplace equation will be easily obtained by the following:i,j ,k i 1,j ,k i 1,j ,k i,j 1,k i,j 1,k i,j ,k 1i,j ,k 116+-+-+-∅=(∅+∅+∅+∅+∅+∅) （6） In order to solve the above equations we apply Gauss-Seidel method and +1 )-th iterative calculations of the potential.In the above computations, as the boundary conditions, a certainpositive number is defined for the obstacle and 0 for the goal. And as the initial conditions the same number is also given for all of the free nodes. By this approach during iterative computations the value of the boundary nodes will not change and the values only for free nodes will be varying. Applying the same potential values as the obstacle and in accordance with the iterative computational process, the small potential around the goal will be gradually propagating like surrounding the obstacle. The potential field will be built based on the above procedure.Using the above potential field from 4 nodal points adjacent to the node on which the space robot exists, the smallest node is selected for the point to move to. This procedure finally leads the space robot to the goal without collision.B. Spline InterpolationThe path given by the above approach does not assure the smoothly connected one. And if the goal is not given on the nodal point, we the cells into much more smaller cells. This will increase the computational load and time.In order to eliminate the above drawbacks we propose the utilization of spline interpolation technique. By assigning the nodal points given by the solution to via points on the path, we try to obtain the smoothly connected path with accurate initial and final points.In this paper the cubic spline was applied by using MATLAB command.C. Configuration SpaceWhen we apply the Laplace potential, the path search is assured only inthe case where the robot is expressed to be a point in the searching space. The configuration space(C-Space), where the robot is expressed as a point, is used for the path search. To convert the real space into the C-Space the calculation to judge the condition of collision is performed and if the collision exists, the corresponding point in the C-space is regarded as the obstacle. In this paper when the potential field was generated, the conditions of all the points in the real space, corresponding to all the nodes, were calculated. The judgment of intersection between a segment constituting the robot arm and a segment constituting the obstacle at each node was made and if the intersection takes place, this node is treated as the obstacle in the C-Space.IV.NUMERICAL SIMULATIONSBased on the above approach the path planning for capturing a target satellite was examined using a space robot model. In this paper we assume the space robot with two dimensional and 2 DOF robotic arm as shown in Fig.1.The length of each link is given as follows:l1 =1.4[m], l2 = 2.0[m], l3 = 2.0[m] ,and the target satellite was assumed 1m square. The grasp the geometrical relation between the space robot and the target satellite. When we consider the operation after capturing the target, it is desirable for the space robot to this paper the end-effecter will reach the target when the manipulability is maximized. In the 3DOF case, not depending on the spacecraft body attitude, the manipulability is measured by. And if we assume the end-effector of the space robot should be vertical to the target,then all of the joints angles are predetermined as follows:123160.7,32.8,76.5o o o θθθ===As all the joints angles are determined, the relative position between the spacecraft and the target is also decided uniquely. If the spacecraft is assumed to locate at the origin of the inertial frame (0, 0), the goal is given by (-3.27, -2.00) in the above case. Based on these preparations, we can search the path to the goal by moving the arm in the configuration space.Two simulations for path planning were carried out and the results are shown below.A. 2 DOF RobotIn order to simplify the situation, the attitude angle(Link 1 joint angle) is assumed to coincide with the desirable angle from the beginning. The coordinate system was assumed as shown in Fig.2.was taken into consideration for the calculation of the initial condition of the Link 2 and its goal angles:Innitial condition:Goal condition:In this case the potential field was computed for the C-Space with 180 segments. Fig.3 shows the C-Space and the in the center is given by the obstacle mapped by the spacecraft body. The left side portion is a mapping of the target satellite. Fig.4 shows a generated path and this was spline-interpolated curve by using alternate points of discrete data for smoothing.Fig.3 2 DOF C-SpaceFig.4 Path in C-Space(2 DOF)When we consider the rotation of spacecraft body, -180 degrees are equal to +180 degrees and, then, the state over -180 degrees will be started from +180 degrees and again back to the C-Space. For this reason theperiodic boundary condition was applied in order to assure the continuity of the rotation. For the simplicity to look at the path, the mapped volume by the spacecraft body was omitted. Also for the simplicity of the path expression the chart which of -180 degrees in the direction was illustrated. From this figure it is easily seen that over -180 degrees the path is going toward the goal C. B and C are the same goal point.V. CONCLUSIONIn this paper a path generation method for capturing a target satellite was proposed. And its applicability was demonstrated by numerical simulations. By using interpolation technique the computational load will be decreased and smoothed path will be available. Further research will be recommended to incorporate the attitude motion of the spacecraft body affected by arm motion.中文译文：空间机器人避碰路径规划Yuya Yanoshita and Shinichi Tsuda摘要：本文论述的是空间机器人路径规划，这种规划主要运用的是避碰算法。
讲稿-RobotPathPlanningus
。
1. Introduction
移动机器人障碍物规避算法，就是在约束条件下，比如已知 障碍物O的位置和形状的情况下，找到一条从起点S到目标终点 G的路径。所用的参数都作为算法的输入，输出或者是一条从S 到C最佳的轨迹，或者是与局部最优轨迹相关的方向。通过路 径算法进行补偿函数的最优化可以分两步进行。第一步计算 出轨迹的长度(或者是需要计算出轨迹的时间)。第二步保证路 径的安全性(例如：与障碍物的距离).因此，如何在满足这些要
A PSO parameter tuning PSO参数调整 本节列出了等式(20)中不同的常量设置对算法的影响。如图
2所示，可以观察出几个显著的特点。
parison 在本节中，我们将说明我们的算法与其
他两种算法----Potential Field和 Visibility Graph算法比较的结果。 图5所示为在标准的机器人足球环境下 的3种算法的结果。采用样条的方法在 30次PSO迭代时候就找到了短和平滑的 轨迹。其中，每个种群包含15个粒子。 采用VG算法的机器人，也能够找到最短 路径，但是机器人必须在急转弯的时候
、 求的前提下找到可接受的折衷方案，就是障碍物规避算法的核 心问题。
在当前的机器人文献中，提到了许多障碍物规避算法。不幸的 是，算法中的大部分只是将一些点作为输出，这样造成机器 人执行困难。机器人能够沿着点与点之间的线段移动，但是 这种移动是不连续的。机器人必须在线段的终点停止，调整 其方向后再继续。可以采用相关函数计算插补点，以有利于 机器人的运动。这种方法能够实现快速到达终点的目的，但 是在障碍物的约束下，这些轨迹往往不是最优轨迹，而且会 产生碰撞的可能性。
path planning 移动机器人路径规划方法综述
移动机器人路径规划方法1.1路径规划方法路径规划技术是机器人研究领域中的一个重要课题，是机器人导航中最重要的任务之一,国外文献常将其称为Path Planning,Find-PathProblem,Collision-Free,ObstacleAvoidance, MotionPlanning,etc.所谓机器人的最优路径规划问题，就是依据某个或某些优化准则(如工作代价最小、行走路线最短、行走时间最短等)，在其工作空间中找到一条从起始状态到目标状态的能避开障碍物的最优路径。
路径规划主要涉及的问题包括：利用获得的移动机器人环境信息建立较为合理的模型，再用某种算法寻找一条从起始状态到目标状态的最优或近似最优的无碰撞路径；能够处理环境模型中的不确定因素和路径跟踪中出现的误差，使外界物体对机器人的影响降到最小；如何利用已知的所有信息来引导机器人的动作，从而得到相对更优的行为决策。
这其中的根本问题是世界模型的表达和搜寻策略。
障碍物在环境中的不同分布情况当然直接影响到规划的路径，而目标位置的确定则是由更高一级的任务分解模块提供的[8]。
根据机器人对环境信息掌握的程度和障碍物运动状态的不同，移动机器人的路径规划基本上可分为以下四类:①已知环境下的对静态障碍物的路径规划;②未知环境下的对静态障碍物的路径规划;③已知环境下对动态障碍物的路径规划;④未知环境下对动态障碍物的路径规划。
因此根据机器人对环境信息掌握的程度不同，可将机器人的路径规划问题可分为二大类即：基于环境先验信息的全局路径规划问题和基于不确定环境的局部路径规划问题。
目前，路径规划研究方法大概可分为两大类即：传统方法和智能方法。
1.2传统路径规划方法传统的路径规划方法主要包括：可视图法(V-Graph)、自由空间法(Free Space Approach)、人工势场法（Artificial Potential Field）和栅格法(Grids)等。
⑴可视图法（V-Graph）可视图法是Nilsson1968年在文献[9]中首次提出。
机器人英语翻译
机器⼈英语翻译外⽂翻译专业⼯业⼯程学⽣姓名钱晓光班级BD机制082学号0820101205指导教师邱亚兰外⽂资料出处：Applied Mathematics and Computation 185 (2007) 1149–1159附件： 1.外⽂资料翻译译⽂2.外⽂原⽂灵活的双臂空间机器⼈捕捉物体的控制动⼒学译者：钱晓光⽂摘：在本⽂中,我们提出有效载荷的影响，来控制⼀个双臂空间机器⼈灵活的获取⼀个物体。
该拉格朗⽇公式动⼒学模型推导出了机器⼈系统原理。
源⾃初始条件的动⼒学模型模拟了整个系统的获取过程。
⼀个PD控制器设计,其⽬的是为了稳定机器⼈来捕捉对象，动态模拟执⾏例⼦：例:1.机器⼈系统不受控制发⽣撞击，仿真结果表明影响效果。
2.空间机器⼈捕获物体的成功是伟⼤的。
仿真结果表明,该机器⼈关节⾓和机械⼿的迅速程度已经达到稳定。
关键词:柔性臂;空间机器⼈;冲击;动⼒学;PD控制⽅案:圆柱型机器⼈;技能训练1.介绍空间机器⼈将成为⼈类未来在太空检验、装配和检索故障等⽇常⼯作的主要元素。
空间机器⼈满⾜宇航员额外的活动，对这些来说是很有价值的。
然⽽,⼈类⽣活配套设施的成本和时间对航员是有限制的，⾼度风险使空间机器⼈成为宇航员助⼿的选择。
增加设备的流动性, ⾃由飞⾏系统中⼀个或多个臂安装在⼀艘装有推进器⾥，然⽽,扩展推进器的使⽤却得到了极⼤的限制。
⼀个⾃由浮动的操作模式能增加系统的可操作性。
有很多的研究成果对刚性臂空间机器⼈做了研究。
考虑到空间机器⼈以下的特点:轻质量、长臂、重载荷、灵活、有效性等，切应考虑到良好的控制精度和性能。
与此同时,也存在着许多研究动态建模和单臂空间机器⼈灵活控制的成果。
作者描述了碰撞动⼒学建模⽅案的空间机器⼈和研究了多⼿臂灵活空间机器⼈。
吴中书使⽤假设模态⽅法描述了弹性变形,建⽴了动态模型,研究了拉格朗⽇公式和仿真的柔性双臂空间机械臂。
由两个特定操作阶段:影响阶段和撞击阶段。
影响阶段确定了初始条件的对象。
路径规划毕业论文
基于蚁群算法的机器人路径规划摘要当前机器人朝着智能化的方向发展着，已经能够解决一些人类自身难以完成的任务。
机器人的研究方向分为好多个分支，其中机器人路径规划就是热点问题之一。
主要用于解决机器人在复杂环境下做出路径选择，完成相应任务的问题。
典型的路径规划问题是指在有障碍物的工作环境中，按照一定的评价标准（行走路线最短、所用时间最少等）为机器人寻找一条从起点到终点的运动路径，让机器人在运动过程中能安全、无碰撞地通过所有的障碍物。
基于蚁群算法的机器人路径规划的研究，利用仿真学的基本思想，根据生物蚂蚁协作和觅食的原理，建立人工蚁群系统。
本文介绍了使用基本蚁群算法和改进蚁群算法在机器人路径规划中的应用，以栅格法作为路径规划的环境模型建立方法。
其中改进蚁群算法依据最大最小蚂蚁系统原理和信息素奖励思想，还增加了其它启发信息来指导路径的搜索。
本文中介绍的基本蚁群算法应用蚁周模型对找到的路径进行信息素的更新，而在改进蚁群算法中，则综合使用了局部信息素更新原则和全局信息素更新原则。
另外在本文中介绍的改进蚁群算法使用了回退策略和落入陷阱时的信息素惩罚机制，帮助处理了蚂蚁在寻找路径过程中，落入陷阱后的问题。
不过改进后的蚁群算法的及时寻找到最优解的特性仍然有待于进一步的提高。
关键词：路径规划，蚁群算法，改进Path Planning for Robot Based on Ant ColonyAlgorithmAbstractNow robots are developing in the direction of intelligent, they have been able to solve some hard task as human beings do. Robot research has divide into the direction of large number of branches, where the robot path planning is one of hot issues. it is mainly used to solve the robot path in a complex environment to make choices, to complete the task. A typical path planning problem is that there are obstacles in the work environment, according to certain evaluation criteria (the shortest walking route, the minimum time spent, etc.) to find a robot's movement from origin to destination path, let the robot in motion of safe, collision-free through all the obstacles.Robot path planning research based on ant colony algorithm, is according to the simulation research, use the biological ant principles of feeding and cooperation and the establishment of artificial ant colony system. This article describes the use of basic ant colony algorithm and improved ant colony algorithm in robot path planning applications with using the grid method to establish the environment model of path planning. Improved ant colony algorithm is based on the maximum and minimum ant system theory and pheromone reward ideas. It has added other enlightening information to guide the path research. The basic ant colony algorithm described in this article uses the ant-cycle model to update the pheromone for the found path, in the improved ant colony algorithm, uses both the local pheromone updating principles and global pheromone updating the principles. Improved ant colony algorithm in this paper uses the fallback strategy, and the pheromone punishment mechanism when falling into trap to help deal with the ants in the process of finding a path falling into the trap. But the improved ant colony algorithm to find the optimal solution remains to be further improved in the optimal properties.Keywords: path planning, ant colony algorithm, improvedII目录第1章引言 (1)1.1问题的提出 (1)1.1.1研究的背景 (1)1.1.2研究的意义 (2)1.2本文研究路线 (3)1.2.1主要工作内容 (3)1.2.2目标 (3)1.3论文的主要内容 (3)第2章蚁群算法与机器人路径规划研究概述 (5)2.1蚁群算法和机器人路径规划的发展历史，现状，前景 (5)2.1.1蚁群算法的发展历史，现状，前景 (5)2.1.2移动机器人路径规划的发展历史，现状，前景 (6)2.2蚁群算法的特点 (7)2.2.1并行性 (7)2.2.2健壮性 (7)2.2.3 正反馈 (8)2.2.4局部收敛 (8)2.3基于蚁群算法的机器人路径规划实现的开发方式 (8)2.3.1开发语言的选择 (8)2.3.2开发工具的选择 (8)2.4蚁群算法介绍 (9)2.4.1 基本蚁群算法 (9)2.4.2 基本蚁群算法改进方案简介 (11)2.5机器人路径规划的环境模型建立 (11)2.5.1 栅格法 (11)2.6使用matlab仿真 (12)2.6.1 matlab仿真介绍 (12)2.7本章小结 (12)第3章基于蚁群算法的机器人路径规划分析与设计 (13)3.1基于蚁群算法的机器人路径规划需求设计 (13)3.2基于蚁群算法的机器人路径规划的要求 (13)3.3 主要的数据结构 (13)3.4基本蚁群算法实现机器人路径规划功能模块 (14)3.4.1程序入口模块 (14)3.4.2 算法运行的主体函数模块 (14)3.4.3 程序运行的清理模块 (15)3.4.4 下一步选择模块 (15)3.4.5 随机性选择模块 (16)3.4.6 路径处理和信息记录模块 (17)3.5 基本蚁群算法实现机器人路径规划整体逻辑设计 (17)3.5.1基本蚁群算法实现机器人路径规划整体结构图 (17)3.5.2基本蚁群算法实现机器人路径规划逻辑结构图 (19)3.6改进蚁群算法实现机器人路径规划功能模块 (20)3.6.1 程序运行环境处理修改部分 (20)3.6.2 下一步选择的修改部分 (20)3.6.3信息素更新和路径处理修改部分 (21)3.7 改进蚁群算法实现机器人路径规划整体逻辑设计 (22)3.7.1改进蚁群算法实现机器人路径规划整体结构图 (22)3.7.2改进蚁群算法实现机器人路径规划逻辑结构图 (23)3.8系统开发环境介绍 (24)3.8.1开发环境 (24)3.8.2调试环境 (24)3.8.3测试环境 (24)第4章基于蚁群算法的机器人路径规划的实现 (25)4.1基于基本蚁群算法的实现 (25)4.1.1算法运行的主体函数模块 (25)4.1.2 下一步选择模块 (26)4.2基于改进蚁群算法的实现 (27)4.2.1下一步选择模块 (28)4.2.2随机性选择模块 (29)4.3本章小结 (31)第5章基于蚁群算法实现机器人路径规划的仿真实验 (32)5.1运行环境 (32)5.2基于基本蚁群算法实现机器人路径规划仿真实验 (32)5.2.1 仿真步骤 (32)5.2.2 使用地图模型为5-1的仿真 (32)5.2.3 使用基本蚁群算法仿真结果 (33)IV5.2.4基于改进蚁群算法的仿真 (35)5.3 多次重复仿真实验记录 (36)5.4 本章小结 (37)第6章结论 (38)致谢 (39)参考文献 (40)基于蚁群算法的机器人路径规划第1章引言1.1问题的提出1.1.1研究的背景蚁群算法(ant colony optimization, ACO)，又称蚂蚁算法，是一种用来在图中寻找优化路径的机率型算法。
机器人路径规划
1绪论1.1机器人简介1.1.1什么是机器人机器人一词不仅会在科幻小说、动画片等上看到和听到，有时也会在电视上看到在工厂进行作业的机器人，在实际中也有机会看到机器人的展示。
今天，说不定机器人就在我们的身过，但这里我们要讨论的是什么是机器人学研究的机器人。
机器人（robot）一词来源下1920年捷克作家卡雷尔. 查培克（Kapel Capek）所编写的戏剧中的人造劳动者，在那里机器人被描写成像奴隶那样进行劳动的机器。
后来作为一种虚构的机械出现在许多作品中，代替人们去完成某些工作。
20世纪60年代出现了作为可实用机械的机器人。
为了反这种机器人同虚构的机器人及玩具机器人加以区别，称其为工业机器人。
工业机器人的兴起促进了大学及研究所开展机器人的研究。
随着计算机的普及，又积极地开展了带有智能的机器人的研究。
到70年代，机器人作为工程对象已经被确认，机器人一词也受到公认。
目前，机器人学的研究对象已不仅仅是工业机器人了。
即便是实际存在的机器人，也很难把它定义为机器人，而且其定义也随着时代在变化。
这里简单地反具有下述性质的机械看作是机器人：1.代替人进行工作：机器人能像人那样使用工具和机械，因此，数控机床和汽车不是机器人。
2.有通有性：既可简单地变换所进行的作为，又能按照工作状况的变化相应地进行工作。
一般的玩具机器人不能说有通用性。
3.直接对个界作工作：不仅是像计算机那样进行计算，而且能依据计算结果对外界结果对外界产生作用。
机器人学把这样定义的机器人作为研究对象。
1.1.2机器人的分类机器人的分类方法很多，这里我们依据三个有代表性的分类方法列举机器人的种类。
首先，由天机器人要代替人进行作业，因此可根据代替人的哪一个器官来分类：操作机器人（手）：利用相当于手臂的机械手、相当于手指的手爪来使物体协作。
移动机器人（腿）：虽然已开发出了2足步行和4足步行机器人，但实用的却是用车轮进行移动的机器人。
（本文以轮式移动机器人作为研究对象）视觉机器人（眼）：通过外观检查来除掉残次品，观看人的面孔认出是谁。
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Three-Dimensional Space
Shortest path passes through none of the vertices
Computing the shortest collision-free path in a polyhedral space is NP-hard
Configuration Space: Tool to Map a Robot to a Point
Problem
free space
s free path
g
Problem
semi-free path
Types of Path Constraints
Local constraints: lie in free space Differential constraints: have bounded curvature Global constraints: have minimal length
Robot Robot
Attractive and Repulsive fields
ห้องสมุดไป่ตู้
Local-Minimum Issue
Perform best-first search (possibility of combining with approximate cell decomposition) Alternate descents and random walks Use local-minimum-free potential (navigation function)
Trapezoidal decomposition
Trapezoidal decomposition
Trapezoidal decomposition
Trapezoidal decomposition
Trapezoidal decomposition
…
critical events criticality-based decomposition
1. Roadmap
Represent the connectivity of the free space by a network of 1-D curves Decompose the free space into simple cells and represent the connectivity of the free space by the adjacency graph of these cells Define a function over the free space that has a global minimum at the goal configuration and follow its steepest descent
2. Cell decomposition
3. Potential field
Cell-Decomposition Methods
Two classes of methods: Exact cell decomposition The free space F is represented by a collection of non-overlapping cells whose union is exactly F Example: trapezoidal decomposition
Complexity
Simple algorithm: O(n3) time Rotational sweep: O(n2 log n) Optimal algorithm: O(n2) Space: O(n2)
Rotational Sweep
Rotational Sweep
Rotational Sweep
Goal Goal
FGoal = − k p ( x − xGoal )
Go al F
o Obstacle F
⎧ ⎛ 1 1 ⎞ 1 ∂ρ ⎪η ⎜ − ⎟ 2 ⎜ ρ ρ ⎟ ρ ∂x if ρ ≤ ρ 0 , FObstacle = ⎨ ⎝ 0⎠ ⎪ 0 if ρ > ρ 0 ⎩
orc
e
rce
n Motio
2. Cell decomposition
3. Potential field
Potential Field Methods
Approach initially proposed for real-time collision avoidance [Khatib, 86]. Hundreds of papers published on it.
Path-Planning Approaches
1. Roadmap
Represent the connectivity of the free space by a network of 1-D curves Decompose the free space into simple cells and represent the connectivity of the free space by the adjacency graph of these cells Define a function over the free space that has a global minimum at the goal configuration and follow its steepest descent
g
s
Simple Algorithm
Install all obstacles vertices in VG, plus the start and goal positions 2. For every pair of nodes u, v in VG 3. If segment(u,v) is an obstacle edge then 4. insert (u,v) into VG 5. else 6. for every obstacle edge e 7. if segment(u,v) intersects e 8. then goto 2 9. insert (u,v) into VG 10. Search VG using A* 1.
Homotopy of Free Paths
Motion-Planning Framework
Continuous representation Discretization Graph searching
(blind, best-first, A*)
Path-Planning Approaches
2. Cell decomposition
3. Potential field
Roadmap Methods
Visibility graph
Introduced in the Shakey project at SRI in the late 60s. Can produce shortest paths in 2D configuration spaces
Rotational Sweep
Rotational Sweep
Reduced Visibility Graph
can’t be shortest path
tangent segments
Eliminate concave obstacle vertices
Generalized (Reduced) Visibility Graph
Simple Navigation Function
2 1 2 3 4 5 1 0 2 1 3 2 3 4
Octree Decomposition
Sketch of Algorithm
1. 2. 3. 4. 5. 6. 7. 8. Compute cell decomposition down to some resolution Identify start and goal cells Search for sequence of empty/mixed cells between start and goal cells If no sequence, then exit with no path If sequence of empty cells, then exit with solution If resolution threshold achieved, then exit with failure Decompose further the mixed cells Return to 2
Roadmap Methods
Visibility graph Voronoi diagram Silhouette
Probabilistic roadmaps
First complete general method that applies to spaces of any dimension and is singly exponential in # of dimensions [Canny, 87]
Trapezoidal decomposition
Planar sweep O(n log n) time, O(n) space
Cell-Decomposition Methods
Two classes of methods: Exact cell decomposition Approximate cell decomposition F is represented by a collection of non-overlapping cells whose union is contained in F Examples: quadtree, octree, 2n-tree