自主移动机器人运动规划的若干算法研究
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摘要
地面自主移动机器人是机器人研究领域中的一个重要分支,集人工智能、智能控制、信息处理等专业技术为一体,其发展对国防、社会、经济和科学技术具有重大的影响力,已成为各国高科技领域的战略性研究目标。机器人运动规划是自主移动机器人导航的核心关键技术之一。
移动机器人运动规划是指设计一个适当的控制输入使系统沿某一轨迹从一开始位置运动到另一终点位置,包含两方面内容：路径规划和跟踪控制。
本文围绕这两个内容,对移动机器人的路径规划和轨迹跟踪分别进行了研究,在传统方法的基础上,提出了一些改进算法及新的解决方案,以提高算法的计算效率,扩展其使用范围。具体的研究内容包括以下几个方面：
1.将第二类偏微分方程引入到移动机器人路径规划问题求解中,探讨了偏微分方程在路径规划中的应用,扩展了路径规划的求解算法种类。该算法克服了其它路径规划算法的缺点,比如经典势场算法中的极小问题、RRT算法的无谓耗费等。算法的数学结构和求解时的自适应网格细化保证了该算法的适应性。
2.针对快速扩展随机树RRT算法只能在已知环境中进行移动机器人路径规划的限制,将RRT算法与基于滚动窗口的路径规划相结合,提出了一种改进的移动机器人路径规划算法。该算法只考虑窗口环境地图,避免了全局搜索,使得RRT算法可以在未知环境下的移动机器人路径规划中应用。算法引入启发式估价函数,使得随机树易于朝目标点方向生长,同时运用回归分析生成新节点,避免了可能产生的局部极小,增强了算法搜索未知空间的能力。
3.为了提高移动机器人在未知环境下的运行效率,将应激式爬行虫Bug算法和滚动路径规划相结合,只考虑当前状态下所必须的传感数据,不计算障碍物的边线解析式,节省了存储空间,保证了规划算法的实时性。运用虚拟障碍的概念,解决了该算法在陷阱区域容易左右徘徊的问题。为了保证路径规划的完备性和Bug算法的全局最优,同时给出了全局收敛标准。
4.详细分析了三次螺线作为移动机器人跟踪路径所具有的各种优异的几何特性,定义路径光滑成本函数,利用三次螺线对规划路径光滑化,使得移动机器人易于跟踪所规划的路径,扩展了移动机器人的应用领域。
5.详细分析了履带式移动机器人的受力特点,提出了一种适于进行控制器设计的履带移动机器人模型。根据履带式移动机器人动力学模型和运动学模型,设计了机器人的轨迹跟踪控制器。在控制器的设计中考虑了履带—地面作用,引入参数对其描述。考虑到机器人动力学约束,同时引入机器人速度、加速度控制策略以保证机器入运动平滑。
6.研究了未知环境下非完整轮式移动机器人的运动规划问题。将Bug算法与基于滚动窗口的路径规划相结合来规划移动机器人路径,根据建立的移动机器人通用动力学模型和无打滑非完整运动约束条件,采用非线性反馈线性化方法设计轮式机器人的轨迹跟踪控制器。建模时直接以两驱动后轮的角速度为控制输入,降低了跟踪误差。通过仿真实验和对比实验,验证了方法的有效性。
本文在最后对全文进行了总结,并且对今后进一步的研究方向进行了展望。
Autonomous mobile robot is an important branch of robot. It involves artificial intelligence, intelligent control, information procession, image procession and detection and conversion. The development of autonomous mobile robot has imposing on the defense, society, economy and academy, and becomes the tactic research object of high technology of all countries. Motion planning for autonomous mobile robot is one of the most critical technologies in the autonomous navigation researches.
The motion planning is to generate control input for the mobile robot to drive from an initial configuration to a goal configuration. Path planning and tracking control are two fundamental issues in the motion planning robotics.
This dissertation is focused on the path planning and the trajectory tracking. Several improved methods and novel solutions are presented in order to improve computational efficiency, and additionally extend application domains. The main content of this dissertation include the following aspects:
1. This dissertation introduced the second kind of partial differential equation in mobile robot path planning, has exploited the application of PDE method in mobile robot path planning problem, then new technology and method are provide for mobile robot path planning research. The algorithm overcame disadvantages of the other path planning algorithms, such as local minimization of classical potential field algorithm, unnecessary cost of RRT algorithm and so on. The mathematics principle of this algorithm and adaptive mesh has guaranteed this algorithm compatibility.
2. To solve the limitations of Rapidly-Exploring Random Tree (RRT) algorithm, which only can be used in path planning when the environment is known, with combination of RRT algorithm and rolling path planning, this dissertation proposes an improved path planning. Only the local environmental map is calculated in the planning, thus the searching all environmental map is avoided, so that the RRT algorithm can be used in path planning not only when the environment is known but also unknown. By introducing the heuristic evaluation function, the exploring random tree can grow in the direction of target point. The regression analysis, which avoids local minima, enhances the capability of searching unknown space.
3. In order to enhance the planning efficiency for mobile robot in unknown environment, this dissertation combined Bug algorithm and rolling path planning. Only the necessary sensing data instead of the analytical expression of the obstacle are calculated in planning so as to save memory, thus the planning in real-time is guaranteed. As one of the innate limitations of algorithm, the mobile robot tends to enter the trap situation due to local minima, so this dissertation solves this problem utilizing the concept of virtual obstacle. In order to maintain the planner's completeness, a global criterion is added in order to guarantee convergence to the goal.
4. The cubic spiral for mobile robot path tracking is well studied here and some excellent characteristics are found. Then the cubic spiral curve is used to smooth the collision-free path by defining the cost functions of path for smoothness. Therefore the mobile robot is easy to track and application field of mobile robot is extended.
5. A kind of tracked mobile robot model that is suitable for the design of controller is proposed through analyzing the force characteristics of the tracked mobile robot. Based on the dynamic model and kinematics constraints of tracked mobile robot, a trajectory tracking controller is designed. Parameters are introduced to describe the track-soil interactions. Considering the dynamics of mobile robot, the limited control strategy is introduced to guarantee the robot's smooth motion.
6. The motion planning of nonholonomic wheeled mobile robot working in the unknown environment is researched. This dissertation combined the Bug algorithm and rolling path planning in the path planning for mobile robot. Based on the general dynamic model and non-slipping nonholonomic kinematics constraint of mobile robot, a trajectory tracking control system is designed by nonlinear feedback linearization. The angular velocities of the two back driving wheels are the input data so that the tracking errors are decreased. The simulation and experimental results verified the algorithm's effectiveness.
A summary of the research conclusions and a discussion on the most promising paths of future research work are presented in the last chapter of this dissertation.
移动机器人运动规划是指设计一个适当的控制输入使系统沿某一轨迹从一开始位置运动到另一终点位置,包含两方面内容：路径规划和跟踪控制。
本文围绕这两个内容,对移动机器人的路径规划和轨迹跟踪分别进行了研究,在传统方法的基础上,提出了一些改进算法及新的解决方案,以提高算法的计算效率,扩展其使用范围。具体的研究内容包括以下几个方面：
1.将第二类偏微分方程引入到移动机器人路径规划问题求解中,探讨了偏微分方程在路径规划中的应用,扩展了路径规划的求解算法种类。该算法克服了其它路径规划算法的缺点,比如经典势场算法中的极小问题、RRT算法的无谓耗费等。算法的数学结构和求解时的自适应网格细化保证了该算法的适应性。
2.针对快速扩展随机树RRT算法只能在已知环境中进行移动机器人路径规划的限制,将RRT算法与基于滚动窗口的路径规划相结合,提出了一种改进的移动机器人路径规划算法。该算法只考虑窗口环境地图,避免了全局搜索,使得RRT算法可以在未知环境下的移动机器人路径规划中应用。算法引入启发式估价函数,使得随机树易于朝目标点方向生长,同时运用回归分析生成新节点,避免了可能产生的局部极小,增强了算法搜索未知空间的能力。
3.为了提高移动机器人在未知环境下的运行效率,将应激式爬行虫Bug算法和滚动路径规划相结合,只考虑当前状态下所必须的传感数据,不计算障碍物的边线解析式,节省了存储空间,保证了规划算法的实时性。运用虚拟障碍的概念,解决了该算法在陷阱区域容易左右徘徊的问题。为了保证路径规划的完备性和Bug算法的全局最优,同时给出了全局收敛标准。
4.详细分析了三次螺线作为移动机器人跟踪路径所具有的各种优异的几何特性,定义路径光滑成本函数,利用三次螺线对规划路径光滑化,使得移动机器人易于跟踪所规划的路径,扩展了移动机器人的应用领域。
5.详细分析了履带式移动机器人的受力特点,提出了一种适于进行控制器设计的履带移动机器人模型。根据履带式移动机器人动力学模型和运动学模型,设计了机器人的轨迹跟踪控制器。在控制器的设计中考虑了履带—地面作用,引入参数对其描述。考虑到机器人动力学约束,同时引入机器人速度、加速度控制策略以保证机器入运动平滑。
6.研究了未知环境下非完整轮式移动机器人的运动规划问题。将Bug算法与基于滚动窗口的路径规划相结合来规划移动机器人路径,根据建立的移动机器人通用动力学模型和无打滑非完整运动约束条件,采用非线性反馈线性化方法设计轮式机器人的轨迹跟踪控制器。建模时直接以两驱动后轮的角速度为控制输入,降低了跟踪误差。通过仿真实验和对比实验,验证了方法的有效性。
本文在最后对全文进行了总结,并且对今后进一步的研究方向进行了展望。
Autonomous mobile robot is an important branch of robot. It involves artificial intelligence, intelligent control, information procession, image procession and detection and conversion. The development of autonomous mobile robot has imposing on the defense, society, economy and academy, and becomes the tactic research object of high technology of all countries. Motion planning for autonomous mobile robot is one of the most critical technologies in the autonomous navigation researches.
The motion planning is to generate control input for the mobile robot to drive from an initial configuration to a goal configuration. Path planning and tracking control are two fundamental issues in the motion planning robotics.
This dissertation is focused on the path planning and the trajectory tracking. Several improved methods and novel solutions are presented in order to improve computational efficiency, and additionally extend application domains. The main content of this dissertation include the following aspects:
1. This dissertation introduced the second kind of partial differential equation in mobile robot path planning, has exploited the application of PDE method in mobile robot path planning problem, then new technology and method are provide for mobile robot path planning research. The algorithm overcame disadvantages of the other path planning algorithms, such as local minimization of classical potential field algorithm, unnecessary cost of RRT algorithm and so on. The mathematics principle of this algorithm and adaptive mesh has guaranteed this algorithm compatibility.
2. To solve the limitations of Rapidly-Exploring Random Tree (RRT) algorithm, which only can be used in path planning when the environment is known, with combination of RRT algorithm and rolling path planning, this dissertation proposes an improved path planning. Only the local environmental map is calculated in the planning, thus the searching all environmental map is avoided, so that the RRT algorithm can be used in path planning not only when the environment is known but also unknown. By introducing the heuristic evaluation function, the exploring random tree can grow in the direction of target point. The regression analysis, which avoids local minima, enhances the capability of searching unknown space.
3. In order to enhance the planning efficiency for mobile robot in unknown environment, this dissertation combined Bug algorithm and rolling path planning. Only the necessary sensing data instead of the analytical expression of the obstacle are calculated in planning so as to save memory, thus the planning in real-time is guaranteed. As one of the innate limitations of algorithm, the mobile robot tends to enter the trap situation due to local minima, so this dissertation solves this problem utilizing the concept of virtual obstacle. In order to maintain the planner's completeness, a global criterion is added in order to guarantee convergence to the goal.
4. The cubic spiral for mobile robot path tracking is well studied here and some excellent characteristics are found. Then the cubic spiral curve is used to smooth the collision-free path by defining the cost functions of path for smoothness. Therefore the mobile robot is easy to track and application field of mobile robot is extended.
5. A kind of tracked mobile robot model that is suitable for the design of controller is proposed through analyzing the force characteristics of the tracked mobile robot. Based on the dynamic model and kinematics constraints of tracked mobile robot, a trajectory tracking controller is designed. Parameters are introduced to describe the track-soil interactions. Considering the dynamics of mobile robot, the limited control strategy is introduced to guarantee the robot's smooth motion.
6. The motion planning of nonholonomic wheeled mobile robot working in the unknown environment is researched. This dissertation combined the Bug algorithm and rolling path planning in the path planning for mobile robot. Based on the general dynamic model and non-slipping nonholonomic kinematics constraint of mobile robot, a trajectory tracking control system is designed by nonlinear feedback linearization. The angular velocities of the two back driving wheels are the input data so that the tracking errors are decreased. The simulation and experimental results verified the algorithm's effectiveness.
A summary of the research conclusions and a discussion on the most promising paths of future research work are presented in the last chapter of this dissertation.
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