本文为荷兰代尔夫特理工大学（作者：W.W.F. Spierenburg）的硕士论文，共88页。
我们介绍了一种运动规划基础框架、一套新的距离函数集和一种控制函数。与忽略速度或假设速度恒定的路径规划器不同，运动规划器用于机器人设计中，以便通过允许可变速度来规划现实中的运动变化。本文的主要目标是设计一个具有最小输入的规划基础框架，以解决各种机器人的运动规划问题。这些运动规划都在合理的时间范围之内，并且不需要进行预处理。这里的状态空间是所有可能的位置和速度的组合。
为了找到这种解决方案，快速探索随机树（Rapidly-exploring Random Tree，RRT）运动规划器已经适用于在状态空间中使用，并用一个UR5机器人手臂模型进行了测试。已经证明该规划器不能连接两个状态，甚至在将100000个状态添加到随机树之后也不能。从而验证了常用欧氏距离度量中的新一套简单diIn结论：概率完整运动规划RRT适用于状态空间，并结合控制功能，基于创建的gostance函数可以找到两个状态之间的一种非最优连接，并已通过计算实际运动和考虑RRT中行为的相关性进行了验证。对于这些距离函数，能够观察到相关性的强弱，但在状态之间没有建立连接。
最后创建了一个控制函数PID-connect，它使用PID控制器将开始状态和目标状态都连接到零速度状态。PID-connect能够在短时间内可靠地计算两个状态之间的运动（0.02±0.01s，n＝1000）。总之，RRT的概率完全变型已经被用于状态空间，它与控制函数结合可以找到行驶中两个状态之间的非最优运动。本研究为该领域的进一步发展提供了坚实的基础。
We introduce a motion planninginfrastructure, a new set of distance functions and a steering function. Motionplanners are used in robotics in order to plan realistic motions by allowingfor variable velocities, as opposed to path planners which either neglect orconsider velocities as constant. The main goal of this thesis is to design aplanning infrastructure with minimal input, which can solve the motion planningproblem for various robots. This all within a reasonable time frame and withoutpreprocessing. Here the state space is the combination of all possible positionsand velocities. To find this solution the Rapidly-exploring Random Tree (RRT)[1] motion planner has been adapted for use in the state space and was testedusing a UR5 robot arm model. By itself it was shown to be unable to connect twostates, even after adding 100000 states to its tree. Thus to verify thecommonly used euclidean distance metric a new set of simple diIn conclusion theprobabilistically complete motion planner RRT has been adapted for the statespace, which in combination with the steering function can find a non optimalconnection between two states on the gostance functions has been created, whichhave been verified by calculating their correlation with actual motions andconsidering their behavior in RRT. Both strong and weak correlations wereobserved for these distance functions, yet no connections were establishedbetween states. Finally a steering function has been created, PID-connect,which connects both the start and the goal state to a zero velocity state usinga PID-controller. PID-connect is able to compute a motion between two statesreliably in a short time (0.02 ± 0.01s, n = 1000). In conclusion aprobabilistically complete variant o RRT has been adapted for use in the state space,which in combination with the steering function can find a non optimal motionbetween two states on the go. This research provides a solid basis from whichfurther advancements in this field can be made.
1 引言
2 运动规划器
3 模块化运动规划
4 距离函数
5 控制函数
6 讨论
7 结论
8 建议
附录A 如何实现状态空间OMPL
附录B RRT树
附录C 控制输入选择
附录D LWPR
附录E PID控制器权值
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