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[转载]【计算机科学】【2019.05】高维空间中的路径规划算法

已有 147 次阅读 2020-9-23 17:39 |系统分类:科研笔记|文章来源:转载

本文为美国乔治亚理工学院(作者:FlorianHauer)的博士论文,共128页。

 

路径规划的应用范围很广,从视频游戏中搜索一个智能体的轨迹,到了解蛋白质是如何折叠的,到仓库中驾驶自动机器人,或者为自动驾驶汽车找到避开汽车和行人的轨迹。在路径规划算法的求解中,经常会发现三个主要特征:(1解决方案应避免与障碍物的碰撞,(2)解决方案应是动态可行的,(3)解决方案应是最优的(根据应用的最优性准则:最短的长度、最快的时间、最低能耗、乘客舒适度、乘客安全性……)。

 

根据所涉及系统的类型存在许多公式。一个主要区别是作用于连续搜索空间的系统与作用于离散搜索空间的系统之间的区别。在这两种情况下,搜索空间的大小会影响找到解决方案的速度。对于连续空间,空间的维数是决定求解收敛速度的主要变量。对于离散空间,空间的基数是最重要的:最坏情况下的运行时间与空间基数成线性增加关系,在最佳情况下会比一般情况更快。

 

在这篇论文中,我们提出了新的演算法,利用搜寻空间的多尺度数据结构来加速离散搜寻空间的路径规划。在基于采样的路径规划算法中,我们也使用了更传统的优化技术来提高这些算法的收敛速度。

本文的主要贡献是:

1.一种在任意维n中利用多尺度信息的路径规划算法(MSPP算法),它将以前仅限于2D问题的公式扩展到任意维。该算法被证明是完整的,并且该算法所使用的底层多尺度数据结构可以直接与感知算法协同工作,以实现实时应用。理论分析表明,该算法的复杂度从指数级降低到线性。

2.MSPP算法(MSPP-S算法)的概率实现。此变体允许使用MSPP算法,而无需先验的多尺度数据结构。用抽样方法估计障碍物概率,并给出了完备概率的界。无需构建多尺度数据结构,算法的运行时间减少了多个数量级。

3.展示了基于抽样的规划算法收敛性的数值实验(超立方体对角实验)。实验结果表明这些算法的收敛极限是搜索空间维数的函数,与理论分析相吻合:收敛所需的样本数随搜索空间的维数呈指数增长。

4.通过一种优化设置在搜索空间中重新定位样本来减少函数值的误差。结果表明,该优化算法易于计算,特定样本的梯度只需要局部信息。优化结果良好,特别是恢复了多边形障碍物最短路径的可见性图。

5.一种基于采样的算法(DRRT算法),它在快速探索随机树的框架内集成了函数值误差的优化。DRRT算法保持了对RRT族搜索空间的快速探索,以快速找到第一个解,同时增加了优化步骤,提高了算法的收敛速度。

 

Path-planningcovers a wide range of applications, from fifinding the trajectory of an agentin a video game, to understanding how protein folds, to driving autonomousrobots in a warehouse, or fifinding a trajectory that avoids cars andpedestrians for a self-driving car. Three main characteristics are often lookedfor in the solution of a path-planning algorithm: (1) the solution should avoidcollisions with obstacles, (2) the solution should be dynamically feasible, and(3) the solution should be optimal (with the optimality criterion depending onthe application: shortest length, fastest time, lowest energy consumption,passenger comfort, passenger safety,...).

Many formulationsexist depending on the type of system involved. One major distinction isbetween systems acting on a continuous search space versus systems acting on adiscrete search space. In both cases, the size of the search space affects howfast a solution can be found. For continuous spaces, the dimensionality of thespace is a major variable in how fast the solution converges. For discretespaces, the cardinality of the space is of prime importance: the worst-caseruntime increases linearly with the cardinality of the space, in the best case,or even faster, in the general case.

In this thesis, wepropose novel algorithms that take advantage of a multi-scale data structurerepresentation of the search-space in order to accelerate path-planning ondiscrete search spaces. We also make use of more conventional optimizationtechniques within sampling-based path-planning algorithms to increase theconvergence rate of these algorithms.

The maincontributions of this thesis are:

1. A path-planning algorithm (the MSPP algorithm) that exploitsmulti-scale information in any dimension n. This extends previous formulations, which were limited to 2D problems,to any dimension. The algorithm is proven to be complete and the underlyingmulti-scale data structure used by the algorithm is shown to work directly withperception algorithms for real-time applications. A theoretical analysis demonstratesthe reduction of the complexity from exponential to linear.

2. A probabilisticimplementation of the MSPP algorithm (the MSPP-S algorithm). This variantallows the use of the MSPP algorithm without an a priori multi-scale datastructure. Sampling is used to estimate the obstacle probabilities, and boundson the probability of losing completeness are derived. Removing the need tobuild the multi-scale data structure reduces the runtime of the algorithm bymultiple orders of magnitude.

3. A numericalexperiment to exhibit convergence properties of sampling-based planningalgorithms (the Hypercube Diagonal Experiment). This experiment shows theconvergence limits of these algorithms as a function of the dimension of thesearch space, and matches the theoretical analysis: the number of samplesrequired for convergence increases exponentially with the dimension of thesearch space.

4. An optimizationsetup to reduce the error of the value function by repositioning the samples inthe search space. The optimization is shown to be easily computable,specififically, the gradient for a specifific sample only requires localinformation. The optimization exhibits good results, in particular, it recoversthe visibility graph for a shortest path with polygonal obstacles.

5. Asampling-based algorithm (the DRRT algorithm) that integrates the optimizationof the error of the value function within the framework of Rapidly-exploringRandom Trees. The DRRT algorithm keeps the quick exploration of the searchspace from the RRT family in order to fifind a fifirst solution rapidly, whilethe added optimization step improves the convergence rate of the algorithm.

 

1. 引言与文献回顾

2. 离散搜索空间

3. 连续搜索空间

4. 结论与展望

附录有界加速度、有界速度、时间最优轨迹


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