The Affine Geometric Heat Flow and Motion Planning for Dynamic Systems
The Affine Geometric Heat Flow and Motion Planning for Dynamic Systems
复制标题
动态系统的仿射几何热流和运动规划
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
M. Belabbas
中科院分区：
文献类型：
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作者：
Shenyu Liu;Yinai Fan;M. Belabbas
提出了一种新的控制系统运动规划方法。该方法的目的是提供一个自然的计算框架，其中广泛的一类运动规划问题，可以铸造，包括完整和非完整约束，漂移动力学，障碍物的约束和应用控制的幅度上的约束的问题。该方法，它发现它的灵感在最近的工作中所谓的几何热流和曲线缩短流，依赖于由此引入的偏微分方程，我们称之为仿射几何热流，它演变成一个任意可微的路径连接初始到最终状态的配置空间的路径，满足对问题施加的约束。从该路径，可以提取要应用于系统的控制。我们提供的条件，保证提取的控制将驱动系统任意接近所需的最终状态，同时满足所施加的约束，并说明了三个典型的例子的方法。
We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and non-holonomic constraints, drift dynamics, obstacle constraints and constraints on the magnitudes of the applied controls. The method, which finds its inspiration in recent work on the so-called geometric heat flows and curve shortening flows, relies on a hereby introduced partial differential equation, which we call the affine geometric heat flow, which evolves an arbitrary differentiable path joining initial to final state in configuration space to a path that meets the constraints imposed on the problem. From this path, controls to be applied on the system can be extracted. We provide conditions guaranteeing that the controls extracted will drive the system arbitrarily close to the desired final state, while meeting the imposed constraints and illustrate the method on three canonical examples.
DOI：
10.1016/j.automatica.2013.02.016
发表时间：
2011-09
期刊：
Autom.
影响因子：
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作者：
Hans-Bernd Dürr;M. Stanković;C. Ebenbauer;K. Johansson
通讯作者：
Hans-Bernd Dürr;M. Stanković;C. Ebenbauer;K. Johansson