Montés Nicolas, Chinesta Francisco, Mora Marta C, Falcó Antonio, Hilario Lucia, Rosillo Nuria, Nadal Enrique
Department of Mathematics, Physics and Technological Sciences, University CEU Cardenal Herrera, C/San Bartolome 55, CP Alfara del Patriarca, 46115 Valencia, Spain.
PIMM Lab, ESI Group Chair at ENSAM Institute of Technology, 151 Boulevard de L'Hôpital, 75013 Paris, France.
Sensors (Basel). 2021 Jun 8;21(12):3943. doi: 10.3390/s21123943.
This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGOMINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots.
本文提出了一种基于这些函数的适当广义分解（PGD），使用调和函数（如泊松方程）的移动机器人实时全局路径规划方法。所提出技术的主要特性是，即使机器人受到干扰或目标发生变化，其计算成本在实时情况下也可忽略不计。该方法的主要思想是针对给定环境离线生成移动机器人从任何起始和目标配置出发的整个路径集，即计算手册，它源自调和势场，以便在线用于决策目的。到目前为止，拉普拉斯方程或泊松方程的求解一直基于传统数值技术，这些技术对于实时计算是不可行的。尽管调和函数具有强大的特性，但这一缺点阻碍了它们在自主导航中的广泛应用。扭转这种局面的数值技术是适当广义分解。为了在潜在引导路径规划框架中演示和验证PGD计算手册的特性，已经开发了实际和模拟实现。使用了模拟场景，如L形走廊和基准陷阱，并且展示了一个乐高头脑风暴机器人在具有可变起始和目标配置的静态环境中的实际导航。选择该设备是因为其计算和内存受限的能力，并且它是其特性如何有助于社交机器人开发的一个很好的例子。
