The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） r...The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method（NIPCM） that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.展开更多
The path planning of autonomous mobile robots(PPoAMR)is a very complex multi-constraint problem.The main goal is to find the shortest collision-free path from the starting point to the target point.By the fact that th...The path planning of autonomous mobile robots(PPoAMR)is a very complex multi-constraint problem.The main goal is to find the shortest collision-free path from the starting point to the target point.By the fact that the PPoAMR problem has the prior knowledge that the straight path between the starting point and the target point is the optimum solution when obstacles are not considered.This paper proposes a new path planning algorithm based on the prior knowledge of PPoAMR,which includes the fitness value calculation method and the prior knowledge particle swarm optimization(PKPSO)algorithm.The new fitness calculation method can preserve the information carried by each individual as much as possible by adding an adaptive coefficient.The PKPSO algorithm modifies the particle velocity update method by adding a prior particle calculated from the prior knowledge of PPoAMR and also implemented an elite retention strategy,which improves the local optima evasion capability.In addition,the quintic polynomial trajectory optimization approach is devised to generate a smooth path.Finally,some experimental comparisons with those state-of-the-arts are carried out to demonstrate the effectiveness of the proposed path planning algorithm.展开更多
基金supported by the National Natural Science Foundation of China (No. 51105034)the Doctoral Thesis Build Project of Beijing 2012 (China)
文摘The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method（NIPCM） that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
基金This work was supported by the National Key R&D Funding of China(No.2018YFB1403702)the Zhejiang Provincial Natural Science Foundation of China for Distinguished Young Scholars(No.LR22F030003).
文摘The path planning of autonomous mobile robots(PPoAMR)is a very complex multi-constraint problem.The main goal is to find the shortest collision-free path from the starting point to the target point.By the fact that the PPoAMR problem has the prior knowledge that the straight path between the starting point and the target point is the optimum solution when obstacles are not considered.This paper proposes a new path planning algorithm based on the prior knowledge of PPoAMR,which includes the fitness value calculation method and the prior knowledge particle swarm optimization(PKPSO)algorithm.The new fitness calculation method can preserve the information carried by each individual as much as possible by adding an adaptive coefficient.The PKPSO algorithm modifies the particle velocity update method by adding a prior particle calculated from the prior knowledge of PPoAMR and also implemented an elite retention strategy,which improves the local optima evasion capability.In addition,the quintic polynomial trajectory optimization approach is devised to generate a smooth path.Finally,some experimental comparisons with those state-of-the-arts are carried out to demonstrate the effectiveness of the proposed path planning algorithm.
