By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified wa...By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.展开更多
To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model （IAPFM） was established, then a new path planning method ...To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model （IAPFM） was established, then a new path planning method combining the IAPFM with optimization algorithm （trust region algorithm） is proposed. Attractive force between the robot and the target location, and repulsive force between the robot and the obstacles are both converted to the potential field intensity; and filled potential field is used to guide the robot to go out of the local minimum points ; on this basis, the effect of dynamic obstacles velocity and the robot＇s velocity is consid thers and the IAPFM is established, then both the expressions of the attractive potential field and the repulsive potential field are obtained. The trust region algorithm is used to search the minimum value of the sum of all the potential field inten- sities within the movement scope which the robot can arrive in a sampling period. Connecting of all the points which hare the minimum intensity in every sampling period constitutes the global optimization path. Experiment result shows that the method can meet the real-time requirement, and is able to execute the mobile robot path planning task effectively in the dynamic environment.展开更多
文摘By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.
基金Supported by the National High Technology Research and Development Programme of China（ No. 2006AA04Z245 ） and China Postdoctoral Science Foundation （ No. 200904500988 ）.
文摘To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model （IAPFM） was established, then a new path planning method combining the IAPFM with optimization algorithm （trust region algorithm） is proposed. Attractive force between the robot and the target location, and repulsive force between the robot and the obstacles are both converted to the potential field intensity; and filled potential field is used to guide the robot to go out of the local minimum points ; on this basis, the effect of dynamic obstacles velocity and the robot＇s velocity is consid thers and the IAPFM is established, then both the expressions of the attractive potential field and the repulsive potential field are obtained. The trust region algorithm is used to search the minimum value of the sum of all the potential field inten- sities within the movement scope which the robot can arrive in a sampling period. Connecting of all the points which hare the minimum intensity in every sampling period constitutes the global optimization path. Experiment result shows that the method can meet the real-time requirement, and is able to execute the mobile robot path planning task effectively in the dynamic environment.
