A Darboux transformation is constructed for the modified Veselov-Novikov equation.

A dynamic path planning method based on a gated recurrent unit-recurrent neural network model is proposed for the problem of path planning of a mobile robot in an unknown space. A deep neural network with sensor input is used to generate a new control strategy output to the physical model to control the movement of the robot and thus achieve collision avoidance behavior. Inputs and tags are derived from sample sets generated by an improved artificial potential field and an improved ant colony optimization algorithm. In order to make the ant colony algorithm converge quickly, the pheromone trail and the state transition probability are improved. The field function of the artificial potential field method is modified. Using the end-to-end network model to learn the mapping between input and output in the sample data, the direction and speed of the mobile robot are obtained. The simulation experiments and realistic simulations show that the network model can plan a reasonable path in an unknown environment. Compared with other traditional path planning algorithms, the proposed method is more robust than the traditional path planning algorithms to differences in the robot structure. INDEX TERMS Mobile robot, gated recurrent unit-recurrent neural network, dynamic path planning, ant colony optimization, artificial potential field.

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