Path planning is an important part of realizing robot autonomous movement. The planned path largely determine the performance of the robot in work. Traditional path planning algorithms, such as the dijkstra algorithm based on graph search and its improved version the $A^*$ algorithm, as well as the sampling-based RRT(rapidly-exploring random tree) algorithm and its improved version the RRT^*$ algorithm, only consider obstacle avoidance problems. Algorithms based on interpolation curves can generate smoother trajectories. Algorithms based on numerical optimization can add robot speed, acceleration, etc. to the loss function, which can generate trajectories with better dynamic properties through optimial solving. In current, topographic information are richer and more accurate, and few algorithms can make full use of them. Therefore, based on the digital elevation map(DEM) of the seabed, this paper proposes an extended $A^*$ algorithm and an improved FM(fast marching) algorithm, using prior geographic information to improve the effect of path planning. Through simulation analysis, three algorithms are compared: the extended $A^*$ algorithm, the TC FM(terrian cared fast marching) and the TCFM^*$ algorithm. Simulation results show that the extended $A^*$ algorithm solves faster, its the local planning ability is stronger, and the TCFM$ and TCFM^*$ algorithms find the path shorter and smoother.