3D path planning for AUV in the presence of ocean currents

In order to acquire a time-optimal path in the presence of time-invariant but position-dependent currents, this paper develops a 3D path planning algorithm for AUV traversing from a starting location to the target location using optimal control theory. First, we consider the kinematics of the AUV for the design, which describes the relationship between AUV's velocity in 3D space and the motion speed and its yaw and pitch angles. Then, under the constraints that the motion speed, initial and final positions are given, we obtain an optimal control law for the navigation yaw and pitch angles by using Pontryagin's minimum principle of variational analysis in optimal control theory. Finally, by using the state-space theory of general linear time-invariant dynamical systems, the initial yaw and pitch angles are calculated, after which the optimal transformation time is also obtained. Compared with the existing iterative methods, such as graph search and evolutionary algorithms, this method generates a continuous time-optimal path underthe optimal navigation control law which is more computationally fast. What's more, considering the position-dependent currents, the path planning of AUV in complex environment is realized. It is verified by simulation that this method can obtain the time-optimal path in the 3D plane in the presence of ocean currents.