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This paper presents a kinematic path planning method for a slender autonomous underwater vehicle (AUV) using a technique based on the Rapid-Exploring Random Tree (RRT) algorithm extended to the Euclidean group of motions SE(3). The paths are generated by connecting sub-Riemannian curves on SE(3) that are optimal with respect to a weighted quadratic cost function of the translational and angular velocities subject to the kinematic constraints of the vehicle and are C smooth for translational motions. Unlike the majority of other AUV path planning methods, our framework provides a full description of the rotational and translational position as a function of time and the curves satisfy the differential constraints of the vehicle. The modified RRT method is demonstrated in two scenarios, the first with a sparse obstacle field and the second with a dense obstacle field. In both cases the algorithm successfully generates a six degree-offreedom path from the initial position to a desired final position.

Path planning on SE(3) for AUVs using the RRT method