Adaptive Bearing Sampling for a Constant-Time Surfacing A* Path Planning Algorithm for Gliders Enrique Fern´ andez-Perdomo, Jorge Cabrera-G´ amez, Daniel Hern´ andez-Sosa, Josep Isern-Gonz´ alez, Antonio C. Dom´ ınguez-Brito, V´ ıctor Prieto-Mara˜ n´ on and Antonio G. Ramos Abstract—Unmanned Underwater Vehicles (UUVs) are com- monly used in Oceanography due to their relative low cost and wide range of capabilities. Gliders are a type of UUV particularly suitable for long-range missions because of their large autonomy. They change their buoyancy to dive and climb describing a vertical saw tooth pattern, which produces an effective but low horizontal speed. Consequently, gliders are strongly sensitive to ocean currents, so they might have to adapt the heading to the current field. In this article we outline a novel path planning algorithm for gliders using ocean currents. It bases on the A* family of algorithms and incorporates a probabilistic framework. Our approach intends to alleviate some of the drawbacks that A* has with the problem at hand. Instead of discretizing the search space, a set of bearing angles is sampled at each surfacing point and the glider trajectory is integrated. We propose an Adaptive Bearing Sampling (ABS) procedure which reduces the computational time with low impact on the results, as shown by the tests run with ocean currents of a Regional Ocean Model. I. I NTRODUCTION Gliders are a technology in active development, which has proven very promising in Ocean Research, and it is meant to be an important observational tool in the coming years [1]. This vehicles operate modifying their buoyancy in a cyclic pattern, shown in Fig. 1. This results in a vertical impulsion, transformed into horizontal speed by means of internal mass displacements, the wings and tail, resulting in dive/climb transects. However, due to their low surge speed, they are far more affected by ocean currents than other UUVs. Gliders drift from the expected heading, hence the importance of path planning for glider navigation lies precisely in this fact. There exists a number of path planning techniques that comprises Linear Programming [2], [3], Potential fields [4], probabilistic sampling methods like Rapidly-Exploring Random Trees (RRTs) or Genetic Algorithms (GAs) [5], and Artificial Intelligence (AI) methods like A*, that assures the path optimality [6]. Several authors have applied some of these methods to the scope and singularities of glider navigation using Regional Ocean Models [8]–[10]. In par- ticular, Thompson et al. [11] use a 3D spatiotemporal grid to optimize an earliest valid arrival criterion using wavefront expansion, similar to A*. We find an extension to multiple The first authors are with the University Institute of Sistemas Inteligentes y Aplicaciones Num´ ericas en Ingenier´ ıa (SIANI), Universidad de Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain. { efernandez, jcabrera, dhernandez, jisern, adominguez } @ iusiani.ulpgc.es vprieto@ono.com Antonio G. Ramos is with the Department of Biology, Universidad de Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain. aramos@pesca.gi.ulpgc.es Fig. 1. Diagram of glider operation cycle. vehicles in the work of Smith et al. [12]. They use 3D+T (three spatial plus time) ocean model predictions to solve the path planning problem in order to track the centroid and boundary of evolving ocean processes. Path planning methods require a vehicle motion model to estimate the trajectory. Elaborated glider motion models have been discussed thoroughly in several works [13], [14]. Although the glider kinematics or dynamics might capture the effect of various factors on the glider trajectory, for long- range path planning simplified models might be enough. In this paper we propose a path planning algorithm that incorporates ocean currents and a glider motion model af- fected by them. It is based on A* [7], already adapted to the problem at hand by some authors [8]–[11]. A* discretizes the search space with an uniform grid, so the possible bearings are discretized too, as a consequence, the time between consecutive surfacings is non-constant then. Instead of finding the path over an uniform grid, that would produce unrealistic non-constant time surfacings, we have engineered our path planner to obtain constant time surfacings. It samples a fixed number of bearing angles and integrates the glider trajectory, so it is consistent with the glider behavior and consequently the resulting paths are more realistic and informed. For this reason, we have named our method Constant-Time Surfacing A* (CTS-A*) [15]. Bearings can be sampled uniformly or stochastically, which allows us to sample the space of bearings intelligently. We present a novel ABS procedure for this purpose, that takes the ocean currents and the direction to the goal into account. 2011 IEEE International Conference on Robotics and Automation Shanghai International Conference Center May 9-13, 2011, Shanghai, China 978-1-61284-380-3/11/$26.00 ©2011 IEEE 2350