Cooperative Sampling Path Planning of Underwater Glider Fleet with Simultaneous Launch and Recovery

As low-cost and highly autonomous ocean observation platforms,underwater gliders encounter risks during their launch and recovery,especially when coordinating multi-glider deployments.This work focuses on cooperative path planning of an underwater glider fleet with simultaneous launch and recovery to enhance the autonomy of sampling and reduce deployment risks.Specifically,the gliders collaborate to achieve sampling considering the specified routines of interest.The overall paths to be planned are divided into four rectangular parts with the same starting point,and each glider is assigned a local sampling route.A clipped-oriented line-of-sight algorithm is proposed to ensure the coverage of the desired edges.The pitch angle of the glider is selected as the optimizing parameter to coordinate the overall progress considering the susceptibility of gliders to currents and the randomness of paths produced by complex navigational strategies.Therefore,a multi-actuation deep-Q network algorithm is proposed to ensure simultaneous launch and recovery.Simulation results demonstrate the acceptable effectiveness of the proposed method.

Tracy-Widom distribution, Airy2 process and its sample path properties

Tracy-Widom distribution was rst discovered in the study of largest eigenvalues of high dimensional Gaussian unitary ensembles(GUE),and since then it has appeared in a number of apparently distinct research elds.It is believed that Tracy-Widom distribution have a universal feature like classic normal distribution.Airy2 process is de ned through nite dimensional distributions with Tracy-Widom distribution as its marginal distributions.In this introductory survey,we will briey review some basic notions,intuitive background and fundamental properties concerning Tracy-Widom distribution and Airy2 process.For sake of reading,the paper starts with some simple and well-known facts about normal distributions,Gaussian processes and their sample path properties.

Student’s t Increments

Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t increments are independent draws from not-truncated, truncated, and effectively truncated Student’s t-distributions with shape parameters and can be used to create random walks. It is found that sample paths created from truncated and effectively truncated Student’s t-distributions are continuous. Sample paths for Student’s t-distributions are also continuous. Student’s t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.

Dimension Properties of Sample Paths of Self-Similar Processes

The Hansdorff dimensions of the image and the graph of random fields are given under general conditions.The results can be used to a wider class of self-similar random fields and processes,including Brownian motion,Brownian sheet,fractional Brownian motion,processes with stable or(α,β)-fractional stable components.