This paper presents a method for task-oriented path planning and collision avoidance for a group of heterogeneous holonomic mobile sensors. It is a generalization of the authors' prior work on diffusion-based path planning. The proposed variant allows one to plan paths in environments cluttered with obstacles. The agents follow flow dynamics, i.e., the negative gradient of a function that is the sum of two functions: the first minimizes the distance from desired target regions and the second captures distance from other agents within a field of view. When it becomes necessary to steer around an obstacle, this function is augmented by a projection term that is carefully designed in terms of obstacle boundaries. More importantly, a diffusion term is added intermittently so that agents can exit local minima. In addition, the new approach skips the offline planning phase in the prior approach to improve computational performance and handle collision avoidance with a completely decentralized method. This approach also provably finds collision-free paths under certain conditions. Numerical simulations of three deployment missions further support the performance of ID-based diffusion.

In this paper, we present an approach to local coverage path (CP) planning for a circular mobile sensor. Our family of algorithms provides completed and overlapped coverage control, curvature and path length control, localization, choice of observer's placement based on sensing range, and first-order differentiable CP. Our family of algorithms begins by partitioning the target region (TR) into several regular triangulations (RTs). Based on the size of the RT and the sensing range, the number and location of observers are determined for all RT. All observers found are then used as waypoints (WPs) to generate baseline CP with the Traveling Salesman Problem's nearest neighbor algorithm. The proposed algorithm solved the problems of how to design a differentiable and collision-free CP for all sensing range, limited and sufficient, while providing completed coverage control, overlapped coverage control, curvature and path length control, localization, collision avoidance, and the choice of observer's placement based on sensing range and the environment. The main technical contributions of the proposed approach is to provide a holistic solution that segments any TR, uses triangulation to determine the observation WPs and then compute the smooth and collision-free CP. Computer simulations are provided to validate the effectiveness and correctness of our algorithms.

Curvelets are a multiscale system with very high directional sensitivity. A new detection algorithm is herein described which operates on a curvelet decomposition of acoustic imagery. The algorithm detects the presence of cylindrical targets through a statistical mapping of curvelet coefficients. The coefficients are calculated as an inner product between image features and a curvelet basis element. The similarity in appearance between cylindrical targets and curvelet basis elements yield an accurate detection algorithm with a very low false alarm rate.

A method for the correction of images that are subject to spatial warping is presented. The correction method applies to two-dimensional images and employs the construction of a complex-valued interpolating polynomial. The construction is based on defining a set of points in an image whose desired location is known. The coefficients of the polynomial are shown to satisfy a recursion relation that simplifies implementation and improves evaluation efficiency. Results are presented for a two-dimensional slice from a magnetic resonance image.