This paper presents a new probabilistic algorithm for trajectory planning for autonomous vehicles (AV) in search and security applications. The goal is to compute optimized paths for the AVs in real time which maximize the probability of locating a fixed target, subject to constraints on the vehicle dynamics, within a prespecified time horizon. The likelihood of not detecting the target is modeled in a probabilistic manner based on approximate models of sensor acuity as a function of the distance to (and, the speed of) the sensor vehicle. For any possible vehicle path, a cost function is considered that accumulates the overall likelihood of not locating the target. Using an adjoint-based calculation, the gradient of this cost with respect to the control inputs is determined. The formulation of the cost function and the vehicle dynamics are decoupled, facilitating easy extension of the framework developed to other types of vehicles. The framework can also account for a priori estimates of the probability distribution of the target of interest. To accelerate convergence, we use the projected-search limited-memory reduced Hessian (LRH-B), a recently developed gradient-based optimization method for constrained optimization; the LRH-B method significantly outperforms existing optimization algorithms as implemented in standard packages. Results indicate that our new framework can efficiently coordinate the search over the domain, and that LRH-B reduces the total computational cost during the search.
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