Particle Swarm Optimization (PSO) can be used in swarm robotic search tasks to find extrema that represent targets. PSO assumes that particles can update their positions and velocities instantaneously in each iteration of the algorithm. For optimization purposes, this assumption is acceptable, however, it is not suitable when the algorithm is to be used by a swarm of robots to find a target in a search task. The reason is that robots have physical constraints that inhibit them from updating their position and velocity instantaneously. In this paper, we consider the application of PSO in a search task performed by a swarm of Autonomous Underwater Vehicles (AUVs) with reorientation constraints. Each vehicle has a minimum turn radius and an associated maximum turn angle, therefore, cannot reach the updated velocity and position instantaneously. A vehicle reorientation algorithm consisting of four atomic turn sequences is first introduced, then utilized to extend PSO. This adds realism to PSO and makes it directly usable in AUV controllers. Vehicle controller design, its integration with the modified PSO, and simulation of the latter are also presented.