In this paper, a method for collision-free three-dimensional autonomous navigation of an underactuated coupled non-holonomic unmanned aerial vehicle (UAV) among obstacles was proposed. This method will be the basis for designing a planner for the UAV trajectory guidance in a 3D cluttered environment. The planner assumes that the cost of flying over an area is independent of the path through which the UAV reaches that area, however this is not always true. Moreover, the path problem is not formulated as a matter of numeric cost minimization to be solved by methods like dynamic programming, which is time-consuming. A dynamic model of six degrees of freedom hexacopter equipped with a robotic arm has been formulated using Newton-Euler's method. Then, the equations of motion of the UAV are derived by including disturbances analysis. The derived dynamic model reflects the real motion of the hexacopter with respect to the earth, which is also characterized by nonlinearity, time variance, underactuation and coupling among the equations' variables. This paper suggests bio-inspired and sample-based algorithms in order to solve and optimize the threedimensional path-planning problem. A unique real-time obstacle avoidance approach based on artificial potential field concept in addition to an off-line genetic algorithm were investigated.