Optimal Round Trip Path-Planning of An Aerial Robot by Consideration of Geometric Constraints of Obstacles

This paper is dedicated to the optimal path-planning of a quadrotor to deliver the goods in the form of a round-trip mission. At first, quadrotor modeling is performed by the Newton-Euler method and then the problem is formulated as an optimal control effort problem. Then, by discretization of the equations using the direct colocation method, the problem becomes a nonlinear programming system that can be solved by available optimization methods. This discretization helps to make the derivative values in the equations of motion as simple algebraic expressions and the path optimization problem becomes a standard form of nonlinear programming problem (NLP). In this method, instead of obtaining state and control functions, state and control values are obtained at the beginning and endpoints of smaller time intervals. This method is one of the most explicit methods for the numerical solution of differential equations. It should be noted that in this research, safe areas around urban obstacles are considered fixed cylinders. Extensive simulations are evidence of the usefulness of this method, while the vehicle realizes all geometric, dynamic, and kinematic constraints.