Three-Dimensional Constrained Optimal Motion Planning for a Six-Degree-of-Freedom Quadrotor Helicopter for Urban Traffic Purposes

Traffic issue is an international challenge in the sophisticated countries in which over population is considered as an important factor in creating this problem. Studies show that the accidents’ report during the minimum time is the best way to control the traffics. For this purpose, this paper has been done in such a way that after modeling the flying robot using Newton-Euler equations, a three-dimensional constrained optimal trajectory has been generated through Direct Collocation Approach. In other words, the proposed problem in this paper is first formulated as an optimal control problem. Afterwards, the optimal control problem is discretized through Direct Collocation Technique, which is one of the numerical solving methods of the optimal control problems, and it is transformed into a Nonlinear Programing Problem (NLP). Eventually, the aforementioned nonlinear programming problem is solved via SNOPT which works based on the gradient algorithm like SQP. It should be noted that since the main objective of motion planning in this paper is controlling the urban traffic, the urban constrains are utilized during the trajectory optimization. In other words, all of the high-rise buildings located during the course are modeled by the various cylinders. The efficacy of the aforementioned method is demonstrated by extensive simulations, and in particular it is verified that this method is capable of producing a suitable solution for three-dimensional constrained optimal motion planning for a six-degree-of-freedom quadrotor helicopter for urban traffic purposes.