Using conformal mapping in developing a novel optimal obstacle-avoidance trajectory-planning for a flying robot

In this work, a new systematic method is proposed to enhance the process of optimum trajectory planning in Terrain / Obstacle Avoidance Flights (TOAF) with use of conformal mappings as a facilitator of the effect of the flight altitude restriction on the route selection. The use of Conformal Mapping concept could help to transform a constrained trajectory planning problem, in presence of obstacles or any height constraint, into a simple pseudo obstacle-free optimal trajectory-planning problem. Suitable case studies show that the proposed approach is more consistent with basic flight concepts as well as real world applications. Applicability of the introduced approach is demonstrated by solving a 2-D obstacle-avoidance motion using direct pseudo-spectral method.