Three-dimensional aircraft path planning based on nonconvex quadratic optimization

In this paper, we examine the three-dimensional aircraft path planning problems under field-of-view constraints using a nonconvex quadratic optimization method. The aircraft is assumed to be flying at constant speed with small angle of attack. We focus on determining the attitude of the aircraft when planning the optimal paths. Under this venue, the aircraft kinematics are expressed as quadratic functions in terms of unit quaternions and the path planning problem is reformulated as a general quadratically constrained quadratic programming (QCQP) problem. A semidefinite programming method is then applied to relax the nonconvex QCQP problem to obtain the bounds on the optimal value. Subsequently, an iterative rank minimization approach is proposed to find the optimal solution. Simulation results for planned paths using the proposed method are presented and compared with those obtained from the other method.