Path Planning of Spatial Rigid Motion with Constrained Attitude

This paper presents a general quadratic optimization methodology for autonomous path planning of spatial rigid motion with constrained attitude. The motion to be planned has six degrees of freedom and is assumed under constant velocity in the body frame. The objective is to determine the motion orientation (or attitude), handled as control variables, along the planned paths. A procedure is discussed to transform the rotational constraints and attitude constraints 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 relaxation method is then applied to obtain a bound on global optimal value of the nonconvex QCQP problem. Subsequently, an iterative rank minimization approach is proposed to find the optimal solution. Application examples of aircraft path planning problems are presented using the proposed method and compared with those obtained from the other method.