Building trajectory and control for flying vehicles

A.P.Krishchenko, A.N.Kanatnikov, S.B.Tkachev

Bauman Moscow State Technical University, Moscow, Russia

The problem under consideration is planning of spatial trajectories for a flying vehicle. The methods are based on the six-dimensional model with the longitudinal overload, transversal overload and the roll angle as controls. The problem of the motion planning is solved with given initial and terminal states. The trajectory is constructed in the class of curves with the monotone variation of the mechanical energy of the flying vehicle. The algorithm of constructing the trajectories and calculating controls which stabilize the motion on the selected trajectory is suggested. The work of the algorithm is illustrated by examples.

Complexity of the flight vehicle situation and the high cost of control decisions bring forth the task of planning the flight trajectory. The information about the feasible flight trajectories is of special importance both for making decisions about complex spatial maneuvers and in nonstandard situations. In this and other cases, the acceptable variants of the flight trajectories must be analyzed in real time, which presents special requirements on the methods for seeking feasible flight trajectories.

Determination even of one trajectory is a mathematical challenge because the trajectory must connect the initial and final states, pass through some intermediate states, and be realizable by a particular flight vehicle. Hence the problem lies in developing special methods to solve a rather general problem of the trajectory motion control.

A bulky scientific literature deals with the problem of control of various flight vehicles. We note that the mathematical models of flight vehicle motion are well known. To solve a particular motion control problem, a simplified mathematical model is taken, and the control algorithm is constructed on its basis.

It goes without saying that the decisions made in this way must be tested by mathematical modeling of more precise motion models. This approach was justified by solving control problems such as motion on the vertical plane, rectilinear motion on the horizontal plane, and vertical takeoff and landing.

For simple geometry of the flight trajectory, such problems can be solved using the linear motion models and linear methods of the control theory. However, at modeling of complex spatial maneuvers of the flying vehicle and seeking for the realizing controls, the linear models and linear control methods turn out to be insufficient. More sophisticated nonlinear mathematical models must be used.

This paper presents a solution of the problem of real-time building trajectory with the given initial and final states. The solution is chosen in the class of trajectories with monotone variation of the mechanical energy of the flight vehicle. The trajectory determined is checked to verify that the overloads, the roll angle, and the state variables do not exceed the predefined critical values.

Consider the problem of flying vehicle motion control under the following assumptions: 1) mass is constant; 2) no wind; 3) terrestrial curvature is disregarded.