Solving boundary value problem of trajectory planning for aircraft executing spatial maneuvers

Аuthors

Lam T. T.

Moscow Institute of Physics and Technology (National Research University), 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia

e-mail: tangthanhlam@gmail.com

Abstract

This paper presents a study on two methods of constructing spatial aircraft trajectories: simple method of trajectory planning and Taranenko’s direct method. Both methods are based on the inverse dynamic concept.

We need to find trajectory and control variables for an aircraft from initial point

to terminal point for a specified time interval with initial control vector and final control vector . In this study, three-dimensional point-mass model of an aircraft with zero sideslip angle was used.

With simple method of trajectory planning, solving boundary value problem of flight dynamic accomplished without control and state variables constraints. This method assumes that three coordinates of the aircraft represented analytically as functions of argument τ

Here  — initial and final time. specified time interval.

Aircraft’s coordinates approximated by   

Here k_i, h_i, w_i  — coefficients, а — basis functions.

The coefficients k_i, h_i, w_i were determined by satisfying the boundary conditions and system dynamic equations.

With Taranenko’s direct method, the problem was solved with both control and state variables constraints. The trajectory optimization problem was transformed into a nonlinear programming problem and then solved numerically using an appropriate algorithm.

In example cases, two methods were applied with the same boundary values. The comparison of two methods is given. Analysis of the results leads to a concousion that the simple method of trajectory planning can easily produce unrealizable trajectories and thus it cannot be used for onboard computations.

Keywords:

boundary value problem, inverse dynamic, trajectory planning, direct method

References

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