Real-time trajectory generation: Improving the optimality and speed of an inverse dynamics method

The optimality of a solution to a minimum-time aircraft trajectory generation problem depends on the closeness of the generated airspeed to the maximum airspeed that satisfies all path and boundary constraints. Airspeed is typically determined by nonlinear constrained optimization, hence the degree of the airspeed parameterization affects optimality and computational speed. An alternative approach, directly evaluating maximum feasible airspeed, is described and compared with the optimization approach. Results using Chebyshev polynomials show that, in isolation, parameterizations of degree 8-10 deliver a good trade-off between high degree for optimality and low degree for speed. However, directly evaluating airspeed is closer to optimality and not prone to convergence to a local solution. Accuracy of evaluation of the maxima of constrained variables is investigated using global Chebyshev, local quadratic, and local cubic, interpolation, and results show that quadratic interpolation in particular is computationally efficient, increasing speed while maintaining accuracy.