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SUMMARYThis paper considers the problem of real-time trajectory generation and tracking for nonlinear control systems. We employ a two-degree-of-freedom approach that separates the nonlinear tracking problem into real-time trajectory generation followed by local (gain-scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real-time trajectory generation problem for differentially flat systems with (possibly non-minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included.1998 John Wiley & Sons, Ltd.

No abstract

This paper considers the problem of real‐time trajectory generation and tracking for nonlinear control systems. We employ a two‐degree‐of‐freedom approach that separates the nonlinear tracking problem into real‐time trajectory generation followed by local (gain‐scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real‐time trajectory generation problem for differentially flat systems with (possibly non‐minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included. © 1998 John Wiley & Sons, Ltd.

The use of differential atness for computation of a nominal trajectory for fast transition between ight modes of autonomous vehicles is investigated. Differential atness of an approximate model of the longitudinal dynamics of a thrust-vectored aircraft is used to achieve fast switching between ight modes. We conclude that steering to the trimmed state of the full model is of crucial importance for good performance. Simulations and experimental data for a thrust-vectored ight-control experiment at Caltech are provided to validate the approach.Nomenclature C x = horizontal aerodynamic coef cient C y = vertical aerodynamic coef cient C µ = rotational aerodynamic coef cient N c = mean aerodynamic chord, m D = aerodynamic drag, N J = inertia, kg ¢ m 2 L = aerodynamic lift, N M = aerodynamic moment, Nm m g = gravitational mass, kg m x = inertial mass in x direction, kg m z = inertial mass in z direction, kg Q = pitch rate, rad/s r = distance from center of mass to point where thrust acts, m S = wing surface, m 2 T 1 = forward thrust, N T 2 = downward thrust, N U = forward body velocity, m/s V = absolute velocity, m/s W = downward body velocity, m/s x = spatial horizontal coordinate, m/s, or state of a system x f = x coordinate of the center of oscillation z = spatial vertical coordinate, m/s, or at output z f = z coordinate of the center of oscillation ® = angle of attack, rad ± = elevator, deg 2 = angle of aircraft with the vertical: µ ¡ ¼=2, rad µ = pitch angle, rad ½ = density, kg/m 3