Real‐time trajectory generation for differentially flat systems

Abstract

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.

UAVs Dynamic Mission Management in Adversarial Environments

“…A number of hardware platforms [12][13][14][15][16] are available for those wishing to validate their ideas experimentally. Until recently, much of the work available in literature [14,17] dealt with motion control of vehicles, usually in the form of waypoint following or trajectory tracking. Parallel advances in wireless communication technologies are enabling applications that include cooperative control of multiple UAVs working together to accomplish a greater mission goal.…”

Inversion in indirect optimal control of multivariable systems

“…Observe that ξ (r1+r2−1) 1 is a derivative of ξ 1 which is of an order lower than 2r 1 − 1 because r 2 < r 1 and that, as a vector, the right hand side of equations (41,42) is a function from R 2n to R 2 . Thus, the following proposition holds.…”

“…Thus, the following proposition holds. (16), (23), (41) and (42) are a 2n dimensional state space form set of equations to be satisfied by optimal solutions.…”

Hierarchical trajectory refinement for a class of nonlinear systems

“…Research in trajectory generation for classes of nonlinear control systems has resulted in various approaches for nonholonomic systems [MS93] as well as real-time trajectory generation methods [vNM98] for differentially flat systems [FLMR95]. The rapidly growing interest in unmanned aerial vehicles (UAVs) has also emphasized the need to generate aggressive trajectories for individual UAVs ( [FDF01,HJ00]) as well as large numbers of autonomous UAVs ( [BK04]).…”