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.

Path Planning and Flight Controller Scheduling for an Autonomous Helicopter

“…This makes it possible for us to view these states as separate when planning the paths, at the same time as we still design output trajectories that are compatible with the nonlinear helicopter dynamics [6] (under the assumption that we do not saturate the actuators. )…”

FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments

“…As far as the optimization problem itself is concerned, most of the current state-of-the-art methods exploit the differential flatness of the quadrotors, and, using an integrator model, minimize the squared norm of a derivative of the position to find a dynamically feasible smooth trajectory (Mellinger and Kumar 2011;Van Nieuwstadt and Murray 1998;Richter et al 2016). When there are obstacles present, some methods include them in the optimization problem, while others do not.…”

Search-Based Motion Planning for Aggressive Flight in SE(3)

“…Trajectories for MAVs or, more generally, differentially flat systems [13] are usually represented as piecewise poly-nomials in time since their derivatives can be used to obtain explicit expressions for the system states and control inputs [14]. When collision avoidance is taken into account, more constraints need to be added to the problem formulation to guarantee safety either through anchoring waypoints as in [2], [13] or building a safe flight corridor as in [4], [15], [16].…”