Related papers: A Trajectory-Based Approach to Discrete-Time Flatn…
Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…
The paper addresses the exact linearization of flat nonlinear discrete-time systems by generalized static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts…
The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time…
In this contribution we discuss flat discrete-time nonlinear systems in a general setting including two special subclasses, namely, forward- and backward-flat systems. We relate rank conditions for certain submatrices of the Jacobian of the…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is…
Willems et al. showed that all input-output trajectories of a discrete-time linear time-invariant system can be obtained using linear combinations of time shifts of a single, persistently exciting, input-output trajectory of that system. In…
For many tasks, predictive path-following control can significantly improve the performance and robustness of autonomous robots over traditional trajectory tracking control. It does this by prioritizing closeness to the path over timed…
This paper proposes a tracking controller based on the concept of flat inputs and a dynamic compensator. Flat inputs represent a dual approach to flat outputs. In contrast to conventional flatness-based control design, the regulated output…
We show that the flatness of a nonlinear discrete-time system can be checked by computing a unique sequence of involutive distributions. The well-known test for static feedback linearizability is included as a special case. Since the…
This article addresses the design of a discrete-time flatness-based tracking control for a gantry crane and demonstrates the practical applicability of the approach by measurement results. The required sampled-data model is derived by an…
In this article, we introduce the notion of differential flatness by pure prolongation: loosely speaking, a system admits this property if, and only if, there exists a pure prolongation of finite order such that the prolonged system is…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
We study residual dynamics learning for differentially flat systems, where a nominal model is augmented with a learned correction term from data. A key challenge is that generic residual parameterizations may destroy flatness, limiting the…
Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…
This paper deals with linear time-varying, delay systems. Extensions of the concept of differential flatness \cite{Fliess_95} to this context have been first proposed in \cite{Mounier_95,Fliess_96} (see also \cite{Rudolph_03,Chyzak_05}), by…
We introduce a new definition of $\pi$-flatness for linear differential delay systems with time-varying coefficients. We characterize $\pi$- and $\pi$-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present…
This paper proposes several nonlinear control strategies for trajectory tracking of a quadcopter system based on the property of differential flatness. Its originality is twofold. Firstly, it provides a flat output for the quadcopter…
Differential flatness has been used to provide diffeomorphic transformations for non-linear dynamics to become a linear controllable system. This greatly simplifies the control synthesis since in the flat output space, the dynamics appear…
Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this…