Flatness-based Motion Planning Research Articles

PDE-based multi-agent formation control using flatness and backstepping: Analysis, design and robot experiments

A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling structure parameter information can be distributed within the agent continuum. Flatness-based motion planning and feedforward control are combined with a backstepping-based boundary controller to stabilize the distributed parameter system of the tracking error. The tracking controller utilizes the required state information from a Luenberger-type state observer. By means of an exogenous system the relocation of formation profiles is achieved. The transfer of the control strategy to a finite-dimensional discrete multi-agent system is obtained by a suitable finite difference discretization of the continuum model, which in addition imposes a leader–follower communication topology. The results are evaluated both in simulation studies and in experiments for a swarm of mobile robots realizing the transition between different stable and unstable formation profiles.

Motion planning and tracking control for coupled flexible beam structures

A systematic flatness-based motion planning approach for a structure consisting of coupled flexible bending beams is introduced. The beams are equipped with in-domain piezoelectric macro-fiber composite (MFC) actuators and are coupled by an elastic string, modeled as spring, which connects the tip masses of adjacent beams. This setup provides a challenging benchmark experiment to evaluate control concepts. Hamilton’s principle leads to the equations of motion involving spatially varying parameters due to the different material characteristics of the carrier structure and the attached MFC-actuators. The flat output is constructed by exploiting the spectral system representation and enables a differential parameterization of the system states and inputs. This parameterization transfers the motion planning problem into a trajectory assignment problem for the flat output. The resulting flatness-based feedforward control law is analyzed and evaluated at an experimental setup. To increase the performance and the robustness w.r.t. model uncertainties and external disturbances the flatness-based feedforward control is amended by a feedback controller with observer in the spirit of the two-degrees-of-freedom control approach.

Flatness‐based deformation control of an Euler–Bernoulli beam with in‐domain actuation

This paper addresses the problem of deformation control of an Euler-Bernoulli beam with in-domain actuation. The proposed control scheme consists in first relating the system model described by an inhomogeneous partial differential equation to a target system under a standard boundary control form. Then, a combination of closed-loop feedback control and flatness-based motion planning is used for stabilizing the closed-loop system around reference trajectories. The validity of the proposed method is assessed through well-posedness and stability analysis of the considered systems. The performance of the developed control scheme is demonstrated through numerical simulations of a representative micro-beam.

PDE-based tracking control for multi-agent deployment

Abstract: A two-degree-of-freedom control concept is developed for the deployment of multi-agent systems into desired formation profiles by exploiting a continuum model in terms of a modified viscous Burger’s equation. For this, flatness-based motion planning and feedforward control is combined with a backstepping-based boundary controller to stabilise the distributed parameter tracking error system. An exogenous system is introduced, which is shown to enable translational movement of the complete formation as well as its separation and reunion. The transfer of the control strategy to a finite-dimensional discrete multi-agent system is obtained by proper discretization of the continuum model PDEs, which in addition imposes the required communication topology. The results are evaluated in different simulation scenarios for a leader-follower configuration.

Nonlinear PDE–based motion planning for the formation control of mobile agents

Flatness–based motion planning using formal power series and suitable summation methods is considered for the finite–time deployment of multi–agent systems into planar formation profiles. The collective leader–follower agent dynamics is thereby modeled by two boundary controlled nonlinear PDEs governing the positions of the individual agents in the plane. The discretization of the PDE model directly implies a decentralized communication and interconnection structure for the multi-agent system to obtain the desired formation.

Flatness-based tracking control of a piezoactuated Euler–Bernoulli beam with non-collocated output feedback: theory and experiments†

This paper considers the combination of flatness-based motion planning and feedforward control with output feedback to achieve robust tracking of prescribed trajectories for the tip displacement of a multi-layered piezoelectric cantilever beam. Thereby, the flatness property of the distributed-parameter beam model is exploited to derive the infinite-dimensional tracking error system, which serves as the basis for the design of the output error feedback control. The stability of the resulting closed-loop system involving the infinite-dimensional beam model is proven in an input/output sense by utilizing a Nyquist-type stability criterion. Experimental results illustrate the high tracking performance in view of exogenous disturbances. The presented approach provides a systematic extension of the two-degrees-of-freedom control concept to distributed-parameter systems. †This paper is dedicated to Prof. Michel Fliess on the occasion of his 60th birthday.