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

Abstract

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 stabilise the distributed parameter system of the tracking error. The tracking controller utilises 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.

Preprint submitted to Automatica (accepted as Regular Paper on October 25, 2019)

Cited by in corpus (4)

• Transporting Robotic Swarms via Mean-Field Feedback Control
• Backstepping for Partial Differential Equations:A Survey
• Robust Cooperative Output Regulation for Networks of Hyperbolic PIDE-ODE Systems
• Continuification control of large-scale multiagent systems under limited sensing and structural perturbations