A negative imaginary theory-based time-varying group formation tracking scheme for multi-robot systems: Applications to quadcopters

This paper proposes a new methodology to develop a time-varying group formation tracking scheme for a class of multi-agent systems (e.g. different types of multi-robot systems) utilising Negative Imaginary (NI) theory. It offers a two-loop control scheme in which the inner loop deploys an appropriate feedback linearising control law to transform the nonlinear dynamics of each agent into a double integrator system, while the outer loop applies an NI-based time-varying group formation control protocol on the linearised agents. This approach offers greater flexibility in choosing a controller, easy implementation and tuning, reduces the overall complexity of the scheme, and uses only output feedback (hence reduced sensing requirements) to achieve formation control in contrast to the existing formation control schemes. The paper has also provided lab-based experimental validation results to demonstrate the feasibility and usefulness of the proposed scheme. Two experiments were conducted on a group of small-scale quadcopters connected via a network to test the time-varying group formation tracking performance.