Finite-time multi-agent deployment: A nonlinear PDE motion planning approach

The systematic flatness-based motion planning using formal power series and suitable summability methods is considered for the finite-time deployment of multi-agent systems into planar formation profiles along predefined spatial–temporal paths. Thereby, a distributed-parameter setting is proposed, where the collective leader–follower agent dynamics is modeled by two boundary controlled nonlinear time-varying PDEs governing the motion of an agent continuum in the plane. The discretization of the PDE model directly induces a decentralized communication and interconnection structure for the multi-agent system, which is required to achieve the desired spatial–temporal paths and deployment formations.