Formation of Multiple Groups of Mobile Robots Using Sliding Mode Control

Formation control of multiple groups of agents finds application in large area navigation by generating different geometric patterns and shapes, and also in carrying large objects. In this paper, Centroid Based Transformation (CBT) \cite{c39}, has been applied to decompose the combined dynamics of wheeled mobile robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dynamics of the centroid. Separate controllers have been designed for each subsystem. The gains of the controllers are such chosen that the overall system becomes singularly perturbed system. Then sliding mode controllers are designed on the singularly perturbed system to drive the subsystems on sliding surfaces in finite time. Negative gradient of a potential based function has been added to the sliding surface to ensure collision avoidance among the robots in finite time. The efficacy of the proposed controller is established through simulation results.Comment: 8 pages, 5 figure

On Incremental Stability of Interconnected Switched Systems

In this letter, the incremental stability of interconnected systems is discussed. In particular, we consider an interconnection of switched nonlinear systems. The incremental stability of the switched interconnected system is a stronger property as compared to conventional stability. Guaranteeing such a notion of stability for an overall interconnected nonlinear system is challenging, even if individual subsystems are incrementally stable. Here, preserving incremental stability for the interconnection is ensured with a set of sufficient conditions. Contraction theory is used as a tool to achieve incremental convergence. For the feedback interconnection, the small gain characterisation is presented for the overall system's incremental stability. The results are derived for a special case of feedback, i.e., cascade interconnection. Matrix-measure-based conditions are presented, which are computationally tractable. Two numerical examples are demonstrated and supported with simulation results to verify the theoretical claims