Stability of Multi-Dimensional Switched Systems with an Application to Open Multi-Agent Systems

Extended from the classic switched system, themulti-dimensional switched system (MDSS) allows for subsystems(switching modes) with different state dimensions. In this work,we study the stability problem of the MDSS, whose state transi-tion at each switching instant is characterized by the dimensionvariation and the state jump, without extra constraint imposed.Based on the proposed transition-dependent average dwell time(TDADT) and the piecewise TDADT methods, along with the pro-posed parametric multiple Lyapunov functions (MLFs), sufficientconditions for the practical and the asymptotical stabilities of theMDSS are respectively derived for the MDSS in the presenceof unstable subsystems. The stability results for the MDSS areapplied to the consensus problem of the open multi-agent system(MAS) which exhibits dynamic circulation behaviors. It is shownthat the (practical) consensus of the open MAS with disconnectedswitching topologies can be ensured by (practically) stabilizingthe corresponding MDSS with unstable switching modes via theproposed TDADT and parametric MLF methods.Comment: 12 pages, 9 figure

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved