Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing more effective hybrid controllers. This paper proposes a topological framework to analyze the global dynamics of robot controllers, even data-driven ones, in an effective and explainable way. It builds a combinatorial representation representing the underlying system’s state space and non-linear dynamics, which is summarized in a directed acyclic graph, the Morse graph. The approach only probes the dynamics locally by forward propagating short trajectories over a state-space discretization, which needs to be a Lipschitz-continuous function. The framework is evaluated given either numerical or data-driven controllers for classical robotic benchmarks. It is compared against established analytical and recent machine learning alternatives for estimating the RoAs of such controllers. It is shown to outperform them in accuracy and efficiency. It also provides deeper insights as it describes the global dynamics up to the discretization’s resolution. This allows to use the Morse graph to identify how to synthesize controllers to form improved hybrid solutions or how to identify the physical limitations of a robotic system.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers


    Additional title:

    Springer Proceedings in Advanced Robotics



    Conference:

    International Workshop on the Algorithmic Foundations of Robotics ; 2022 ; , MD, USA June 22, 2022 - June 24, 2022



    Publication date :

    2022-12-15


    Size :

    18 pages





    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English




    Topological analysis of shapes using Morse theory

    Allili, M. / Corriveau, D. | British Library Online Contents | 2007


    Design of Robot Controllers for Cooperative Interactive Dynamics

    Newman, Wyatt / Birkhimer, Craig / Dohring, Mark | AIAA | 2003


    Morse remorse

    British Library Online Contents | 1997



    Analyzing train time table graphs

    Liebers, A. | Tema Archive | 2001