Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers
This provides an effective and explainable tool for safe deployment and synthesis of hybrid controllers in robotics, though it is incremental as it builds on topological methods.
The paper tackles the problem of analyzing the global dynamics of robot controllers, such as identifying attractors and their regions of attraction, by proposing a topological framework that builds a Morse graph from local trajectory probes. It shows that this approach outperforms existing methods in accuracy and efficiency for both numerical and data-driven controllers in robotic benchmarks.
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.