Estimating the region of attraction (RoA) for a robot controller is essential for safe application and controller composition. Many existing methods require a closed-form expression that limit applicability to data-driven controllers. Methods that operate only over trajectory rollouts tend to be data-hungry. In prior work, we have demonstrated that topological tools based on Morse Graphs (directed acyclic graphs that combinatorially represent the underlying nonlinear dynamics) offer data-efficient RoA estimation without needing an analytical model. They struggle, however, with high-dimensional systems as they operate over a state-space discretization. This paper presents Morse Graph-aided discovery of Regions of Attraction in a learned Latent Space (MORALS)**. The approach combines auto-encoding neural networks with Morse Graphs. MORALS shows promising predictive capabilities in estimating attractors and their RoAs for data-driven controllers operating over high-dimensional systems, including a 67-dim humanoid robot and a 96-dim 3-fingered manipulator. It first projects the dynamics of the controlled system into a learned latent space. Then, it constructs a reduced form of Morse Graphs representing the bistability of the underlying dynamics, i.e., detecting when the controller results in a desired versus an undesired behavior. The evaluation on high-dimensional robotic datasets indicates data efficiency in RoA estimation.

This paper aims to improve the computational efficiency of motion planning for mobile robots with non-trivial dynamics through the use of learned controllers. Offline, a system-specific controller is first trained in an empty environment. Then, for the target environment, the approach constructs a data structure, a "Roadmap with Gaps," to approximately learn how to solve planning queries using the learned controller. The roadmap nodes correspond to local regions. Edges correspond to applications of the learned controller that approximately connect these regions. Gaps arise as the controller does not perfectly connect pairs of individual states along edges. Online, given a query, a tree sampling-based motion planner uses the roadmap so that the tree’s expansion is informed towards the goal region. The tree expansion selects local subgoals given a wavefront on the roadmap that guides towards the goal. When the controller cannot reach a subgoal region, the planner resorts to random exploration to maintain probabilistic completeness and asymptotic optimality. The accompanying experimental evaluation shows that the approach significantly improves the computational efficiency of motion planning on various benchmarks, including physics-based vehicular models on uneven and varying friction terrains as well as a quadrotor under air pressure effects. Website: https://prx-kinodynamic.github.io/projects/rogue