Topological stages improve long term robot control across embodiments
Topological Necessities: Mechanism-Invariant Strategic Subgoals for Cross-Embodiment Goal-Conditioned Control
Machine LearningArtificial IntelligenceRobotics
Summary
Many robot control systems break big tasks into smaller steps called subgoals, but these steps are usually specific to the robot that learned them. This paper introduces a way to find essential passing points or stages that any robot must go through to complete a task, based on the shape of the environment and past successful attempts. These stages don’t depend on the robot itself and can be used across very different robots, like simple point agents or humanoid robots. The authors show that using these topological necessities improves performance and transfers well between different robot types.
What this means in practice
- •For robotics engineers: Create robot controllers that use topologically essential waypoints enabling reliable long-horizon task completion across different robot types.
- •For automation system developers: Design task planners that identify unavoidable stages in diverse environments for improved multi-robot navigation and control strategies.
Authors
Hao Shi, Xi Li
Abstract
Long-horizon goal-conditioned reinforcement learning delegates control to a high-level module that proposes subgoals, but existing subgoals are implicit byproducts of value functions or latent actions, tied to the executor that produced them. We study a different object: a route-conditioned order of unavoidable stages that every successful executor must traverse, recoverable from offline trajectories and belonging to none of them. Its defining properties are topological: an unskippable stage is a separating set that every admissible path must cross, and a loop in free space forces a route choice. We read the two by homology in dimensions 0 and 1 over a transport-weighted carrier built from successful trajectories, yielding an enumerable gate set with shell-level certificates; the certified gates are what we call topological necessities. Certified gates enter the decision loop as a recursive topological gate hierarchy. Under a fixed, isomorphic free space, the object survives executor replacement: gates frozen on PointMaze data transfer without retraining to Ant and Humanoid, attaining the highest Humanoid aggregate under a unified interface (96.1), with +36.0 over a map-privileged reference on the multi-route task (p=1.4e-5); the planner saturates PointMaze (100+/-0) and matches or exceeds the strongest baselines on AntMaze (giant +22.9) and Kitchen (+15.8/+12.6).