Generative Flow on Symbolic Abstractions for Embodiment Capability Discovery

Youwei Yu Lantao Liu

Indiana University

CoRL 2026

Paper(soon) Video(soon) Code

Which tasks can a robot actually learn?

FOSA's GFlowNet builds task semantics edit by edit, rewarded for tasks that training makes learnable but not yet mastered.

capabilitygoalenvironmentconstraintafter PPO velocity → rough terrain navigation: 195 tasks velocity → slalom navigation: 13 tasks velocity → friction adaptation: 13 tasks velocity → velocity tracking flat: 13 tasks velocity → dynamic obstacle avoidance: 10 tasks velocity → precision docking: 6 tasks velocity → actuator degradation: 6 tasks rough terrain navigation → friction adaptation: 54 tasks rough terrain navigation → rough terrain navigation: 66 tasks rough terrain navigation → precision docking: 16 tasks rough terrain navigation → dynamic obstacle avoidance: 31 tasks rough terrain navigation → slalom navigation: 16 tasks rough terrain navigation → velocity tracking flat: 11 tasks rough terrain navigation → actuator degradation: 1 tasks slalom navigation → friction adaptation: 2 tasks slalom navigation → precision docking: 3 tasks slalom navigation → dynamic obstacle avoidance: 2 tasks slalom navigation → slalom navigation: 5 tasks slalom navigation → velocity tracking flat: 1 tasks friction adaptation → friction adaptation: 3 tasks friction adaptation → rough terrain navigation: 1 tasks friction adaptation → precision docking: 6 tasks friction adaptation → dynamic obstacle avoidance: 1 tasks friction adaptation → slalom navigation: 1 tasks friction adaptation → velocity tracking flat: 1 tasks velocity tracking flat → friction adaptation: 8 tasks velocity tracking flat → rough terrain navigation: 1 tasks velocity tracking flat → precision docking: 1 tasks velocity tracking flat → velocity tracking flat: 3 tasks dynamic obstacle avoidance → friction adaptation: 1 tasks dynamic obstacle avoidance → rough terrain navigation: 1 tasks dynamic obstacle avoidance → precision docking: 2 tasks dynamic obstacle avoidance → slalom navigation: 1 tasks dynamic obstacle avoidance → velocity tracking flat: 3 tasks dynamic obstacle avoidance → actuator degradation: 2 tasks precision docking → friction adaptation: 2 tasks precision docking → precision docking: 3 tasks precision docking → velocity tracking flat: 1 tasks actuator degradation → rough terrain navigation: 1 tasks actuator degradation → precision docking: 3 tasks actuator degradation → velocity tracking flat: 2 tasks friction adaptation → dynamic obstacle avoidance: 27 tasks friction adaptation → actuator degradation: 12 tasks friction adaptation → velocity tracking flat: 9 tasks friction adaptation → rough terrain navigation: 2 tasks friction adaptation → slalom navigation: 8 tasks friction adaptation → friction adaptation: 9 tasks friction adaptation → precision docking: 3 tasks rough terrain navigation → dynamic obstacle avoidance: 54 tasks rough terrain navigation → actuator degradation: 9 tasks rough terrain navigation → velocity tracking flat: 2 tasks rough terrain navigation → rough terrain navigation: 1 tasks rough terrain navigation → slalom navigation: 1 tasks rough terrain navigation → friction adaptation: 1 tasks rough terrain navigation → precision docking: 2 tasks precision docking → dynamic obstacle avoidance: 12 tasks precision docking → actuator degradation: 5 tasks precision docking → velocity tracking flat: 4 tasks precision docking → rough terrain navigation: 3 tasks precision docking → slalom navigation: 2 tasks precision docking → friction adaptation: 3 tasks precision docking → precision docking: 5 tasks dynamic obstacle avoidance → dynamic obstacle avoidance: 25 tasks dynamic obstacle avoidance → actuator degradation: 2 tasks dynamic obstacle avoidance → velocity tracking flat: 1 tasks dynamic obstacle avoidance → rough terrain navigation: 4 tasks dynamic obstacle avoidance → slalom navigation: 1 tasks dynamic obstacle avoidance → precision docking: 1 tasks slalom navigation → dynamic obstacle avoidance: 13 tasks slalom navigation → actuator degradation: 1 tasks slalom navigation → rough terrain navigation: 7 tasks slalom navigation → slalom navigation: 2 tasks velocity tracking flat → dynamic obstacle avoidance: 5 tasks velocity tracking flat → actuator degradation: 4 tasks velocity tracking flat → velocity tracking flat: 5 tasks velocity tracking flat → rough terrain navigation: 1 tasks velocity tracking flat → slalom navigation: 2 tasks velocity tracking flat → friction adaptation: 2 tasks velocity tracking flat → precision docking: 3 tasks actuator degradation → dynamic obstacle avoidance: 1 tasks actuator degradation → rough terrain navigation: 1 tasks actuator degradation → slalom navigation: 1 tasks dynamic obstacle avoidance → on the frontier: 92 tasks dynamic obstacle avoidance → mastered: 18 tasks dynamic obstacle avoidance → not learned: 27 tasks actuator degradation → on the frontier: 18 tasks actuator degradation → mastered: 8 tasks actuator degradation → not learned: 7 tasks velocity tracking flat → on the frontier: 14 tasks velocity tracking flat → mastered: 3 tasks velocity tracking flat → not learned: 4 tasks rough terrain navigation → on the frontier: 9 tasks rough terrain navigation → mastered: 3 tasks rough terrain navigation → not learned: 7 tasks slalom navigation → on the frontier: 9 tasks slalom navigation → mastered: 2 tasks slalom navigation → not learned: 6 tasks friction adaptation → on the frontier: 5 tasks friction adaptation → mastered: 5 tasks friction adaptation → not learned: 5 tasks precision docking → not learned: 14 tasks velocity 256 rough terrain navigation 195 slalom navigation 13 friction adaptation 13 velocity tracking flat 13 dynamic obstacle avoidance 10 friction adaptation 70 rough terrain navigation 70 precision docking 34 dynamic obstacle avoidance 34 slalom navigation 23 velocity tracking flat 22 dynamic obstacle avoidance 137 actuator degradation 33 velocity tracking flat 21 rough terrain navigation 19 slalom navigation 17 friction adaptation 15 precision docking 14 on the frontier 147 mastered 39 not learned 70

Example task

  1. empty skeleton
  2. add_atomcapabilityvelocity
  3. add_atomconstraintdynamic obstacle avoidance
  4. add_atomenvironmentrough terrain navigation
  5. add_atomgoalrough terrain navigation
  6. refine_argenvironmentterrain type→ pyramid
  7. stop
Navigate the rough terrain avoiding the moving cylinder while maintaining velocity and stability.

Capability Frontier Landscape

Sim-to-Sim Held-out Tasks

Uphill climb
Washboard
Speed bumps
Gravel reverse
Sphere lift
Cuboid turn
Palm ball balance
Cylinder tip
Stair descent
Ice stop
Shove walk
Lateral walk
Crouch hold
Wave while standing
Gentle ramp up
Push stand

Sim-to-Real Held-out Tasks

Grass traversal
Step climbing
Obstacle bypass
×1.5
Cart pushing
Grass traversal
×2
Barrier balance
×4
Mug delivery
×2
Tunnel crawl