Physical AI via�Hierarchical Decision Processes

Yihao Liu

December 12, 2025

Hierarchical Decision Processes

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Recent Trends

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• Reinforcement Learning
• Often seen in navigation and locomotion

RL in IsaacLab [1]

IL Demonstration Trajectories (Sim) [2]

VLA (Nvidia GR00T) Synthetic and Teleop Data [3]

• Imitation Learning
• Often seen in manipulation

• Vision-Language-Action (VLA)

[1] Internship at Astera Institute

[2] Mu, T., Liu, Y., & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[3] Bjorck, J., Castañeda, F., Cherniadev, N., Da, X., Ding, R., Fan, L., ... & Zhu, Y. (2025). Gr00t n1: An open foundation model for generalist humanoid robots. arXiv preprint arXiv:2503.14734.

Recent Trends

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Question 1. Will the emergent behavior happen like in Large Language Models (LLM)?

Question 2. Is the reactive, reflex-like behavior sufficient?

Ganguli, D., Hernandez, D., Lovitt, L., Askell, A., Bai, Y., Chen, A., ... & Clark, J. (2022, June). Predictability and surprise in large generative models. In Proceedings of the 2022 ACM conference on fairness, accountability, and transparency (pp. 1747-1764).

Scaling Law

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• Question 1. Will the emergent behavior happen like in LLMs, given the current trend?
• No yet clear

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• “Action” datasets are relatively tiny and costly
• Text (LLMs) – Trillions of tokens
• Vision (VLMs ¹) – Billions of images
• Action (VLAs ²) – Millions of trajectories

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1 Vision-Language Models

2 Vision-Language-Action Models

Scaling Law

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1 Vision-Language Models

2 Vision-Language-Action Models

• Question 1. Will the emergent behavior happen like in LLMs, given the current trend?
• No yet clear

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• “Action” datasets are relatively tiny and costly
• Text (LLMs) – Trillions of tokens
• Vision (VLMs ¹) – Billions of images
• Action (VLAs ²) – Millions of trajectories

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Models’ Characteristics – Imitation Learning

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[1] Zhao, T. Z., Kumar, V., Levine, S., & Finn, C. (2023). Learning fine-grained bimanual manipulation with low-cost hardware. arXiv preprint arXiv:2304.13705.

[2] Chi, C., Xu, Z., Feng, S., Cousineau, E., Du, Y., Burchfiel, B., Tedrake, R., & Song, S. (2025). Diffusion policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research, 44(10-11), 1684-1704.

Action Chunking Transformer [1]

Diffusion Policy [2]

Question 2. Is the reactive, reflex-like behavior sufficient?

• No, it is not sufficient

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”Scoop Raisins into Bowl”

”Scoop Pretzels into Bowl”

Models’ Characteristics – Imitation Learning

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Action Chunking Transformer [1]

Diffusion Policy [2]

[1] Zhao, T. Z., Kumar, V., Levine, S., & Finn, C. (2023). Learning fine-grained bimanual manipulation with low-cost hardware. arXiv preprint arXiv:2304.13705.

[2] Chi, C., Xu, Z., Feng, S., Cousineau, E., Du, Y., Burchfiel, B., Tedrake, R., & Song, S. (2025). Diffusion policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research, 44(10-11), 1684-1704.

Both are sequence-to-sequence policies

Question 2. Is the reactive, reflex-like behavior sufficient?

Images

Encoder

Robot Action

Encoder

Latent Vector

Decoder

Future Robot Action

Models’ Characteristics – VLA Models

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[1] Bjorck, J., Castañeda, F., Cherniadev, N., Da, X., Ding, R., Fan, L., ... & Zhu, Y. (2025). Gr00t n1: An open foundation model for generalist humanoid robots. arXiv preprint arXiv:2503.14734.

[2] Chi, C., Xu, Z., Feng, S., Cousineau, E., Du, Y., Burchfiel, B., Tedrake, R., & Song, S. (2025). Diffusion policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research, 44(10-11), 1684-1704.

[3] Physical Intelligence. (2025). π_{0.5}: a Vision-Language-Action Model with Open-World Generalization. arXiv preprint arXiv:2504.16054

GR00T N1 [1], SmolVLA [2], pi0.5 [3]

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Question 2. Is the reactive, reflex-like behavior sufficient?

• No, it is not sufficient

Robot Action

Encoder

Latent Vector

Decoder

Future Robot Action

Pretrained Vision-Language Encoder

Images

pi0.5

“Put Green Pepper into Pot”

All are reactive visuomotor policies with some learned implicit planning, and still struggle on long-horizon tasks

• Two-Alternative Cue-Delay-Choice (2ACDC) Experiment [1]
• Animals can use tiny data (post-training) to perform long-horizon tasks

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How Animals Learn to Act and Decide

[1] Sun, W., Winnubst, J., Natrajan, M., Lai, C., Kajikawa, K., Bast, A., ... & Spruston, N. (2025). Learning produces an orthogonalized state machine in the hippocampus. Nature, 640(8057), 165-175.

“State Cells” in Hippocampus

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Sun, W., Winnubst, J., Natrajan, M., Lai, C., Kajikawa, K., Bast, A., ... & Spruston, N. (2025). Learning produces an orthogonalized state machine in the hippocampus. Nature, 640(8057), 165-175.

“State Cells” in Hippocampus

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Sun, W., Winnubst, J., Natrajan, M., Lai, C., Kajikawa, K., Bast, A., ... & Spruston, N. (2025). Learning produces an orthogonalized state machine in the hippocampus. Nature, 640(8057), 165-175.

“Learning produces an orthogonalized state machine in the hippocampus”

Two Layers�Formalism

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Two Layers

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Two Layers

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Two Layers

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States and Transitions

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Markovian

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State machine is a special case of “decision processes” using a tuple

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• Nodes as states and edges as transitions

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Other frameworks may include

• Markov Decision Processes (MDP)
• Semi-Markov Decision Processes
• Symbolic planners
• And a lot more

Different state spaces and time spaces

• State: symbolic, discrete, continuous
• Time: discrete, continuous

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We could define S to be a hybrid by Cartesian product

An Intuitive Example using Finite State Machines

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• For a long-horizon task, we need
• States
• Actions
• Transitions

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[1] Mu, T., Liu, Y. & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[2] Liu, Y., & Armand, M. (2024). A roadmap towards automated and regulated robotic systems. arXiv preprint arXiv:2403.14049.

An Intuitive Example using Finite State Machines

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[1] Mu, T., Liu, Y. & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[2] Liu, Y., & Armand, M. (2024). A roadmap towards automated and regulated robotic systems. arXiv preprint arXiv:2403.14049.

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• Where do we get the states, action, and transitions?

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• Try this: Trusting an LLM as an Oracle

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Text

Executables

Agent

Input to Agent:

Task Description

State Constraints

Operation Constraints

An Intuitive Example using Finite State Machines

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[1] Mu, T., Liu, Y. & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[2] Liu, Y., & Armand, M. (2024). A roadmap towards automated and regulated robotic systems. arXiv preprint arXiv:2403.14049.

• A serialization method to convert between plans and texts

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• State Machine Serialization Language (SMSL)
• JSON files
• readable by both human and machines

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Large�Language

Model

Sim Task Demonstrations ^{[1], [2]}

Robot Models

Generate

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Scripts

Imitation

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Learning

LLMs

What About the Skill Library?

Generating Robotic Tasks for Imitation Learning via LLM in the Literature

[1] Shridhar et al. "Cliport: What and where pathways for robotic manipulation." Conference on robot learning. PMLR, 2022.

[2] Wang et al. "Gensim: Generating robotic simulation tasks via large language models." arXiv:2310.01361 2023.

Challenges

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Generating Robotic Tasks for Imitation Learning via LLM in the Literature

[1] Shridhar et al. "Cliport: What and where pathways for robotic manipulation." Conference on robot learning. PMLR, 2022.

[2] Wang et al. "Gensim: Generating robotic simulation tasks via large language models." arXiv:2310.01361 2023.

Handling state-dependent, long-horizon tasks is particularly challenging

Key Insight: Utilize FSM as a Planner and to Structure Demonstrations

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[1] Mu, T., Liu, Y. & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[2] Liu, Y., & Armand, M. (2024). A roadmap towards automated and regulated robotic systems. arXiv preprint arXiv:2403.14049.

Key Insight: Utilize FSM as a Planner and to Structure Demonstrations

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[1] Mu, T., Liu, Y. & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[2] Liu, Y., & Armand, M. (2024). A roadmap towards automated and regulated robotic systems. arXiv preprint arXiv:2403.14049.

Experiments

Hanoi Tower Task

River Crossing Task

Chess Task

Key Insight: Utilize FSM as a Planner and to Structure Demonstrations

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[1] Mu, T., Liu, Y. & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[2] Liu, Y., & Armand, M. (2024). A roadmap towards automated and regulated robotic systems. arXiv preprint arXiv:2403.14049.

Experiments

• As the complexity increases, both LLMs or Reasoning LLMs fail

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[1] Shojaee, P., Mirzadeh, I., Alizadeh, K., Horton, M., Bengio, S., & Farajtabar, M. (2025). The illusion of thinking: Understanding the strengths and limitations of reasoning models via the lens of problem complexity. arXiv preprint arXiv:2506.06941.

Architecture��Generalize from closed “finite” states to open space

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to Handle Complexity

An Architecture to Handle Complexity

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SMSL – enumerative

• Tree search over a known graph

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Symbolic Planning – factored

• Open exploration with a known set of skills

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Conceptual frameworks

• Linear Temporal Logic (LTL)
• “always avoid X”, “eventually do Y”, “do X before Y”
• Stanford Research Institute Problem Solver (STRIPS)

Handling Complexity by Open Action and Hierarchy

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Handling Complexity by Open Action and Hierarchy

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Abstraction

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Concretization

Handling Complexity by Open Action and Hierarchy

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Abstraction

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Concretization

Pipeline

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1. Sensing -> Estimation

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• Labeling -> Symbolic Update

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• Nominal Planning -> High-Level Action

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• Refinement to Options -> Skills

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• Dispatch and Execution

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• Monitoring and Failure Detection

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• Recovery Selection and Execution

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• Return to Nominal Plan

Overall Architecture

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Symbolic Components

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• Planner
• Visualizer
• Predictor
• Estimator

Symbolic Planner

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Inputs: Current S,

Goal G,

Option Library A

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Outputs: Symbolic Plan [a_0, …, a_{K-1}]

Mu, T., Liu, Y., & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Symbolic Planner

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1. Oracle-Guided
2. Human-Specified
3. Learning-Based

Mu, T., Liu, Y., & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Symbolic Planner

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1. Oracle-Guided
2. Human-Specified
3. Learning-Based

Liu, Y., Kheradmand, A., & Armand, M. (2023). Toward process controlled medical robotic system. arXiv preprint arXiv:2308.05809.

Symbolic Planner

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1. Oracle-Guided
2. Human-Specified
3. Learning-Based

Liu, Y., Kheradmand, A., & Armand, M. (2023). Toward process controlled medical robotic system. arXiv preprint arXiv:2308.05809.

Symbolic Planner

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1. Oracle-Guided
2. Human-Specified
3. Learning-Based

Liu, Y., Kheradmand, A., & Armand, M. (2023). Toward process controlled medical robotic system. arXiv preprint arXiv:2308.05809.

Symbolic Planner

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1. Oracle-Guided
2. Human-Specified
3. Learning-Based

Liu, W., Chen, G., Hsu, J., Mao, J., & Wu, J. (2024). Learning planning abstractions from language. ICLR.

Symbolic Visualizer

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Symbolic Visualizer

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Mu, T., Liu, Y., & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Symbolic Visualizer

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Mu, T., Liu, Y., & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Symbolic Predictor

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Liu, W., Chen, G., Hsu, J., Mao, J., & Wu, J. (2024). Learning planning abstractions from language. ICLR.

Silver, T., Chitnis, R., Tenenbaum, J., Kaelbling, L. P., & Lozano-Pérez, T. (2021, September). Learning symbolic operators for task and motion planning. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 3182-3189). IEEE.

Symbolic Estimator

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Symbolic Estimator

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Liu., Y. Unpublished work.

Symbolic Components

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• Planner
• Visualizer
• Predictor
• Estimator

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• Estimator (and Actor)

Sub-Symbolic Components

• Sensor and Actuator

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• Planner

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• Predictor

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• Visualizer

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• Estimator (and Actor)

Sub-Symbolic Components

• Sensor and Actuator

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• Planner

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• Predictor

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• Visualizer

Sensor and Actuator

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Liu, Y., Kheradmand, A., & Armand, M. (2023). Toward process controlled medical robotic system. arXiv preprint arXiv:2308.05809.

Visual

servoing

Sensor and Actuator

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Liu, Y., Kheradmand, A., & Armand, M. (2023). Toward process controlled medical robotic system. arXiv preprint arXiv:2308.05809.

Visual servoing

Sub-Symbolic Estimator and Actor

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Sub-Symbolic Estimator

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Liu, Y., Zhang, J., Diaz-Pinto, A., Li, H., Martin-Gomez, A., Kheradmand, A., & Armand, M. (2024, April). Segment any medical model extended. In Medical Imaging 2024: Image Processing (Vol. 12926, pp. 411-422). SPIE.

Sub-Symbolic Estimator

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Zhang, J., Zhang, Z., Liu, Y., Chen, Y., Kheradmand, A., & Armand, M. (2024, May). Realtime robust shape estimation of deformable linear object. In 2024 IEEE International Conference on Robotics and Automation (ICRA) (pp. 10734-10740). IEEE.

Sub-Symbolic Actor

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• Learned / programmed reactive visuomotor policies in the skill library
• VLAs like GR00T
• IL models like ACT and Diffusion Policy
• Trained recovery policies

Sub-Symbolic Predictor

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• Learned / analytical world models
• Nvidia Cosmos-Predict
• Nvidia Cosmos-Transfer
• Nvidia Cosmos-Reason

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• They do not output trajectories directly, but provide multiple forecasts of pixels and text descriptions.

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• Observation-level simulator

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• Computationally heavy, so they are best used offline.
• Synthetic data generation for policy training

Sub-Symbolic Predictor

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Internship at Astera Institute

Sub-Symbolic Visualizer

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Ai, L., Liu, Y., Armand, M., Kheradmand, A., & Martin-Gomez, A. (2024, May). On the Fly Robotic-Assisted Medical Instrument Planning and Execution Using Mixed Reality. In 2024 IEEE International Conference on Robotics and Automation (ICRA). IEEE.

Symbolic Planner

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Symbolic Visualizer

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Symbolic Predictor

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Symbolic Estimator

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Sub-Symbolic Estimator and Actor

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Sub-Symbolic Predictor

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Symbolic Visualizer

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Sub-Symbolic Planner and Dispatcher

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Infrastructure

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Robotic System�Data Platform�Calibrations

Robotic Systems

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• Robots
• Visualization platforms
• Teleoperators

Liu, Y., Zhang, J., Ai, L., Tian, J., Sefati, S., Liu, H., ... & Armand, M. (2025). An Image-Guided Robotic System for Transcranial Magnetic Stimulation: System Development and Experimental Evaluation. IEEE Robotics and Automation Letters.

Data Platforms / Digital Twin

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Liu, Y., Ku, Y. C., Zhang, J., Ding, H., Kazanzides, P., & Armand, M. (2025). dARt Vinci: Egocentric Data Collection for Surgical Robot Learning at Scale. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Data Platforms / Digital Twin

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Liu, Y., Ku, Y. C., Zhang, J., Ding, H., Kazanzides, P., & Armand, M. (2025). dARt Vinci: Egocentric Data Collection for Surgical Robot Learning at Scale. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Data Platforms / Digital Twin

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Liu, Y., Ku, Y. C., Zhang, J., Ding, H., Kazanzides, P., & Armand, M. (2025). dARt Vinci: Egocentric Data Collection for Surgical Robot Learning at Scale. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Geometric Calibrations

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• Ensure the hybrid state is expressed correctly, enabling correct symbolic grounding and abstraction

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• Ensure correct correspondence of the transformations in the data platforms and the digital twin systems

Geometric Calibrations

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Liu, Y., Zhang, J., She, Z., Kheradmand, A., & Armand, M. (2024, May). Gbec: Geometry-based hand-eye calibration. In 2024 IEEE International Conference on Robotics and Automation (ICRA) (pp. 16698-16705). IEEE.

Ai, L., Liu, Y., Armand, M., & Martin-Gomez, A. (2024, October). Calibration of Augmented Reality Headset with External Tracking System Using AX= YB. In 2024 IEEE International Symposium on Mixed and Augmented Reality (ISMAR) (pp. 210-218). IEEE.

Hand-eye calibration

Virtual-to-real calibration

Geometric Calibrations

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Hand-eye calibration

Virtual-to-real calibration

Liu, Y., Zhang, J., She, Z., Kheradmand, A., & Armand, M. (2024, May). Gbec: Geometry-based hand-eye calibration. In 2024 IEEE International Conference on Robotics and Automation (ICRA) (pp. 16698-16705). IEEE.

Ai, L., Liu, Y., Armand, M., & Martin-Gomez, A. (2024, October). Calibration of Augmented Reality Headset with External Tracking System Using AX= YB. In 2024 IEEE International Symposium on Mixed and Augmented Reality (ISMAR) (pp. 210-218). IEEE.

Contributions

• Developed a hierarchical architecture that enables robots to make decisions as the world evolves, which
• connects modular classical approaches and emerging learned models
• separates a symbolic layer from the reflex-like sub-symbolic layer

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• Our Examples Included within the Architecture
• An oracle-guided visuomotor task planner
• An egocentric simulation data platform
• State Machine Serialization Language
• An image-guided robot-assisted intervention system
• An AR-based medical navigation platform

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Future Works

• Visuomotor (navigation, manipulation) policies
• Task- / type- specific
• Learning-based symbolic planner
• Task decomposition,
• Task-level world model
• Symbolic estimator
• More accurate phase / task detector
• Faster sub-symbolic predictor
• VLM-based World model

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Publications

• Mu, T., Liu, Y., & Armand, M. (2025). Look Before You Leap: Using Serialized State Machine for Language Conditioned Robotic Manipulation. arXiv preprint arXiv:2503.05114.
• Liu, Y., Ku, Y. C., Zhang, J., Ding, H., Kazanzides, P., & Armand, M. (2025). dARt Vinci: Egocentric Data Collection for Surgical Robot Learning at Scale. arXiv preprint arXiv:2503.05646.
• Liu, Y., Zhang, J., Ai, L., Tian, J., Sefati, S., Liu, H., ... & Armand, M. (2025). An Image-Guided Robotic System for Transcranial Magnetic Stimulation: System Development and Experimental Evaluation. IEEE Robotics and Automation Letters.
• Li, H., Yan, W., Liu, D., Qian, L., Yang, Y., Liu, Y., ... & Wang, G. (2024). Evd surgical guidance with retro-reflective tool tracking and spatial reconstruction using head-mounted augmented reality device. IEEE Transactions on Visualization and Computer Graphics.
• Ai, L., Liu, Y., Armand, M., & Martin-Gomez, A. (2024, October). Calibration of Augmented Reality Headset with External Tracking System Using AX= YB. In 2024 IEEE International Symposium on Mixed and Augmented Reality (ISMAR) (pp. 210-218). IEEE.
• Liu, Y., Tian, J., Martin-Gomez, A., Arshad, Q., Armand, M., & Kheradmand, A. (2024). Autokinesis reveals a threshold for perception of visual motion. Neuroscience, 543, 101-107.
• Liu, Y., Zhang, J., Diaz-Pinto, A., Li, H., Martin-Gomez, A., Kheradmand, A., & Armand, M. (2024, April). Segment any medical model extended. In Medical Imaging 2024: Image Processing (Vol. 12926, pp. 411-422). SPIE.
• Liu, Y., & Armand, M. (2024). A roadmap towards automated and regulated robotic systems. arXiv preprint arXiv:2403.14049.
• Ai, L., Liu, Y., Armand, M., Kheradmand, A., & Martin-Gomez, A. (2024, May). On the Fly Robotic-Assisted Medical Instrument Planning and Execution Using Mixed Reality. In 2024 IEEE International Conference on Robotics and Automation (ICRA) (pp. 13192-13199). IEEE.
• Liu, Y., Zhang, J., She, Z., Kheradmand, A., & Armand, M. (2024, May). Gbec: Geometry-based hand-eye calibration. In 2024 IEEE International Conference on Robotics and Automation (ICRA) (pp. 16698-16705). IEEE.
• Zhang, J., Zhang, Z., Liu, Y., Chen, Y., Kheradmand, A., & Armand, M. (2024, May). Realtime robust shape estimation of deformable linear object. In 2024 IEEE International Conference on Robotics and Automation (ICRA) (pp. 10734-10740). IEEE.
• Liu, Y., Kheradmand, A., & Armand, M. (2023). Toward process controlled medical robotic system. arXiv preprint arXiv:2308.05809.
• Liu, Y., Zhang, J., She, Z., Kheradmand, A., & Armand, M. (2023). Samm (segment any medical model): A 3d slicer integration to sam. arXiv preprint arXiv:2304.05622.
• Liu, Y., Liu, S. J., Sefati, S., Jing, T., Kheradmand, A., & Armand, M. (2022, March). Inside-out tracking and projection mapping for robot-assisted transcranial magnetic stimulation. In Optical architectures for displays and sensing in augmented, virtual, and mixed reality (AR, VR, MR) III (Vol. 11931, pp. 57-70). SPIE.

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Acknowledgement

• National Institute of Deafness and Other Communication Disorders (R01DC018815), PI: Amir Kheradmant
• National Institute of Biomedical Imaging and Bioengineering (R01EB023939), PI: Mehran Armand
• National Institute of Arthritis and Musculoskeletal and Skin Diseases (R01AR080315), PI: Mehran Armand and Amit Jain
• Internal Fundings from the Department of Computer Science, Johns Hopkins University

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Thesis Committee

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My family

Overall Architecture

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