Paper Citation Record · LEDGER

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics

As of 9 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2509.00294.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.00294 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T13:51:19.563950Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy31
unresolved6
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c395cacf-6b9b-4961-b0c1-6c28dd9ce0b3 · outbound

This paper cites an unresolved cited work.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:51:25.344227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 44664d1e-0743-4145-9b4a-54fbf55257bc · outbound

This paper cites Template models for control,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Template models for control,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:25.096204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 31787038-7ba5-42a4-aeb7-85072af03079 · outbound

This paper cites The 3d linear inverted pendulum mode: A simple modeling for a biped walking pattern generation,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics The 3d linear inverted pendulum mode: A simple modeling for a biped walking pattern generation,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:24.892695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4eaa39ee-a608-471f-9fb4-1c84ccd9c91b · outbound

This paper cites 3-d underactuated bipedal walking via h-lip based gait synthesis and stepping stabilization,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics 3-d underactuated bipedal walking via h-lip based gait synthesis and stepping stabilization,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:24.738410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3977231c-be1c-4fac-8941-cf260ad7ad61 · outbound

This paper cites Angular Momentum about the Contact Point for Control of Bipedal Locomotion: Validation in a LIP-based Controller.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Angular Momentum about the Contact Point for Control of Bipedal Locomotion: Validation in a LIP-based Controller

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-05T13:51:17.272211Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ecad6598-af67-4196-9dec-c5b64ed84aaa · outbound

This paper cites Multi-domain walking with reduced-order models of locomotion,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Multi-domain walking with reduced-order models of locomotion,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:24.565265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c3b33d9c-098a-4c96-8f5e-0f069e59e9b2 · outbound

This paper cites The spring-mass model for running and hopping,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics The spring-mass model for running and hopping,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:24.391989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d0a45a05-bd9d-4db6-86a2-7083e304f8d6 · outbound

This paper cites High-speed humanoid running through control with a 3d-slip model,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics High-speed humanoid running through control with a 3d-slip model,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:24.256991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3b812a77-0b12-498b-80d2-ae59bf50bc5a · outbound

This paper cites Capture point: A step toward humanoid push recovery,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Capture point: A step toward humanoid push recovery,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:24.136252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d183e079-24b8-480f-b875-4b91f6d858b6 · outbound

This paper cites Bipedal walking control based on capture point dynamics,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Bipedal walking control based on capture point dynamics,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:23.987058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8d1fdb59-029f-48d7-ab6d-f0c7deb7bb1c · outbound

This paper cites Three-dimensional bipedal walking control based on divergent component of motion,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Three-dimensional bipedal walking control based on divergent component of motion,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:23.842245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b3d5ae0e-83f0-41a3-b709-bae15d63047b · outbound

This paper cites Dynamic walking on compliant and uneven terrain using dcm and passivity-based whole-body control,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Dynamic walking on compliant and uneven terrain using dcm and passivity-based whole-body control,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:23.712978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0ea5d0e6-fd5c-4de9-927c-27fd3d152ca5 · outbound

This paper cites Learning spring mass locomotion: Guiding policies with a reduced- order model,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Learning spring mass locomotion: Guiding policies with a reduced- order model,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:23.510282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2265010e-9351-43f8-9d02-636f00780b95 · outbound

This paper cites Rl-augmented mpc framework for agile and robust bipedal footstep locomotion planning and con- trol,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Rl-augmented mpc framework for agile and robust bipedal footstep locomotion planning and con- trol,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:23.370392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f9a4ec18-1c60-4d72-a7ef-75ab00783d9d · outbound

This paper cites Reduced-Order Model Guided Contact-Implicit Model Predictive Control for Humanoid Locomotion.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Reduced-Order Model Guided Contact-Implicit Model Predictive Control for Humanoid Locomotion

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-05T13:51:18.010322Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b68946d6-e871-4281-aea7-9e6680709305 · outbound

This paper cites Terrain- adaptive, alip-based bipedal locomotion controller via model predic- tive control and virtual constraints,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Terrain- adaptive, alip-based bipedal locomotion controller via model predic- tive control and virtual constraints,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:23.184124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ea36b88c-83b6-44a6-afb8-6781c89f9237 · outbound

This paper cites Dynamic walking on highly underactuated point foot humanoids: Closing the loop between hzd and hlip,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Dynamic walking on highly underactuated point foot humanoids: Closing the loop between hzd and hlip,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:23.024123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5c4d8141-dfd4-4f4c-9d43-f4cc674f23c9 · outbound

This paper cites Decoupled control of bipedal locomotion based on hzd and h-lip,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Decoupled control of bipedal locomotion based on hzd and h-lip,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:22.800891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 33c1f05b-7456-46e6-948c-6d254bc81db9 · outbound

This paper cites Robust agility via learned zero dynamics policies,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Robust agility via learned zero dynamics policies,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:22.612466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b01ffae5-625f-4deb-9800-a4a9e408ba09 · outbound

This paper cites Reinforcement learning for reduced-order models of legged robots,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Reinforcement learning for reduced-order models of legged robots,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:22.387012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e07924bd-b32b-4859-b1ba-8e9d138b614e · outbound

This paper cites Combining trajectory optimization, supervised machine learning, and model structure for mitigating the curse of dimensionality in the control of bipedal robots,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Combining trajectory optimization, supervised machine learning, and model structure for mitigating the curse of dimensionality in the control of bipedal robots,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:22.212491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 582d3d4c-06bc-4624-af3b-12b4153c0910 · outbound

This paper cites Hierarchical control system design using approximate simulation,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Hierarchical control system design using approximate simulation,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:22.020785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 297cc8d5-f061-44e8-b1db-9c0a5e023f7a · outbound

This paper cites Formal connections between template and anchor models via approximate simulation,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Formal connections between template and anchor models via approximate simulation,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:21.819480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8507755e-6a26-49e1-a0ff-3f1b581e27aa · outbound

This paper cites Approximate simulation for template-based whole-body control,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Approximate simulation for template-based whole-body control,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:21.649715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0d34da53-90c4-4fb3-a5f2-c53c5e3388fe · outbound

This paper cites Hybrid zero dynamics of planar biped walkers,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Hybrid zero dynamics of planar biped walkers,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:21.475819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3ac1c0cd-5713-436c-8ce0-6bb89d5530a4 · outbound

This paper cites Dynamic multi-domain bipedal walking with atrias through slip based human-inspired control,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Dynamic multi-domain bipedal walking with atrias through slip based human-inspired control,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:21.320288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c4365495-6cb8-4108-b7c7-a3a621438287 · outbound

This paper cites an unresolved cited work.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:51:21.134347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a7a86dc0-aacb-45be-8888-54c2bdb8771e · outbound

This paper cites Realizing dynamic and efficient bipedal locomotion on the humanoid robot durus,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Realizing dynamic and efficient bipedal locomotion on the humanoid robot durus,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:21.044383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ecadec38-0385-4545-9953-48e857cb888f · outbound

This paper cites Dynamic walking with compliance on a cassie bipedal robot,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Dynamic walking with compliance on a cassie bipedal robot,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:20.854312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c36cbd96-a4b0-4530-85e9-f0af1c38d7ea · outbound

This paper cites Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-05T13:51:19.002333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2190baeb-421c-43c0-bb7a-b854ad57ded0 · outbound

This paper cites Constructive nonlinear control of underactuated systems via zero dynamics policies,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Constructive nonlinear control of underactuated systems via zero dynamics policies,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:20.710563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2083af66-62fe-40b5-82c7-5c9af7261c23 · outbound

This paper cites Rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:20.547560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f9b0ca93-e4ef-49b7-b213-4dd1afdb4ad2 · outbound

This paper cites an unresolved cited work.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:51:20.408547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation aef99394-4c34-4faa-a011-35d212b7f13c · outbound

This paper cites Input-to-state stability of periodic orbits of systems with impulse effects via poincar ´e analysis,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Input-to-state stability of periodic orbits of systems with impulse effects via poincar ´e analysis,

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:20.247333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 77a76d46-9e2a-4224-8e83-0ea97009b783 · outbound

This paper cites Input-to-state stability for discrete-time nonlinear systems,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Input-to-state stability for discrete-time nonlinear systems,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:20.099251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3e05936b-127d-4eee-bd07-1c1bae83b2a5 · outbound

This paper cites A converse lyapunov theorem for discrete- time systems with disturbances,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics A converse lyapunov theorem for discrete- time systems with disturbances,

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:19.960536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d4f5e42d-7bb5-4ec5-9d3b-e3837d2e6116 · outbound

This paper cites Input to state stabilizing control lyapunov functions for robust bipedal locomotion,.

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics Input to state stabilizing control lyapunov functions for robust bipedal locomotion,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:51:19.787604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.