Frame-Coded Legged Locomotion over Noisy Terrain
Lav R. Varshney · N/A · 2026
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Summary
Open-loop multilegged locomotion over rough terrain has been interpreted as matter transport over a noisy channel: leg-ground interactions are discrete basic active contacts, terrain deletes or perturbs those contacts, and spatial redundancy concentrates the resulting thrust and arrival time. Tha...
Abstract Summary
Key Points
- Open-loop multilegged locomotion over rough terrain has been interpreted as matter transport over...
- That construction is repetition-like because every module carries the same scalar locomotion task
- It consequently provides neither a positive task rate nor a decoder that changes with the survivi...
- Here we formulate locomotion instead as a quantized finite-frame expansion with erasures
- A d-dimensional body-level command is mapped into N>d heterogeneous local contact commands
Frame-Coded Legged Locomotion over Noisy Terrain
|Authors: Lav R. Varshney
|Venue: arXiv preprint | Year: 2026
|arXiv: 2609.10273v1
Abstract
Open-loop multilegged locomotion over rough terrain has been interpreted as matter transport over a noisy channel: leg-ground interactions are discrete basic active contacts, terrain deletes or perturbs those contacts, and spatial redundancy concentrates the resulting thrust and arrival time. That construction is repetition-like because every module carries the same scalar locomotion task. It consequently provides neither a positive task rate nor a decoder that changes with the surviving contact set. Here we formulate locomotion instead as a quantized finite-frame expansion with erasures. A d-dimensional body-level command is mapped into N>d heterogeneous local contact commands. Rough terrain erases or corrupts frame coefficients, while a contact-gated compliant morphology physically realizes the weighted active-subframe decoder. For a linear-Gaussian model, mechanical equilibrium is exactly the posterior mean, tangent stiffness is posterior precision, and mechanical compliance is posterior covariance. Equal-norm Parseval frames are shown to be minimax optimal against one missing contact, two-contact robustness is governed by frame coherence, and a harmonic frame gives a directly realizable gait family. For independently surviving contacts of probability q, random Gaussian gait frames admit exact reconstruction at every analog dimension rate R<q, with a binomial reliability exponent, whereas recovery of arbitrary commands is impossible for R>q. Residual contact noise yields an asymptotic per-mode amplification 1/(q-R) and a vanishing mechanical stiffness margin at the threshold. An information-locomotion inequality and an exact incremental-redundancy rule direct the next gait component toward the softest task-relevant unresolved mode. The resulting analog frame-coding theorem establishes a finite relative redundancy and converse as part of a fundamental limit theory of legged locomotion.
Key Contributions
- Open-loop multilegged locomotion over rough terrain has been interpreted as matter transport over…
- That construction is repetition-like because every module carries the same scalar locomotion task
- It consequently provides neither a positive task rate nor a decoder that changes with the survivi…
- Here we formulate locomotion instead as a quantized finite-frame expansion with erasures
- A d-dimensional body-level command is mapped into N>d heterogeneous local contact commands
Topics
- locomotion
Code & Data
No code repository linked in paper metadata.
BibTeX
@article{Varshney2026_260910273v1,
title = {Frame-Coded Legged Locomotion over Noisy Terrain},
author = {Lav R. Varshney},
year = {2026},
eprint = {2609.10273v1},
archivePrefix = {arXiv},
primaryClass = {cs.IT},
url = {https://arxiv.org/abs/2609.10273v1}
}
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