Physics-Informed Neural Networks with Unscented Kalman Filter for Sensorless Joint Torque Estimation in Humanoid Robots

์ €์ž: Ines Sorrentino, Giulio Romualdi, Lorenzo Moretti, Silvio Traversaro, Daniele Pucci | ๋‚ ์งœ: 2025-07-14 | URL: https://arxiv.org/abs/2507.10105 📄 PDF


Essence

Figure 2

Fig. 2: Block diagram of the multi-layer torque control architecture implemented on the ergoCub humanoid robot. The

๋ณธ ๋…ผ๋ฌธ์€ Physics-Informed Neural Networks (PINNs)์™€ Unscented Kalman Filter (UKF)๋ฅผ ๊ฒฐํ•ฉํ•˜์—ฌ ํœด๋จธ๋…ธ์ด๋“œ ๋กœ๋ด‡์˜ ๊ด€์ ˆ ํ† ํฌ ์„ผ์„œ ์—†์ด ์ „์‹  ํ† ํฌ ์ œ์–ด๋ฅผ ์ˆ˜ํ–‰ํ•˜๋Š” ํ”„๋ ˆ์ž„์›Œํฌ๋ฅผ ์ œ์‹œํ•œ๋‹ค. ์ด ๋ฐฉ์‹์€ ๋งˆ์ฐฐ ๋ชจ๋ธ๋ง๊ณผ ํ† ํฌ ์ถ”์ •์„ ํ†ตํ•ฉํ•˜์—ฌ ์‹ค์‹œ๊ฐ„ ํ† ํฌ ์ œ์–ด ์•„ํ‚คํ…์ฒ˜๋ฅผ ๊ตฌํ˜„ํ•œ๋‹ค.

Motivation

Achievement

Figure 4

Fig. 4: CoM tracking comparison: RNEA-PINN (left) vs. UKF-PINN (right). Green rectangles indicate external contacts.

How

Figure 2

Fig. 2: Block diagram of the multi-layer torque control architecture implemented on the ergoCub humanoid robot. The

Originality

Limitation & Further Study

Evaluation

Novelty: 4/5 Technical Soundness: 3/5 Significance: 4/5 Clarity: 4/5 Overall: 4/5

์ดํ‰: ๋ณธ ๋…ผ๋ฌธ์€ PINNs๊ณผ UKF์˜ ํ˜์‹ ์  ํ†ตํ•ฉ์„ ํ†ตํ•ด ์„ผ์„œ ์—†๋Š” ํ† ํฌ ์ œ์–ด๋ผ๋Š” ์‹ค์งˆ์  ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๋ฉฐ, ergoCub์—์„œ์˜ ์—„๋ฐ€ํ•œ ์‹คํ—˜ ๊ฒ€์ฆ๊ณผ ํ™•์žฅ์„ฑ ์‹œ์—ฐ์œผ๋กœ ํœด๋จธ๋…ธ์ด๋“œ ๋กœ๋ด‡์˜ ์‹ค์‹œ๊ฐ„ ์ค€์ˆ˜ ์ œ์–ด๋ฅผ ์œ„ํ•œ ๊ฐ•๋ ฅํ•œ ๊ธฐ์ดˆ๋ฅผ ์ œ๊ณตํ•œ๋‹ค.

๊ฐ™์ด ๋ณด๋ฉด ์ข‹์€ ๋…ผ๋ฌธ

๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
The invariant extended Kalman filter as a stable observer ๋…ผ๋ฌธ์€ ์ƒํƒœ ์ถ”์ •์˜ ์ด๋ก ์  ๊ธฐ๋ฐ˜์„ ์ œ๊ณตํ•˜์—ฌ ๋ณธ ์—ฐ๊ตฌ์˜ UKF ์ ์šฉ ์ด์œ ๋ฅผ ๋ช…ํ™•ํžˆ ํ•ด์ค๋‹ˆ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
Contact-Aided Invariant Extended Kalman Filtering์€ ๋งˆ์ฐฐ ๋ฐ ์ ‘์ด‰ ์ถ”์ • ๊ธฐ๋ฐ˜ ์ „์‹  ์ƒํƒœ ์ถ”์ •์—์„œ ์ œ์–ด ์ ํ•ฉ์„ฑ ๋ฐ Kalman ํ•„ํ„ฐ ํ™•์žฅ์— ๋Œ€ํ•œ ์ด๋ก ์  ๋ฐฐ๊ฒฝ์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
PINN(Physics-Informed Neural Networks) ์ด๋ก ๊ณผ ์ฃผ์š” ์‘์šฉ ๋ฐ ๋ฌธ์ œ์ ์„ ์‹ฌ๋„ ์žˆ๊ฒŒ ๋‹ค๋ฃจ๋ฏ€๋กœ, ๋ณธ ๋…ผ๋ฌธ์˜ ํ”„๋ ˆ์ž„์›Œํฌ ์ดํ•ด์— ์ด๋ก ์  ๊ธฐ๋ฐ˜์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
PINN ๋ฐ ๊ทธ ํ™•์žฅ ๊ธฐ๋ฒ•์˜ ์ด๋ก ์ ยท์‹ค์ „์  ๋…ผ์˜๋ฅผ ์ œ๊ณตํ•ด, UKF ๊ฒฐํ•ฉ PINN์˜ ๋ฐœ์ „ ๋งฅ๋ฝ์„ ์ดํ•ดํ•˜๋Š” ๋ฐ ๊ธฐ๋ฐ˜์ด ๋ฉ๋‹ˆ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
Neural Operator ๋ฐ ๋ฐ์ดํ„ฐ ๊ธฐ๋ฐ˜ ๋™์—ญํ•™ ์‹œ์Šคํ…œ์˜ ์‹ค์ œ ์ ์šฉ๊ณผ ๊ฒ€์ฆ ์‚ฌ๋ก€๋ฅผ ๋‹ค๋ค„, 621์˜ PINN ํ™•์žฅ ๋ฒ„์ „ ๊ฐœ๋ฐœ์˜ ๊ธฐ๋ฐ˜์ด ๋œ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
AutoOdom ๋…ผ๋ฌธ์€ ์˜คํ† ๋ฆฌ๊ทธ๋ ˆ์‹œ๋ธŒ ๋ฐฉ์‹์œผ๋กœ ๊ด€์ ˆ ํ† ํฌ์™€ ์ƒํƒœ ์ถ”์ •์„ ๊ฒฐํ•ฉํ•ด, UKF ๊ธฐ๋ฐ˜ ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ์˜ ์‹ค์‹œ๊ฐ„ ์ œ์–ด์— ์ด๋ก ์  ๊ธฐ๋ฐ˜์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
Physics-Informed Neural Networks with Unscented Kalman Filter ๋…ผ๋ฌธ์€ PINN๊ณผ ์นผ๋งŒ ํ•„ํ„ฐ ๊ฒฐํ•ฉ์˜ ์›๋ฆฌ๋ฅผ ์†Œ๊ฐœํ•ด Neural EnKF ๋…ผ๋ฌธ์˜ ๊ธฐ๋ฐ˜์ด ๋œ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
621์˜ ๋ฌผ๋ฆฌ์ •๋ณด์‹ ๊ฒฝ๋ง๊ณผ ์นผ๋งŒํ•„ํ„ฐ ๊ฒฐํ•ฉ ๊ฐœ๋…์€ 3377์˜ ์ž๋™์žฌํ˜„ยท์„ฑ๋Šฅ ์ตœ์ ํ™”๋ฅผ ์œ„ํ•œ ์‹ ๋ขฐ์„ฑ ์žˆ๊ณ  ๋ˆ„์  ๊ฐ€๋Šฅํ•œ ํ™˜๊ฒฝ ๊ตฌํ˜„์— ๊ธฐ์ดˆ๊ฐ€ ๋  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
๊ธฐ๋ฐ˜ ์—ฐ๊ตฌ
Physics-Informed Neural Networks with Unscented Kalman Filter ๋…ผ๋ฌธ์€ PINN์˜ state-๋ณต์› ๋ฐ ํŒŒ๋ผ๋ฏธํ„ฐ ์‹๋ณ„ ํ†ตํ•ฉ ๋ฌธ์ œ์— ์ง์ ‘์ ์œผ๋กœ ์˜๊ฐ์„ ์ฃผ์—ˆ๋‹ค.
๋‹ค๋ฅธ ์ ‘๊ทผ
์ƒ˜ํ”Œ ํšจ์œจยท์ผ๋ฐ˜ํ™” ๋ฌธ์ œ๋ฅผ ๊ฐ•ํ™”ํ•™์Šตยท์ตœ์ ํ™”(1์ฐจ ์ •์ฑ…, sharpness-aware)๋กœ ํ•ด๊ฒฐํ•˜๋ ค๋Š” ๋‹ค๋ฅธ ๋กœ๋ด‡ ์ œ์–ด๋ฐฉ์‹์ž…๋‹ˆ๋‹ค.
๋‹ค๋ฅธ ์ ‘๊ทผ
๊ณผํ•™ LLM ๋ฐ ํŒŒ์šด๋ฐ์ด์…˜ ๋ชจ๋ธ์— ๋Œ€ํ•œ ์ข…ํ•ฉ ์„œ๋ฒ ์ด๋กœ, PINN๊ณผ๋Š” ๋‹ค๋ฅธ AI ๊ธฐ๋ฐ˜ ๊ณผํ•™๊ธฐ์ˆ  ๋ฌธ์ œ ์ ‘๊ทผ์„ ๋ณด์—ฌ์ค๋‹ˆ๋‹ค.
๋‹ค๋ฅธ ์ ‘๊ทผ
Geometry-Aware Predictive Safety Filters on Humanoids ๋…ผ๋ฌธ์€ ์ ‘์ด‰ ๋ฐ ํž˜ ์ถ”์ •์˜ ์•ˆ์ „์„ฑ ์ธก๋ฉด์—์„œ ๋‹ค๋ฅธ ์ตœ์ ํ™”์  ์ ‘๊ทผ๋ฒ•์„ ๋ณด์—ฌ์ค๋‹ˆ๋‹ค.
๋‹ค๋ฅธ ์ ‘๊ทผ
UKF์™€ ๊ฐ™์ด ์™ธ๋ถ€ ์ •๋ณด ๋™๊ธฐํ™”๋ฅผ ์‚ฌ์šฉํ•˜๋Š” PINN ๋ณ€ํ˜•๊ณผ gradient-free estimator์˜ ์ ์šฉ ์ฐจ์ด๋ฅผ ์ •ํ™•ํ•˜๊ฒŒ ํŒŒ์•…ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
ํ›„์† ์—ฐ๊ตฌ
Physics-Informed Neural Networks์— Unscented Kalman Filter์ฒ˜๋Ÿผ ์ถ”๊ฐ€์ ์ธ ๋ถˆํ™•์‹ค์„ฑ ์ถ”๋ก ๋ฒ•์„ ๊ฒฐํ•ฉํ•œ ์‘์šฉ์‚ฌ๋ก€์ž…๋‹ˆ๋‹ค.
ํ›„์† ์—ฐ๊ตฌ
LLM ๊ธฐ๋ฐ˜ ๊ณผํ•™์  ๊ฐ€์„ค ์ƒ์„ฑ ๋ฐ ๋งคํ•‘ ๋Šฅ๋ ฅ์˜ ํ‰๊ฐ€๋ฅผ ํ†ตํ•ด, 621์˜ PINN-Kalman ์œตํ•ฉ๋ฐฉ๋ฒ•์ด ์‹ค์„ธ๊ณ„ ๋ฌธ์ œ ํ•ด๊ฒฐ์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์„ ๋ถ„์„ํ•œ๋‹ค.
ํ›„์† ์—ฐ๊ตฌ
PINN ๊ธฐ๋ฐ˜ ์‹ค์‹œ๊ฐ„ ํ† ํฌ ์ œ์–ด ํ”„๋ ˆ์ž„์›Œํฌ๊ฐ€ ์‹ค์ œ ๋กœ๋ด‡ ์‹œ์Šคํ…œ์—์„œ ๊ฒ€์ฆ๋จ์œผ๋กœ์จ ์ด๋ก ์  ๋ชจ๋ธ์˜ ํ™•์žฅ ๋ฐ ์‹ค์šฉ์„ฑ์„ ๋ณด๊ฐ•ํ•ฉ๋‹ˆ๋‹ค.
์‘์šฉ ์‚ฌ๋ก€
PINN๊ณผ Unscented Kalman Filter์˜ ๊ฒฐํ•ฉ์„ ํ†ตํ•ด 3390์˜ ์ด๋ก ์„ ๋กœ๋ด‡ ์ œ์–ด ๋ถ„์•ผ์— ์‹ค์ œ ์ ์šฉํ•œ ์‚ฌ๋ก€๋‹ค.
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๐ŸŽง Audio Overview

์ด ๋…ผ๋ฌธ ๋ฆฌ๋ทฐ๋ฅผ ํŒŸ์บ์ŠคํŠธํ˜• ์˜ค๋””์˜ค๋กœ ์ƒ์„ฑํ•ฉ๋‹ˆ๋‹ค. (Gemini ยท ํ‚ค๋Š” ๋ธŒ๋ผ์šฐ์ €์—๋งŒ ์ €์žฅ ยท ์™„์„ฑ๋ณธ์€ ์ด๋ฉ”์ผ๋กœ๋„ ์ „์†ก)
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