Synergy-based Gaussian Mixture Model to anticipate reaching - - PowerPoint PPT Presentation
Synergy-based Gaussian Mixture Model to anticipate reaching direction identification for robotic applications Tortora S., Michieletto S. and Menegatti E. I NTELLIGENT A UTONOMOUS S YSTEMS L AB EMG control of robotic devices IAS-L AB Regression
Tortora S., Michieletto S. and Menegatti E.
Regression
feedback
Assistive devices
x Continuous and direct control is unfeasible x Dangerous behavior due to spastic movements and tremors
Rehabilitation devices
x For severe disability
stretching x Movement guidance requires known end-points
feedback
Continuous control through regression model Discrete control through classification model Shared autonomy through on-board intelligence Classification
Protocol:
Preprocessing Non-Negative Matrix Factorization (NMF) Gaussian Mixture Model (GMM) Non-Negative Least Squares GMM Classification Evidence accumulation Normalization Layer
nSRE nSRE H W
π, μ, Σ 𝑞 𝜎 𝜕
training
Notch (50 Hz), BPF (5-200 Hz), rectify, smoothing, normalization w(t)
Preprocessing Non-Negative Matrix Factorization (NMF) Gaussian Mixture Model (GMM) Non-Negative Least Squares GMM Classification Evidence accumulation Normalization Layer
nSRE nSRE H W
π, μ, Σ 𝑞 𝜎 𝜕
training
w(t)
X H W
Non-Negative Matrix Factorization: find H and W by
minimizing the divergence D(X||HW), subjects to the constraints W, H ≥ 0
𝑦𝑛 𝑢 =
𝑜=1 𝑂𝑡𝑧𝑜
ℎ𝑛,𝑜𝑥𝑜(𝑢)
𝑊𝐵𝐺 = 1 − σ𝑗( ത 𝑌 − 𝑌)2 σ𝑗 𝑌2 Minimum Nsyn for which: 1. Total VAF ≥ 90% 2. For each muscle VAF ≥ 90% or ΔV AF < 5% 3. For each target V AF ≥ 90% or ΔV AF < 5%
𝐸(𝑌| 𝐼𝑋 =
𝑛,𝑜
𝑌𝑛,𝑜 log 𝑌𝑛,𝑜 (𝐼𝑋)𝑛,𝑜 − 𝑌𝑛,𝑜 − (𝐼𝑋)𝑛,𝑜
Non-Negative Least Squares: find w solving min
𝑥
𝐼𝑥 − 𝑦
2 2 ,
𝑥ℎ𝑓𝑠𝑓 𝑥 ≥ 0 training test
Preprocessing Non-Negative Matrix Factorization (NMF) Gaussian Mixture Model (GMM) Non-Negative Least Squares GMM Classification Evidence accumulation Normalization Layer
nSRE nSRE H W
π, μ, Σ 𝑞 𝜎 𝜕
training
w(t)
t
wn(t)
𝑙=1 𝐿
Weighted sum of K Gaussian components
Nsyn synergies activation vector Target direction
movement related to w
Class 1 Class 2 Class L 2
T
1
…
2. Column normalization 𝑞𝑠𝑝𝑐𝑏𝑐𝑗𝑚𝑗𝑢𝑧 𝑞 𝜂 𝑥
𝑞𝑒𝑔 𝜂 𝑥 =
𝑙=1 𝐿 𝜌𝑙𝒪(𝑥|𝜈𝑥,𝑙, Σ𝑥,𝑙 )
σ𝑗
𝐿 𝒪(𝑥|𝜈𝑥,𝑗,Σ𝑥,𝑗) 𝐹[𝜎𝑙|𝑥]
1.
Preprocessing Non-Negative Matrix Factorization (NMF) Gaussian Mixture Model (GMM) Non-Negative Least Squares GMM Classification Evidence accumulation Normalization Layer
nSRE nSRE H W w(t)
π, μ, Σ 𝑞 𝜎 𝑥(𝑢)
training 𝑔𝑔𝑒𝑒
𝑞 𝜎 𝑥(𝑢) = 𝑞 𝜎 𝑥(𝑢) +
𝜐=0 𝑢−1
𝑞 𝜎 𝑥(𝜐)
1. 2.
𝑞 𝜎 𝑥(𝑢) = 𝑞 𝜎 𝑥(𝑢) /
𝑚 𝑀
𝑞 𝑚 𝑥(𝑢)
3. 𝑇𝑓𝑚𝑓𝑑𝑢 𝑑𝑚𝑏𝑡𝑡 𝜂: max
𝜂
𝑞 𝜎 𝑥(𝑢)
The proposed method achieved: Task-indipendent synergies representing movement primitives 98% of accuracy (K = 3) at 20% of reaching distance
(about 100 ms after movement onset)
Respect of real-time constraints Limitations and future works:
(check the repatability of the synergy modules and develop a healthy-like model)
(Rehabilitation therapy exploiting the healthy-like model)
(To identify sudden changing of direction)