1. “Human Control of an Anthropomorphic Robot Hand”
Brown University, CS Department
“Human Control of an Anthropomorphic Robot Hand”
Aggeliki Tsoli
Odest Chadwicke Jenkins

2. Motivation: Lost physical functionality restoration
Prosthetic hands
human (brain) controlled
anthropomorphic

3. Sparse Control Problem
High-dimensional robot hand
up to 30 DOFs
Low-dimensional human input
neural decoding: DOFs
1-to-1 mapping not enough!

4. Approach
Manifold
Learning

5. What is manifold learning?
Topological space locally Euclidean
Manifold Learning (i.e. Dimension Reduction)
Derive model of d-dimensional manifold embedded in D- dimensional space, d << D
Methods based on proximity graphs (i.e. neighborhood graphs)
2D manifold in 3D space
unfolded 2D manifold

6. Neighborhood graphs issue
Noise-free neighborhood graph
Embedding
Noisy neighborhood graph
Embedding
Solution: Neighborhood Denoising!

7. BP-Isomap: Procedure Neighborhood graph from D-dimensional input data
k-NN or ε-radius ball
Neighborhood Denoising
Shortest paths for all vertex pairs
d-dimensional embedding using Multi- Dimensional Scaling (MDS) [Torgerson 1952]
preserve shortest-path distances in embedding

8. Step 2: Neighborhood denoising
Neighbors may not represent correct distances along manifold
latent distance

9. Denoising Procedure
Markov Random Field (MRF) model on neighborhood graph
Belief Propagation [Yedidia et al. 2003] (BP) on MRF
Use threshold to identify noisy edges

10. A. Markov Random Field (MRF) model
For each edge ij
xij : latent distance (random variable)
yij : observed (Euclidean) distance
2 types of functions
local evidence function
compatibility function
neighborhood graph
MRF over
neighborhood graph

11. a. Local Evidence function
Latent distance xij close to observed distance yij

12. b. Compatibility function
Correlates the latent distances of adjacent edges
Check non-common vertices
Euclidean distance good indication of latent distance
Possible noisy edges

13. B. Belief Propagation on MRF
Until convergence,
Select random neighboring edges jm, ij
Message from jm to ij
Latent distance probability distribution (belief) in ij
Discrete belief over given distances jm ij m ij

14. C. Threshold to determine noisy edges
For each edge ij
Pick mode v of latent distance xij
Noisy edge: v > T

15. Result I:Noisy 3D Swiss Roll
noisy neighborhood graph
denoised neighborhood graph
2D embeddings
Isomap
BP-Isomap
PCA

16. Noisy 3D Swiss Roll Evaluation
Method
2D Embedding Error
PCA
x 1012
Isomap
x 1011
BP-Isomap
x 108

17. Result II: Hand motion embedding
~500 frames, 25 DOFs
tapping - powergrasp - precisiongrasp
PCA
BP-Isomap / Isomap

18. Motion embedding evaluation

19. BP-Isomap Limitations
Doesn’t handle many adjacent bad links
Discrete latent variables xij
Tuning of method parameters
α, β, T, σ

20. Future Work Extension for adjacent bad links
Denoise neighborhoods for ST-Isomap [Jenkins et al. 2004]
Predict teleoperation failure from tactile and force sensor embeddings [Peters, Jenkins 05]

21. Questions ?