Sparse Control of Robot Sparse Control of Robot Grasping from 2D SubspacesGrasping from 2D Subspaces

Aggeliki TsoliAggeliki Tsoli

Committee: Michael Black

David Laidlaw

Odest Chadwicke Jenkins

OutlineOutline

• IntroductionIntroduction• MethodologyMethodology• ResultsResults• ConclusionConclusion

Motivation 1: Motivation 1: Restoration of lost physical Restoration of lost physical

functionalityfunctionality• Prosthetic handsProsthetic hands

human (brain) controlled systems human (brain) controlled systems grasp and manipulate objects grasp and manipulate objects

www.amputee-coalition.org

Motivation 2: Motivation 2: Usable control of high-DOF robotsUsable control of high-DOF robots

• Simple manipulation tasks Simple manipulation tasks are often error proneare often error prone

• Teleoperation incurs a high Teleoperation incurs a high cognitive burdencognitive burden Humans typically Humans typically

functional between 30 min functional between 30 min to just over 1 hourto just over 1 hour

http://robonaut.jsc.nasa.gov/

The problemThe problem

• Low-dimensional user Low-dimensional user input (brain signal)input (brain signal) Neural decoding currently Neural decoding currently

limited to 2-3 DOFslimited to 2-3 DOFs

• High-dimensional robot High-dimensional robot handhand Up to 30 DOFsUp to 30 DOFs

• Mapping from high-Mapping from high-dimensional robot dimensional robot configuration space to low-configuration space to low-dimensional user input is dimensional user input is imperativeimperative! !

http://www.faulhaber-group.com

ContributionContribution

1.1. Data-driven sparse control of robotsData-driven sparse control of robots Learn low-D control subspace (manifold) Learn low-D control subspace (manifold)

and mapping to high-D hand pose spaceand mapping to high-D hand pose space Demonstrate control of 13 DOFs robot hand Demonstrate control of 13 DOFs robot hand

from 2D mouse inputfrom 2D mouse input

2.2. Neighborhood denoising for manifold Neighborhood denoising for manifold learninglearning

reduce sensitivity of manifold learning to reduce sensitivity of manifold learning to noise in estimating nearest neighborsnoise in estimating nearest neighbors

OutlineOutline

• IntroductionIntroduction• MethodologyMethodology• ResultsResults• ConclusionConclusion

ApproachApproach

subspace embedding

Related Work:Related Work:Sparse Robot ControlSparse Robot Control

• Neural motor prostheses [Donoghue et al 2004]Neural motor prostheses [Donoghue et al 2004]

• EEG mobile robot control [Millan et al 2004]EEG mobile robot control [Millan et al 2004]

• EMG direct mapping to 7DOF robot arm [Crawford et al EMG direct mapping to 7DOF robot arm [Crawford et al 2005]2005]

• EMG mapping to poses of 13DOF robot hand [Bitzer EMG mapping to poses of 13DOF robot hand [Bitzer 2006]2006]

• cortical implant control of 5DOF robot arm [Hochberg et cortical implant control of 5DOF robot arm [Hochberg et al 2006]al 2006]

• 2D mouse control over 25DOF simulated hand [Jenkins 2D mouse control over 25DOF simulated hand [Jenkins 2006]2006]

learned 2D subspace from human hand motionlearned 2D subspace from human hand motion applied several manifold learning techniquesapplied several manifold learning techniques

What is manifold learning?What is manifold learning?

• ManifoldManifold Topological space locally EuclideanTopological space locally Euclidean

• Manifold Learning (i.e. Dimension Reduction)Manifold Learning (i.e. Dimension Reduction) Derive model of d-dimensional manifold embedded in D-Derive model of d-dimensional manifold embedded in D-

dimensional space, d << Ddimensional space, d << D Use finite set of sample pointsUse finite set of sample points

• Depend on noise-free proximity graphsDepend on noise-free proximity graphs Isomap Isomap [Tenenbaum et al. 2000][Tenenbaum et al. 2000]

Maximum Variance Unfolding (MVU) Maximum Variance Unfolding (MVU) [Weinberger et al. 2004][Weinberger et al. 2004]

Locally Linear Embedding (LLE) Locally Linear Embedding (LLE) [Roweis et al. 2000][Roweis et al. 2000]

IsomapIsomap• Construct neighborhood graphConstruct neighborhood graph

k-NN or ε-radius ballk-NN or ε-radius ball

• Compute shortest pathsCompute shortest paths• Construct d-dimensional embeddingConstruct d-dimensional embedding

preserve high-dimensional distancespreserve high-dimensional distances

initial pointsinitial points neighborhood graphneighborhood graph embeddingembedding

Problem:Problem:Noisy neighborhoodsNoisy neighborhoods

• SolutionSolution: Neighborhood Denoising!: Neighborhood Denoising!

Noisy neighborhoodNoisy neighborhood EmbeddingEmbedding

BP-Isomap: ProcedureBP-Isomap: Procedure

• Construct a neighborhood graph Construct a neighborhood graph between input data (hand poses) using between input data (hand poses) using k-Nearest Neighborsk-Nearest Neighbors

• Denoise neighborhood graph edgesDenoise neighborhood graph edges• Run shortest-path algorithm on the Run shortest-path algorithm on the

denoised neighborhood graphdenoised neighborhood graph• Produce embedding using MDSProduce embedding using MDS[Torgerson 1952][Torgerson 1952]

Step 2: Neighborhood denoisingStep 2: Neighborhood denoising

• ProblemProblem: distance between : distance between observedobserved neighboring points might not be neighboring points might not be representative of their distance on their representative of their distance on their underlying manifoldunderlying manifold

• SolutionSolution: infer true latent neighborhood : infer true latent neighborhood distances using Belief Propagationdistances using Belief Propagation

• [Yedidia et al. 2003][Yedidia et al. 2003]

Step 2: Neighborhood denoisingStep 2: Neighborhood denoising

• For each edge For each edge ijij in the neighborhood in the neighborhood graphgraph

xxijij : latent distance : latent distance yyijij : observed (Euclidean) distance : observed (Euclidean) distance

• Estimate xEstimate xijij for all edges for all edges ijij using Belief using Belief

PropagationPropagation

• Remove edges with xRemove edges with xijij > τ > τ

Belief Propagation for Belief Propagation for Neighborhood DenoisingNeighborhood Denoising

• Define a Markov Random Field (MRF) withDefine a Markov Random Field (MRF) with vertices located on the neighborhood graph edgesvertices located on the neighborhood graph edges edges between vertices that correspond to adjacent edges between vertices that correspond to adjacent

edges in the neighborhood graphedges in the neighborhood graph

initial neighborhood initial neighborhood graphgraph

MRF overMRF over

neighborhood graphneighborhood graph

Belief Propagation for Belief Propagation for Neighborhood DenoisingNeighborhood Denoising

• Maintain a probability distribution (belief) about each latent variable xij (neighborhood edge distance) : local evidence function at edge ij : message to ij from neighboring edge jm

about the distribution of xij

Discrete belief over given distances

Local Evidence functionLocal Evidence function

• Inclines the edge distance xInclines the edge distance x ijij to preserve the to preserve the

observed Euclidean edge distance yobserved Euclidean edge distance y ijij

ddijij : assumed value for variable x : assumed value for variable x ijij

yyijij : observed (Euclidean) distance of edge : observed (Euclidean) distance of edge ijij

Message passingMessage passing

• Message from edge jm to neighboring edge ij regarding the latent variable of ij : local evidence function from source edge jm : compatibility function between edges ij, jm : message to edge jm from a neighboring

edge mk

Compatibility functionCompatibility function

• Compatibility of assumed lengths dCompatibility of assumed lengths d ijij, d, djmjm of of

edges ij, jm defined through the relationship of edges ij, jm defined through the relationship of vertices m,ivertices m,i m,i adjacent OR m,i have common neighbors; m,i adjacent OR m,i have common neighbors;

• their initial (Euclidean) distance is a good indication of their true their initial (Euclidean) distance is a good indication of their true distancedistance

m,i not related edgem,i not related edge ij ij or or jmjm might be noisy; might be noisy;

• big distances between m,i are more likely than small onesbig distances between m,i are more likely than small ones

BP-Isomap LimitationsBP-Isomap Limitations

• Discrete allowable values for the latent Discrete allowable values for the latent variables xvariables xijij

• Tuning of method parametersTuning of method parameters α, β, α, β, ττ

OutlineOutline

• IntroductionIntroduction• MethodologyMethodology• ResultsResults

Synthetic swissroll datasetsSynthetic swissroll datasets Robot hand controlRobot hand control

• ConclusionConclusion

Noisy Swiss RollNoisy Swiss Roll

noisy neighborhood graphnoisy neighborhood graph denoised neighborhood graphdenoised neighborhood graph

2D embeddings2D embeddings

PCAPCA FastMVUFastMVU IsomapIsomap BP-FastMVUBP-FastMVU BP-IsomapBP-Isomap

• 3D swiss roll; 3 noisy neighborhood edges added

Noisy Swiss RollNoisy Swiss Roll

PCAPCA 1.2580 x 101.2580 x 101212

FastMVUFastMVU 2.7928 x 102.7928 x 101212

IsomapIsomap 8.7271 x 108.7271 x 101111

BP - FastMVUBP - FastMVU 2.1027 x 102.1027 x 101212

BP - IsomapBP - Isomap 1.2099 x 101.2099 x 1088

MethodMethod 2D Embedding Error2D Embedding Error

Table 1Table 1: Squared error between Euclidean distances in the noisy : Squared error between Euclidean distances in the noisy swissroll embedding and ground truth distances (distances along swissroll embedding and ground truth distances (distances along the high-dimensional manifold)the high-dimensional manifold)

Swiss RollSwiss Rollwith Adjacent Noisy Edgeswith Adjacent Noisy Edges

• 2D swiss roll with 5 Nearest Neighbors2D swiss roll with 5 Nearest Neighbors• 3 adjacent bad links 3 adjacent bad links • Multiple denoising iterationsMultiple denoising iterations

noisy neighborhood graphnoisy neighborhood graph 11stst denoising iteration denoising iteration 2nd denoising iteration2nd denoising iteration

Embedding hand motionEmbedding hand motion• Input: Sequence of 25 DOFs human hand motion capture

data• ~500 frames• tapping - powergrasp - precisiongrasp

• Output: 2D embedding (k = 8)

BP-Isomap / Isomap

Robot Hand ControlRobot Hand Control

• No ground truth => evaluation through No ground truth => evaluation through robot hand controlrobot hand control

• VideoVideo Demonstration of input grasping sequenceDemonstration of input grasping sequence Interactive grasping by user mouse inputInteractive grasping by user mouse input

• power grasppower grasp• precision graspprecision grasp

Robot hand control commentsRobot hand control comments

• Results very similar with the results of Isomap but BP-Isomap takes more time and memory

• Results much better than using simple PCA!

BP-Isomap / Isomap PCA

OutlineOutline

• IntroductionIntroduction• MethodologyMethodology• ResultsResults• ConclusionConclusion

Future WorkFuture Work

• User studiesUser studies Evaluate control or robot handEvaluate control or robot hand

• Denoise neighborhoods for ST-Isomap Denoise neighborhoods for ST-Isomap [Jenkins et al. 2004][Jenkins et al. 2004]

Predict teleoperation failure from tactile and force sensor Predict teleoperation failure from tactile and force sensor embeddings [Peters, Jenkins 05]embeddings [Peters, Jenkins 05]

• Combine autonomous and user controlCombine autonomous and user control Human brain gives basic commands, robot hand controls Human brain gives basic commands, robot hand controls

grasping detailsgrasping details

• Motion graph denoisingMotion graph denoising Motion graph Motion graph [Kovar et al 2002][Kovar et al 2002] builds a directed graph builds a directed graph

encapsulating transitions learned from motion capture dataencapsulating transitions learned from motion capture data Widely used in human figure animation, but even transitions with Widely used in human figure animation, but even transitions with

low probability are modeledlow probability are modeled Identify and break low probability transitions in motion graphsIdentify and break low probability transitions in motion graphs

AcknowledgementsAcknowledgements

• Committee: Committee: Michael Black Michael Black David Laidlaw David Laidlaw Chad JenkinsChad Jenkins

• Panagiotis Artemiadis, Stefan Roth Panagiotis Artemiadis, Stefan Roth • Gregory ShakhnarovichGregory Shakhnarovich• Office of Naval Research (ONR) – Defense Office of Naval Research (ONR) – Defense

University Research Instrumentation ProgramUniversity Research Instrumentation Program ((DURIP) awardDURIP) award

• Jean, Babis, Olga, Nikos, “graphics lab” peopleJean, Babis, Olga, Nikos, “graphics lab” people

Questions ?Questions ?