3. Imitation learning of object manipulation [Sugiura+ 07]
• Difficulty: Clustering trajectories in the world coordinate system does not work
• Proposed method
– Input: Position sequences of all objects
– Estimation of reference point and coordinate system by EM algorithm
– Number of state is optimized by cross-validation
Place A on B
4. Imitation learning using reference-point-dependent HMMs
[Sugiura+ 07][Sugiura+ 11]
• Delta parameters
:Position at time t
= …
= …
Searching optimal coordinate system
Reference object ID
HMM
parameters
Coordinate system
type
* Sugiura, K. et al, “Learning, Recognition, and Generation of Motion by …”, Advanced Robotics, Vol.25, No.17, 2011
5. Results: motion learning
Place-on Move-closer Raise Rotate
Jump-over Move-away Move-down
Loglikelihood
Position
Velocity
Training-set likelihoodMotion “place A on B”
No verb is estimated to have WCS
-> Reference-point-dependent verb
6. Trajectory HMMs for imitating motion and speech
[Sugiura, IROS 2011]
“Place A on B” Motion
Speech
: State sequence
: HMM parameters
: Sequence of position, velocity &
acceleration
Maximum likelihood trajectory
: Matrix of OPDF’s covariance
matrices
: Vector of OPDF’s mean vectors
*Tokuda, K. et al, “Speech parameter generation algorithms for HMM-based speech synthesis”, 2000
7. Trajectory HMMs for imitating motion and speech
: State sequence
: HMM parameters
: Sequence of position, velocity &
acceleration
Maximum likelihood trajectory
: Matrix of OPDF’s covariance
matrices
: Vector of OPDF’s mean vectors
*Tokuda, K. et al, “Speech parameter generation algorithms for HMM-based speech synthesis”, 2000
: vector of mean vectors
: matrix of covariance
matrices of each OPDF
: filter ( )
: time series of position