sa-1 body scheme learning through self-perception jürgen sturm, christian plagemann, wolfram...
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SA-1
Body Scheme Learning Through Self-Perception
Jürgen Sturm, Christian Plagemann, Wolfram Burgard
Research question
Can we learn a body scheme for a manipulator?
Outline
Introduction The concept of Body Schemes in
Neurophysiology Approach
Problem formulation Structure learning Forward and inverse models
Demo / Experiments / Evaluation Future work
Introduction
Sensor model Motion model
I.e., for manipulators: Kinematic model Dynamic model
Introduction
Typically, those models are derived analytically in advance fixed up to a number of parameters require (manual) calibration
Introduction
Problems with fixed models: Wear-and-tear (wheel diameter, air
pressure) Recovery from failure
(malfunctioning actuators) Tool use (extending the model) Re-configurable robots (unknown
model structure)
Biological inspiration
Same problems in humans/animals: Changing body properties (growth) Injured body parts Simple tool use (writing, operating a
gripper) Complex tool use (riding a bike)
The concept of Body Scheme in Neurophysiology
Multi-modal mapping Localize and track sensations Spatially coded Modular Coherent Plasticity Interpersonal
Research question
Can we learn a body scheme for a manipulator?
Elements: Proprioception (joint configurations) Spatial representation Visual perception (body part locations
in space)
Related Work
Neurophysiology: Adaptive body schemes [Maravita and Iriki,
2004] Mirror neurons [Holmes and Spence, 2004]
Robotics: Self-calibration [Roy and Thrun, 1999] Cross-model maps [Yoshikawa et al., 2004] Structure learning [Dearden and Demiris,
2005]
Problem formulation
Proprioception of m actuators (actions):
Spatial representation of n body parts:
Visual self-perception of n body parts:
Unknown correspondences between actuators and body parts!
(observation noise)
(homogeneous transformation matrix,6D position in space)
Mathematical formulation
State vector (unobservable)
Observation vector
Observation history (Evidence)
Assumption: actions are noise-free observable
Mathematical formulation
Body scheme as the probabilistic cross-modal map:
Full mapping
Forward model
Inverse model
Earlier work
Learning the body scheme with function approximation: Nearest neighbor Neural nets Gaussian processes
Earlier work
Learning the full mapping is a high-dimensional problem requires lots of training examples
Idea: Factorize the body scheme (e.g. body parts)
Idea: Body Scheme Factorization
Body scheme represents a kinematic chain:
Bayesian network:
(remember that we previously defined )
Local forward models Define local transform between body part i and j
Define local action subset
Learn local forward models
These local forward modelscan be approximated with GPs!
Local forward models
• Example approximation of
Body Scheme Factorization
Consider ALL local forward models:
..
Total number of local models:
Minimum Spanning TreeForward Model Compose the full body scheme by
concatenating the local models of the minimum spanning tree:
Body Scheme Factorization
Find minimal spanning tree: Translate each local model into nodes and
edges
Nodes: body parts Edges:
Large search space! Heuristic search (from simple to complex
local models)
Model selection
Split the data in two parts:
Training set To train local models
Test set To evaluate data likelihood of each local
model Also possible: prediction accuracy
Inverse model
Given a target pose, find the configuration
Compute Jacobians of forward model Gradient Descent towards target pose
Evaluation
Demo video (real robot, 2-DOF) Experiment 1: Prediction Experiment 2: Control
Demo video (simulated robot, 7-DOF) Experiment 3: Partial observability
Demo video
Real robot 2-DOF manipulator 3 body parts
Experiment 1: Prediction
Real robot 2-DOF manipulator 3 body parts
Experiment 1: Prediction
Real robot Simple models
learn faster than complex models
High accuracy Decomposition
into two 1st-order local models
Experiment 2: Posture Control
Real robot Same body scheme Gradient descent Approach target
position
Demo video
Simulated robot 7-DOF manipulator 10 body parts
Experiment 3: Partial observability
Simulated robot 7-DOF manipulator 10 body parts Hidden body part 2nd-order local
model needed
Experiment 3: Partial observability
Simulated robot 7-DOF manipulator 10 body parts Hidden body part 2nd-order local
model needed
Experiment 3: Partial observability
Simulated robot 7-DOF manipulator 10 body parts Hidden body part 2nd-order local
model needed
Summary
Body scheme learning without prior knowledge Structure learning Model learning
Purely generated from self-perception
Fast convergence Accurate prediction Accurate control
Future work
Track natural visual features Identify geometrical structure (joint
types, rotation axes..) Dynamic adaptation of the body
scheme, e.g., during tool-use Imitation and imitation learning
Questions?
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