Body Scheme Learning Through SelfPerception

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Body Scheme Learning Through Self-Perception

• Jürgen Sturm, Christian Plagemann, Wolfram Burgard

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Research question

• Can we learn a body scheme for a manipulator?

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Outline

• Introduction
• The concept of Body Schemes in Neurophysiology
• Approach
• Problem formulation
• Structure learning
• Forward and inverse models
• Demo / Experiments / Evaluation
• Future work

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Introduction

• Sensor model
• Motion model
• I.e., for manipulators
• Kinematic model
• Dynamic model

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Introduction

• Typically, those models are
• derived analytically in advance
• fixed up to a number of parameters
• require (manual) calibration

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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)

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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)

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The concept of Body Scheme in Neurophysiology

• Multi-modal mapping
• Localize and track sensations
• Spatially coded
• Modular
• Coherent
• Plasticity
• Interpersonal

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Research question

• Can we learn a body scheme for a manipulator?
• Elements
• Proprioception (joint configurations)
• Spatial representation
• Visual perception (body part locations in space)

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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

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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!

(homogeneous transformation matrix, 6D position
in space)
(observation noise)
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Mathematical formulation

• State vector (unobservable)
• Observation vector
• Observation history (Evidence)

Assumption actions are noise-free observable
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Mathematical formulation

• Body scheme as the probabilistic cross-modal map
• Full mapping
• Forward model
• Inverse model

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Earlier work

• Learning the body scheme with function
  approximation
• Nearest neighbor
• Neural nets
• Gaussian processes

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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)

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Idea Body Scheme Factorization

• Body scheme represents a kinematic chain
• Bayesian network

(remember that we previously defined
)
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Local forward models

• Define local transform between body part i and j
• Define local action subset
• Learn local forward models
• These local forward models
• can be approximated with GPs!

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Local forward models

• Example approximation of

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Body Scheme Factorization

• Consider ALL local forward models
• ..
• Total number of local models

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Minimum Spanning TreeForward Model

• Compose the full body scheme by concatenating the
  local models of the minimum spanning tree

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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)

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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

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Inverse model

• Given a target pose, find the configuration
• Compute Jacobians of forward model
• Gradient Descent towards target pose

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Evaluation

• Demo video (real robot, 2-DOF)
• Experiment 1 Prediction
• Experiment 2 Control
• Demo video (simulated robot, 7-DOF)
• Experiment 3 Partial observability

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Demo video

• Real robot
• 2-DOF manipulator
• 3 body parts

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Experiment 1 Prediction

• Real robot
• 2-DOF manipulator
• 3 body parts

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Experiment 1 Prediction

• Real robot
• Simple models learn faster than complex models
• High accuracy
• Decomposition into two 1st-order local models

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Experiment 2 Posture Control

• Real robot
• Same body scheme
• Gradient descent
• Approach target position

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Demo video

• Simulated robot
• 7-DOF manipulator
• 10 body parts

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Experiment 3 Partial observability

• Simulated robot
• 7-DOF manipulator
• 10 body parts
• Hidden body part
• 2nd-order local model needed

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Experiment 3 Partial observability

• Simulated robot
• 7-DOF manipulator
• 10 body parts
• Hidden body part
• 2nd-order local model needed

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Experiment 3 Partial observability

• Simulated robot
• 7-DOF manipulator
• 10 body parts
• Hidden body part
• 2nd-order local model needed

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Summary

• Body scheme learning without prior knowledge
• Structure learning
• Model learning
• Purely generated from self-perception
• Fast convergence
• Accurate prediction
• Accurate control

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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

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Questions?