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?