1. SA-1 Robotic Self-Perception and Body Scheme Learning Jürgen Sturm Christian Plagemann Wolfram Burgard University of Freiburg Germany

2. Motivation Existing robot models are typically specified (geometrically) in advance calibrated manually

3. Motivation Problems with fixed robot models: Wear-and-tear wheel diameter, air pressure Recovery from failure malfunctioning actuators Tool use extending the model Unknown model re-configurable robots

4. Problems with fixed robot models: Wear-and-tear wheel diameter, air pressure Recovery from failure malfunctioning actuators Tool use extending the model Unknown model re-configurable robots Similar problems in humans/animals? Motivation

5. Problems with fixed robot models: Wear-and-tear wheel diameter, air pressure Recovery from failure malfunctioning actuators Tool use extending the model Unknown model re-configurable robots Similar problems in humans/animals? Motivation growth, aging injured body parts writing riding a bike

6. Related Work Neuro-physiology Mirror neurons [Rizzolatti et al., 1996] Body Schemes [Maravita and Iriki, 2004] Robotics Self-calibration [Roy and Thrun, 1999] Cross-modal maps [Yoshikawa et al., 2004] Structure learning [Dearden and Demiris, 2005]

7. Problem motivation Fixed-model approaches fail when parameters change over time geometric model is not available Bootstrapping of the body scheme and Life-long adaptation using visual self-observation Our Contribution

8. Sense 6D Poses Act Joint angles Think Bootstrap, monitor, and maintain internal representation of body Problem Description

9. Problem Formulation Visual self-perception of n body parts: Actuators (m action signals): Learn the mapping p ( X 1 ;:::; X n j a 1 ;:::; a m ) X 1 ;:::; X n 2 R 4 £ 4 Body pose Configuration a 1 ;:::; a m 2 R

10. Existing Methods Analytic model + parameter estimation Function approximation Nearest neighbor Neural networks Requires prior knowledge High-dimensional learning problem Requires large training sets

11. Body Scheme Factorization Idea: Factorize the model We represent the kinematic chain as a Bayesian network

12. Bootstrapping Learning the model from scratch consists of two steps: 1.Learning the local models (conditional density functions) 2.Finding the network/body structure

13. Learning the Local Models Using Gaussian process regression Learn 1D  6D transformation function for each (action, marker, marker) triple p ( ¢ 12 j a 1 ) = p ( X ¡ 1 1 X 2 j a 1 )

14. Finding the Network Structure Select the most likely network topology Corresponding to the minimum spanning tree Maximizing the data likelihood p ( M j D )

15. Model Selection

16. 7-DOF example Fully connected BN

17. Model Selection 7-DOF example Fully connected BN Selected minimal spanning tree

18. Forward Kinematics Purpose: prediction of end-effector pose in a given configuration Approach: integrate over the kinematic chain in the Bayesian network by concatenating Gaussians approximate the result efficiently by one Gaussian p ( X n j X 1 ; a 1 ;:::; a m ) = Z ::: Z p M 1 p M 2 ::: d X 2 ;:::; d X n ¡ 1

19. Inverse Kinematics Purpose: Generate motor commands for reaching a given target pose Approach: Estimate Jacobian of end- effector using forward kinematics prediction Use standard IK techniques Jacobian pseudo-inverse rX n ( a ) = · @ X n ( a ) @ a 1 ;:::; @ X n ( a ) @ a m ¸

20. Experiments

21. Evaluation: Forward Kinematics Fast convergence (approx. 10-20 iterations) High accuracy (higher than direct perception)

22. Evaluation: Inverse Kinematics Accurate control using bootstrapped body scheme

23. Life-long Adaptation Robot’s physical properties will change over time Predictive accuracy of body scheme needs to be monitored continuously Localize mismatches in the Bayesian network Re-learn parts of the network

24. Life-long Adaptation Initial Error is detected and is localized Robot re-learns some local models

25. Life-long Adaptation

26. Evaluation Quick localization of error Robust recovery

27. Summary Novel approach learning body schemes from scratch using visual self-perception Model learning using Gaussian process regression Model selection using data likelihood as criterion Efficient adaptation to changes in robot geometry Accurate prediction and control

28. Future Work Active self-exploration, optimal control, POMDPs Marker-less self-perception Moving robot Tool use