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 models can 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 Tree Forward 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?