The Weizmann Institute of Science
Faculty of Mathematics and Computer Science
Vision and Robotics Seminar
Elizabeth B. Torres
Sloan-Swartz Center for Theoretical Neurobiology
California Institute of Technology
will speak on
A Geometric Model of Motion Control
Abstract:
In voluntary actions, the tasks context determines the outcome of the motion. For example, riding a bike
up hill from point A to point B results in a zigzag path if we try to traverse it as fast and as easily
as possible. However, when the surface is flat, the resulting path is a straight line. In each case the
motion path is the most efficient with respect to the geometry imposed by the task at hand. How does the
nervous system solve the problem of finding the most adequate motion path in response to a set of goals?
In this talk I will describe a general solution to this problem using the framework of differential geometry
in the context of voluntary arm motions. Two smooth manifolds X (dim n) and Q (dim m) are used to represent
the targets/current-hand configuration and the postures respectively. Given a task, the method consists
of first identifying important features of the behavior. These features are then used to define a scalar
function (cost) operating on these spaces and acting as the norm. The minimizing gradient flow of this
function under the appropriate metric generates a connected path in Q with an image path in X joining
a starting posture in Q to some given target point in X. We show that these paths are locally geodesics.
This geometric construction builds a local isometric imbedding operating on the tangent spaces to the 2
manifolds. We show in each task the partitioning of the tangent space to Q into the tangential (relevant
degrees of freedom) and normal (redundant dof) components. The method is described in the context of tasks
involving voluntary arm motions. I present 4
examples: simple pointing, reaching while matching the orientation of an obstacle, the same but also
matching a given forearm orientation, and obstacle avoidance in a monkey. In all cases the Q space has
7 dimensions spanned by 7 joint angles defining an arm posture. The dimensions of X are a function of
the relevant features of the given task. A simple feed forward neural network easily learns this method
and makes testable predictions in the context of reach-to-grasp motion-path generation. The advantages of
using this approach to study brain movement control are discussed.
The lecture will take place in the
Lecture Hall, Room 1, Ziskind Building
on Thursday, June 19, 2003
at noon