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