Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 13, Iss. 1, January, 2009, pp. 99-121 @2009 Society for Chaos Theory in Psychology & Life Sciences Attractor and Lyapunov Models for Reach and Grasp Movements with Application to Robot-assisted Therapy Abstract: The principles of attractors and Lyapunov exponents were used to develop
a reaching-to-grasp model for use in a robotic therapy system for stroke patients.
Previously known models for these movements, the fifth order minimum jerk and
the seventh order polynomial, do not account for the change in grasp aperture
of the hand. The Lyapunov model was tested with reaching-to-grasp movements performed
by five neurologically intact subjects and produced an average R-square = .97 over 15
replications for 41 different task events, reflecting a notable advantage over the
fifth order (average R-square = .58) and seventh order (average R-square = .67) models. A similar
level of success was obtained for the Lyapunov model that was specific to grasp
aperture. The results indicated that intentional movements can be accurately characterized
as attractor trajectories, and as functions of position along two Cartesian coordinates
rather than as functions of time. The Lyapunov exponent model requires fewer parameters
and provides an efficient platform for real-time implementation. Keywords: reaching-to-grasp, minimum jerk, attractor, Lyapunov exponent, psychomotor coordination and control |