Attractor and Lyapunov Models for Reach and Grasp Movements with Application to Robot-assisted Therapy

Stephen J. Guastello, Marquette University, Milwaukee, WI
Dominic E. Nathan, Marquette University, Milwaukee, WI
Michelle J. Johnson, Medical College of Wisconsin & Marquette University, Milwaukee, WI

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