A model-independent definition of attractor behavior applicable to interactive tasks

Both in designing teleoperators or haptic interfaces and in fundamental bio logical motor control studies, it is important to characterize the motor co mmands and mechanical impedance responses of the operator (or subject). Alt hough such a characterization is fundamentally impossible for isolated move ments when these two aspects of motor behavior have similar time scales (as is the case with humans), it is nonetheless possible, if we are dealing wi th repeated movements, to measure a trajectory which is analogous to the cu rrent source in Norton-equivalent electrical circuits. We define the attrac tor trajectory to be this equivalent source and show that it rigorously emb odies the notion of the attractor point of a time-evolving system. We demon strate that most previous attempts to test a controversial motor control hy pothesis known as the equilibrium point or virtual trajectory hypothesis ar e based on inadequate models of the neuromuscular system and we propose her e a model-independent means of testing the hypothesis based on a comparison of measurable attractor trajectories at different levels of the motor syst em. We present and demonstrate means of making such measurements experiment ally and of assigning error bounds to the estimated trajectories.