This work studies spatial reaching motion in healthy humans. Research suggests that for individual instances of movement, the central nervous system (CNS) composes an explicit wrist path, which is transformed into joint motions in a time-invariant fashion. This is the time invariance hypothesis (TIH), and its validation for spatial motion is the first goal of this study. The human arm is typically modeled as a multi-link, serial chain. When one joint of a serial chain is actuated, it simultaneously causes movement at other joints because of interaction effects. Based on horizontal-plane reaching studies, the leading joint hypothesis (LJH) proposes that the interaction effects at (mostly) the proximal joint in the multi-link serial-chain model of the arm are low. Therefore, the CNS ignores this interaction effect to simplify the computation of joint torques and control of the joint trajectory. The second objective of this dissertation is to validate the LJH for spatial motion.
In a spatial reaching experiment, healthy subjects performed point-to-point reaching movements at three distinct speeds. Data analysis revealed time-invariant wrist paths only for some subjects in some reaching tasks, suggesting that the TIH is not a truly general organizing principle for spatial reaching motion. Therefore, this hypothesis needs refinement and further investigation. On the other hand, the interaction effects at the shoulder joint were small for a majority of the movements in this experiment so, the LJH was successfully extended to spatial motion.
The TIH identifies the inputs and outputs of the first stage in the process of composing the muscle activations for a given motor task. A computational algorithm that can potentially be used to execute this transformation was developed next. The algorithm, called speed-ratio control, also has beneficial applications in commercial robot control. It is demonstrated that the application of this algorithm to robotic serial chains provides greater navigational accuracy in the vicinity of certain kinds of singularities.
Speed ratio control applies to non-redundant serial chains. The simplest model of the human arm consists of three-degree-of-freedom spherical joints at the shoulder and the wrist and a revolute joint at the elbow. This yields seven degrees of freedom for the arm. For positioning and orienting the hand relative to the thorax, only six degrees of freedom are necessary. The human arm is, therefore, a redundant serial chain. The formal process of extending the algorithm to redundant serial chains is undertaken. Initial work in which three- and four-degree-of-freedom planar chains track point paths is presented. Speed ratio control allows the resolution of the redundancy in the mechanism by maximizing the output-space tracking accuracy. Examples show superior local tracking performance with this approach compared to path tracking using unweighted pseudoinverse solutions.