Motor redundancy in neuromuscular systems exists on multiple levels. The term ”motor redundancy” represents the availability of infinitely many different solutions to perform a motor task. This dissertation is concerned with three particular of those levels:​ muscle redundancy, wrench redundancy and posture redundancy, which are successively more general forms of redundancy, each of which will be explained in detail.

The first level corresponds to the phenomenon that for a given constant vector of submaximal limb endpoint force in isometric tasks, an infinite multitude of muscle coordination patterns exists. The motor control research community refers to this kind of redundancy as muscle redundancy, and traditionally, the selection of a particular muscle coordination pattern has been considered a computational problem for the nervous system. Mathematically, the possible muscle activations span an n-dimensional space - n being the number of independently controlled muscles - and the mapping between this space and that of isometrically generated endpoint forces is projective, therefore giving rise to a null space. The null space comprises those muscle activation vectors that do not have an effect on the endpoint forces, due to the mutual cancellations of generated forces. Specifically, the space of endpoint force vectors is 6-dimensional, consisting of three linear and three rotational components, leaving n-6 degrees of freedom. In the present work, I am studying a potential benefit of muscle redundancy, namely the mitigation of muscle fatigue through the dynamic switching between muscle activation patterns. Based on my results, I am proposing to abandon the view of muscle redundancy as a computational problem for the nervous system, since in the presence of muscle fatigue even the alleged simplification of this problem, that is, dimension reduction through muscle synergies requires awareness of the full dimensionality of the motor task. Instead, future research should focus on how the nervous system responds flexibly to the challenge of time-variance due to fatiguing and actually leverages muscle redundancy.

The second level of motor redundancy is concerned with the phenomenon that in addition to the redundancy of muscles, infinitely many different combinations of endpoint forces and moments all achieve successful task performance. Again, this redundancy has been considered a computational problem for the nervous system and various ways of how it simplifies the selection of a particular wrench have been proposed. Note that the selected solution in terms of endpoint forces constrains the muscle coordination solution space, in which a particular solution has to be found. Hence, wrench redundancy is a generalization of muscle redundancy. In the case of three-finger grasp, for instance, different fingertip force vector combinations result in an absence of net forces and moments applied to a grasped object, due to mutual cancellation of forces and moments applied by the fingertips. For example, one way to vary the applied forces is to squeeze the object harder and still succeed at the motor task of static grasp. I refer to this kind of redundancy as wrench redundancy:​ the same 6-dimensional wrench vector applied to an object can be produced by a multitude of force vectors individually acting on the object. Wrench redundancy can possibly help to mitigate effects of fatigue, namely through the dynamic shifting between endpoint force vector combinations, just like shifting between coordination patterns achieves this at the muscle level. In the present work, however, I am pursuing a different path of research:​ In the first study, looking at the normal force dynamics in static tripod grasp, I will show how mathematically independent wrench space dimensions are actually controlled in quite different ways, reflecting their specific roles in achieving dexterous manipulation. This work shows that a purely spatial analysis of endpoint force variability is not sufficient and that temporal correlations can reveal important aspects of motor control. In particular, the dynamics of forces indicate a hierarchy of task dimensions in terms of task-relevance and contradict the view held by some that task variables can be separated into task-relevant and -irrelevant (i.e. the Uncontrolled Manifold Hypothesis). According to this view, large variability in a mechanically task-irrelevant dimension reflects the lack of control of this dimension by the nervous system. Based on these results, I am proposing to abandon the view of wrench redundancy as a purely spatial problem and to espouse the use of time series analysis to determine neural control strategies. In the second study of wrench dynamics, I will show how in a non-redundant dexterous manipulation task, where all wrench dimensions are task-relevant due to simultaneous force and motion requirements, the control of different task dimensions is likely coupled through neurophysiological pathways, whose separation during evolution has been incomplete. Specifically, I will show how different wrench space dimensions of the motor task, though mathematically independent, are nevertheless coupled in the performance of the task, thus limiting the ability to match the perfect mechanical solution of the task. We see here an important interaction between the wrench and the muscle level:​ when the wrench level becomes non-redundant, the muscle level also seems to hit a boundary and reveals limitations in the independence of control of muscles across fingers.

Finally, the third level is concerned with postural redundancy, meaning that during the performance of a motor task the task goal can be achieved with different limb configurations, described in terms of joint angles. Once again, this level of redundancy is a generalization of the previous level and potentially extends the potential benefits of the former:​ a selected posture that enables motor task performance will constrain the admissible endpoint force space, which in turn will constrain the muscle coordination space. One common task taking advantage of postural redundancy is quiet stance. During quiet bipedal stance, two-legged animals are usually swaying or shifting from one posture to another, the former of which can be attributed to motor noise and the latter of which is likely a fatigue mitigation strategy. In this dissertation, I will present results of an analysis of postural control in one-day old domestic chicks (Gallus gallus) that reveal differences in prenatal motor development, which were induced by different amounts of light exposure during incubation.4

In summary, it can be said that the nervous system is remarkable in that it is capable of monitoring and reconciling continuously multiple levels of redundancy during performance of common motor tasks, in particular, since the kinematic degrees of freedom of limbs are not controlled directly by the brain. Instead, their actuation is achieved through a complex mapping starting with the degrees of freedom found at the brain level, where the task is likely represented very differently from joint angles. Importantly however, not even the three levels studied and discussed here are exhaustive:​ at one end, muscle redundancy specializes to the little studied motor unit redundancy, whereby different subsets of motor units in a single muscle generate the same muscle force. Motor units represent the control subunits that make up and provide graded control of muscle activity. At the other end of the redundancy spectrum, postural redundancy generalizes to behavioral redundancy, that is, using different strategies to achieve a task, for instance, walking vs. running, etc. Personally, I found that the separation of motor control into different levels of redundancy espoused here to be uncommon in the literature and the field, although it has helped me tremendously in forming hypotheses, designing experiments and attributing causes of failure in motor tasks to specific neuromuscular factors, and would certainly help the field of motor control research as well. I hope that the following work induces the reader to consider adopting this hierarchical view of motor redundancy, which is different from, and can potentially exist alongside other, hierarchical views of the neuromuscular system.