The complex bio-mechanics of human body is capable of generating an unlimited repertoire of movements, which on one hand yields highly versatile motor behavior but on the other hand presents a formidable control problem for the brain. Understanding the computational process that allows us to easily perform various motor tasks with a high degree of coordination is of central interest to both neuroscience and robotics control. In recent decades, it became widely accepted that the observed movement features can be understood as a result of the brain's effort of optimizing the motor behaviors. However, a major challenge for the optimal control models is deciding how the motor task should be represented. In this thesis, (1) I compare the existing representations in literature (2) derive a novel formulation using the principles and analytic tools from physics, (3) predict previously unreported features of human movements, and (4) conrm them in psychophysics experiments. I also explore implementing the optimal controller with articial neural networks, which may potentially lead to a deeper understanding of neural computation. The obtained controller generates realistic target-directed hand movements in real-time, and reproduces many of reported neuro-physiology data in primary motor cortex

In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the -1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the -1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and -2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.

Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called "drive," that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.