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Biologically Plausible Control of Fast Reaching Movements Using Non-Traditional Cost Functions

Abstract

Optimal control has been used as a technique to uncover mathematical principles which are observed regularly in the dynamics of human movement. We present two new models of human reaching movements. While both are rooted in optimal control theory, the models were conceived by questioning basic tenets and typical practices used in optimal control as applied to human movement. In the first model, we use cost functions that measure various control signals via the L_infinity norm as opposed to the commonly used L_2 norm. Doing so models human reaching movements as well as current approaches, but results in control signals that can be reasoned about in terms of neural spikes and their timing. In the second model, we change the organization of the terms within a single, multi-term cost function by transforming it into many single-term cost functions. This approach yields sub-optimal results with regard to cost, yet produces equal or better results when applied to accuracy in modeling human reaching movements. The traditional optimal control approach to modeling human movement assumes that humans have an optimal design in terms of the anatomy and physiology of their motor systems. This design is assumed to optimally minimize costs such as energy consumption, or error while attaining a goal. However, it is more likely that in changing environments/niches, humans and other animals are still evolving, and therefore have not yet arrived at an optimal design. By reorganizing the terms of a cost function in a cost-suboptimal way, while achieving high accuracy with regard to modeling the movements, we challenge the basic premise of cost-optimality that underlies optimal control based models of human movement. Additionally, this reorganization of cost function terms into multiple cost functions results in multiple, interacting control signals, making it possible to combine the these signals in ways that resemble the connectivity of the human motor system, which contains a diverse set of neural signals working in concert, each with its own character and purpose. For this reason, we introduce a framework that generalizes these concepts, which can be utilized for further modeling of human movement. The framework expands upon traditional optimal control as applied to modeling human movements by supporting multiple interacting control signals. This allows for experiments which more closely resemble the neural architecture of the motor system, thereby making it easier to reason about experimental results in terms of the construction of the human motor system.

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