Movement science faces the challenge of reconciling parallel sequences of discrete behavioral goals with observed fluid, context-sensitive motion. This challenge arises with a vengeance in the speech domain, in which gestural primitives play the role of discrete goals. The task dynamic framework has proved effective in modeling the manner in which the gestural primitives of articulatory phonology can result in smooth, biologically plausible, movement of model articulators. We present a variant of the task dynamic model with 1 significant innovation: Tasks are not abstract and context free but are embodied and tied to specific effectors. An advantage of this approach is that it allows the definition of a parametric cost function that can be optimized. Optimization generates gestural scores in which the relative timing of gestures is fully specified. We demonstrate that movements generated in an optimal manner are phonetically plausible. Highly nuanced movement trajectories are emergent based on relatively simple optimality criteria. This addresses a long-standing need within this theoretical framework and provides a rich modeling foundation for subsequent work.