Optimal control of non-ballistic muscular movements: a constraint-based performance criterion for rising from a chair

To understand how humans perform non-ballistic movements, we have developed an optimal control model to simulate rising from a chair. The human body was modeled as a three-segment, articulated, planar linkage, with adjacent links joined together by frictionless revolutes. The skeleton was actuated by eight musculotendinous units with each muscle modeled as a three-element entity in series with tendon. Because rising from a chair presents a relatively ambiguous performance criterion, we chose to evaluate a number of different performance criteria, each based upon a fundamental dynamical property of movement; muscle force. Through a quantitative comparison of model and experiment, we found that neither a minimum-impulse nor a minimum-energy criterion is able to reproduce the major features of standing up. Instead, we introduce a performance criterion based upon an important and previously overlooked dynamical property of muscle: the time derivative of force. Our motivation for incorporating such a quantity into a mathematical description of the goal of a motor task is founded upon the belief that non-ballistic movements are controlled by gradual increases in muscle force rather than by rapid changes in force over time. By computing the optimal control solution for rising from a static squatting position, we show that minimizing the integral of a quantity which depends upon the time derivative of muscle force meets an important physiological requirement: it minimizes the peak forces developed by muscles throughout the movement. Furthermore, by computing the optimal control solution for rising from a chair, we demonstrate that multi-joint coordination is dictated not only by the choice of a performance criterion but by the presence of a motion constraint as well.