Keywords: human movements, optimization, mechanisms, muscular forces.

This paper discusses a few aspects of human movements when seen as an optimal control problem for mechanisms. In particular, the redundancy of the muscle force actuators is a main concern. The redundancy due to several parallel force producing muscles over most joints is present in even models of static posture, and emphasized by simplified models of human geometry. A dynamic simulation of a movement, seen as a movement from an initial to a final configuration also creates a dynamic redundancy, even if force actuators are unique. The redundancy demands optimization to decide the force distribution.

In any form of optimization, the criteria governing the force distribution in human posture or movement are far from fully known, but a general optimization setting allows investigation of alternatives. The paper discusses aspects of both static and dynamic optimization problems in this context. A temporal finite element formulation is used for the dynamic problem, when both the movement and the forces creating it are a priori unknown. This formulation of the dynamic problem is considerably more efficient and reliable when compared to shooting-type methods, and allows various criteria for optimal performance. Several well-established general optimization algorithms have been implemented and compared for the resulting problem setting. Some alternative time interpolations and optimization routines are discussed.

The numerical description of muscular force production is complex, and its history dependence only partially known. The present algorithm only allows a rather un-sophisticated form of muscular forces, with limits for the possible forces, but without history effects in activation and force production. The possible improvements are discussed.

The method is demonstrated by a few aspects of a weight-lifting problem. It is seen from the examples, and from simulations previously reported, that the viewpoint and algorithm can give results of interest for the bio-mechanical motion planning, with reasonable computational resources. In particular, it is shown that the fixed-time setting is not a major drawback of the present formulation.

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