Advances in Mathematical Modeling, Optimization and Optimal Control by Jean-Baptiste Hiriart-Urruty Adam Korytowski Helmut Maurer & Maciej Szymkat

Author:Jean-Baptiste Hiriart-Urruty, Adam Korytowski, Helmut Maurer & Maciej Szymkat
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2 Mathematical Models for Motion Studies in Medical and Rehabilitation Engineering

This section discusses challenges related to the formulation of mathematical models of humans and technical devices for optimization-based motion studies and medical and rehabilitation applications. From the mathematical perspective, it should not be expected that human whole-body models in a form that is numerically suitable for optimization are available from the medical or biomechanical field. Existing models are quite often too simple or sometimes mechanically wrong, and they typically include discontinuities and non-differentiabilities. In the past, we have therefore developed in our group two different modeling tools which represent general multibody systems modeling tools but serve in our case the primary goal to generate whole-body human and humanoid models. The first one, named RBDL, [19, 20], is based on an order n recursive algorithm by Featherstone [18], the other one, named Dynamod [38], is based on explicit code generation. The choice of the level of detail of the model is not straightforward and depends on the particular question asked. We will discuss different choices in the context of the applications in Sects. 6–10. All models involve many anthropomorphic parameters. Model data is highly individual and very hard to identify. Some data can be measured (but measurements may be expensive), whereas others can only be estimated, and there is no way to measure them. We will also comment on some data choices within this section and the sections on the different applications.

In this section, we first present rigid body models that describe the whole-body actions of the human assuming that there are torques acting on the joints. After that, we discuss what would have to be added to the model in order to describe how these torques result from the actions of the neuromuscular system. In the end of this section, we describe how models of medical and rehabilitation devices can be set up and integrated with the human models. Due to lack of space, none of these sections is meant to give a complete overview of the respective area. Instead, we try to give a flavor of the challenges and of the types of models that are to be faced, and present some solution approaches.

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