Multi-Body Ski Jumper Model with Nonlinear Dynamic Inversion Muscle Control for Trajectory Optimization

Abstract

This paper presents an approach to model a ski jumper as a multi-body system for an optimal control application. The modeling is based on the constrained Newton-Euler-Equations. Within this paper the complete multi-body modeling methodology as well as the musculoskeletal modeling is considered. For the musculoskeletal modeling and its incorporation in the optimization model, we choose a nonlinear dynamic inversion control approach. This approach uses the muscle models as nonlinear reference models and links them to the ski jumper movement by a control law. This strategy yields a linearized input-output behavior, which makes the optimal control problem easier to solve. The resulting model of the ski jumper can then be used for trajectory optimization whose results are compared to literature jumps. Ultimately, this enables the jumper to get a very detailed feedback of the flight. To achieve the maximal jump length, exact positioning of his body with respect to the air can be displayed.

Robust Trajectory Optimization of a Ski Jumper for Uncertainty Influence and Safety Quantification

“…The model for the OC is based on a MBS representation of a ski jumper presented in [4]. The structure of the model that uses a feedforward-feedback nonlinear dynamic inversion (NDI) [7] controller as illustrated in Figure 1.…”

“…The structure of the model that uses a feedforward-feedback nonlinear dynamic inversion (NDI) [7] controller as illustrated in Figure 1. Further details on the implementation can be found in [4]. We use a symmetric four-body representation of the ski jumper (torso, arm, leg, and ski) with the generalized coordinates:…”

“…Currently, this topic is of growing interest in the ski jumping community. The complex model will be a multi-body simulation (MBS) model, developed by the authors in a recent study [4]. The uncertainty modeling is based on the method of generalized polynomial chaos (gPC) [5].…”