Multi-Phase Trajectory Optimization for Alpine Skiers Using an Improved Retractable Body Model

Congying Cai and Xiaolan Yao ()
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Congying Cai: Beijing Institute of Technology
Xiaolan Yao: Beijing Institute of Technology

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 3, No 4, 1063-1088

Abstract: Abstract In this paper, an improved retractable body model (IRBM) is established, which has an advantage in simulating the flexion-and-extension motion of skier’s legs during carved turning and straight gliding. The trajectory optimization problem for the nonlinear alpine skiing system is transformed into a multi-phase optimal control (MPOC) problem. Subsequently, a constrained multi-phase trajectory optimization model is developed based on the optimal control theory, where the optimization target is to minimize the total skiing time. The optimization model is discretized by using the Radau pseudospectral method (RPM), which transcribes the MPOC problem into a nonlinear programming (NLP) problem that is then solved by SNOPT solver. Through numerical simulations, the optimization results under different constraints are obtained using MATLAB. The variation characteristics of the variables and trajectories are analyzed, and four influencing factors related to the skiing time are investigated by comparative experiments. It turns out that the small turning radius can reduce the total skiing time, the flexion-and-extension motion of legs is beneficial to skier’s performance, and the large inclination angle can shorten skier’s turning time, while the control force has a slight effect on the skiing time. The effectiveness and feasibility of the proposed models and trajectory optimization strategies are validated by simulation and experiment results.

Keywords: Improved retractable body model; Nonlinear alpine skiing system; Multi-phase trajectory optimization; Optimal control; Nonlinear programming (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02422-5

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