Dynamic analysis and trajectory optimization for the nonlinear ski-skier system

Dynamic analysis and trajectory optimization are of great significance for an understanding of the alpine skiing mechanism as well as the improvement of skiers’ performance. In this paper, the whole ski-skier system is modeled as a rigid body to study physical dynamic characteristics and global path planning. A multi-phase alpine skiing trajectory optimization model is established based on the optimal control theory, in which the objective is to minimize the runtime from the starting point to the finish line. Next, Radau pseudospectral method (RPM) is applied for the solution to the trajectory optimization problem. The optimization results under different constraints are obtained through numerical simulations, and the changes of the states and control variable are analyzed. Three factors that may influence the total skiing time are discussed, including the turning radius, skier's weight, and height. Some trajectory optimization strategies are put forward in the hope of providing training reference and improving competition performance for alpine skiers.