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Frontiers of Information Technology & Electronic Engineering  1998 Vol.-1 No.-1 P.

10.1631/FITEE.1900586


Trajectory optimization with constraints for alpine skiers based on multiple-phase nonlinear optimal control


Author(s):  Cong-ying CAI, Xiao-lan YAO

Affiliation(s):  School of Automation, Beijing Institute of Technology, Beijing 100081, China

Corresponding email(s):   yaoxiaolan@bit.edu.cn

Key Words:  Trajectory optimization, Optimal control, Pseudospectral method, Optimal trajectory, Numerical solution


Cong-ying CAI, Xiao-lan YAO. Trajectory optimization with constraints for alpine skiers based on multiple-phase nonlinear optimal control[J]. Frontiers of Information Technology & Electronic Engineering, 1998, -1(-1): .

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Abstract: 
The super giant slalom (Super-G) is a “speed” event in alpine skiing, in which the skier trajectory has a significant influence on the athletes’ performances. It is a challenging task to determine an optimal trajectory for the skiers along the entire course because of the complexity and difficulty in the convergence of the optimization model. In this paper, a trajectory optimization model for alpine skiers competing in the Super-G is established based on optimal control theory, in which the objective function is the time between the starting point and the finish line. The original trajectory optimization problem is converted into a multiple-phase nonlinear optimal control problem that is solved with a pseudospectral method, and the trajectory parameters are optimized to discover the time-optimal trajectory. Using numerical solution in the MATLAB optimization toolbox, the optimal trajectory is obtained under some equality and inequality constraints. The simulation results reveal the effectiveness and rationality of the trajectory optimization model. A test is carried out to show that our code works properly. In addition, some practical proposals are provided to help alpine skiers improve their training and skiing performance.

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