【摘要】 超级大回转是一项高山滑雪速度系列运动项目,滑雪轨迹对运动员比赛成绩有重要影响。由于优化模型复杂且难以收敛,确定滑雪者全程最优轨迹具有挑战性。本文基于最优控制理论,以滑行时间最小为优化指标,建立高山滑雪运动员在超级大回转中的轨迹优化模型。将轨迹优化问题转化为多阶段非线性最优控制问题,采用伪谱法求解,并优化轨迹参数。MATLAB仿真结果验证了所提轨迹优化模型的有效性和合理性。此外,提出一些切实可行的滑雪策略,帮助高山滑雪运动员提高训练水平和比赛成绩。更多还原

【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 study, a trajectory optimization model for alpine skiers competing in the Super-G is established based on the optimal control theory, in which the objective is to minimize the runtime between the starting point and the finish line. The original trajectory optimization problem is converted into a multi-phase nonlinear optimal control problem solved with a pseudospectral method, and the trajectory parameters are optimized to discover the time-optimal trajectory. Using numerical solution carried out by the MATLAB optimization toolbox, the optimal trajectory is obtained under several equality and inequality constraints. 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, several practical proposals are provided to help alpine skiers improve their training and skiing performance.更多还原