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.

超级激流回旋（Super-G）是高山滑雪中的一项速度项目，滑雪者的运动轨迹对运动员的表现有重大影响。由于优化模型收敛的复杂性和困难性，为整个滑雪者确定最佳轨迹是一项艰巨的任务。在这项研究中，基于最佳控制理论，建立了在Super-G竞赛中高山滑雪运动员的轨迹优化模型，其目的是最大程度地减少起点和终点之间的运行时间。将原始轨迹优化问题转化为使用伪谱方法求解的多相非线性最优控制问题，并优化轨迹参数以发现时间最优轨迹。使用由MATLAB优化工具箱执行的数值解，可以在多个等式和不等式约束下获得最佳轨迹。仿真结果表明了轨迹优化模型的有效性和合理性。测试表明我们的代码可以正常工作。另外，提供了一些实用的建议以帮助高山滑雪者提高其训练和滑雪性能。