Trajectories are optimized for a two-dimensional simplified skateboarding system to allow it to perform a fundamental skateboarding trick called an "ollie". A methodology for generating trick trajectories by controlling the position of a point-mass relative to a board is presented and demonstrated over a range of peak jump heights. A hybrid dynamics approach is taken to perform this optimization, with contact constraints applied along a sequence of discrete timesteps based on the board's position throughout designated sections of the trick. These constraints introduce explicit and implicit discontinuities between chosen sections of the trick sequence. The approach has been shown to be successful for a set of realistic system parameters.

翻译：针对一个二维简化的滑板系统，对其轨迹进行优化，使其能够完成一种名为“奥利”的基础滑板技巧。本文提出了一种通过控制质点相对于滑板的位置来生成技巧轨迹的方法，并在不同峰值跳跃高度范围内进行了验证。采用混合动力学方法进行优化，在技巧执行过程中，根据滑板在指定阶段的位置，沿一系列离散时间步施加接触约束。这些约束在技巧序列的选定阶段之间引入了显式和隐式的不连续性。结果表明，该方法对于一组实际系统参数是有效的。