Offline evolutionary-based methodologies have supplied a successful motion planning framework for the quadrupedal jump. However, the time-consuming computation caused by massive population evolution in offline evolutionary-based jumping framework significantly limits the popularity in the quadrupedal field. This paper presents a time-friendly online motion planning framework based on meta-heuristic Differential evolution (DE), Latin hypercube sampling, and Configuration space (DLC). The DLC framework establishes a multidimensional optimization problem leveraging centroidal dynamics to determine the ideal trajectory of the center of mass (CoM) and ground reaction forces (GRFs). The configuration space is introduced to the evolutionary optimization in order to condense the searching region. Latin hypercube sampling offers more uniform initial populations of DE under limited sampling points, accelerating away from a local minimum. This research also constructs a collection of pre-motion trajectories as a warm start when the objective state is in the neighborhood of the pre-motion state to drastically reduce the solving time. The proposed methodology is successfully validated via real robot experiments for online jumping trajectory optimization with different jumping motions (e.g., ordinary jumping, flipping, and spinning).

翻译：基于进化的离线方法已为四足跳跃提供了成功的运动规划框架。然而，离线进化跳跃框架中大规模种群进化导致的耗时计算问题，严重制约了其在四足领域的普及。本文提出一种基于元启发式差分进化、拉丁超立方采样与配置空间（DLC）的时间友好型在线运动规划框架。该框架利用质心动力学建立多维优化问题，以确定质心理想轨迹与地面反作用力。在进化优化中引入配置空间以缩减搜索区域。拉丁超立方采样在有限采样点下提供更均匀的初始种群，加速逃离局部最小值。本研究还构建了预运动轨迹集合，当目标状态处于预运动状态邻域时作为热启动，显著降低求解时间。通过真实机器人实验，该方法的在线跳跃轨迹优化在不同跳跃动作（如常规跳跃、空翻、旋转）中均得到成功验证。