Optimization fabrics are a geometric approach to real-time local motion generation, where motions are designed by the composition of several differential equations that exhibit a desired motion behavior. We generalize this framework to dynamic scenarios and non-holonomic robots and prove that fundamental properties can be conserved. We show that convergence to desired trajectories and avoidance of moving obstacles can be guaranteed using simple construction rules of the components. Additionally, we present the first quantitative comparisons between optimization fabrics and model predictive control and show that optimization fabrics can generate similar trajectories with better scalability, and thus, much higher replanning frequency (up to 500 Hz with a 7 degrees of freedom robotic arm). Finally, we present empirical results on several robots, including a non-holonomic mobile manipulator with 10 degrees of freedom and avoidance of a moving human, supporting the theoretical findings.

翻译：优化织物是一种基于几何的实时局部运动生成方法，通过组合若干微分方程来设计运动，这些方程展现出期望的运动行为。我们将这一框架推广至动态场景和非完整约束机器人，并证明其基本性质可得以保持。我们表明，通过简单的组件构造规则，可以保证向期望轨迹的收敛性以及对移动障碍物的规避。此外，我们首次将优化织物与模型预测控制进行定量比较，并指出优化织物能以更优的可扩展性生成相似轨迹，从而支持更高的重规划频率（对于7自由度机械臂可达500赫兹）。最后，我们在多种机器人上展示实验结果，包括一台10自由度的非完整移动机械臂及其对移动行人的规避，这些结果佐证了理论发现。