  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.
