Dynamic Optimization Fabrics for Motion Generation

Abstract

Optimization fabrics represent a geometric approach to real-time motion planning, where trajectories are designed by the composition of several differential equations that exhibit a desired motion behavior. We generalize this framework to dynamic scenarios and prove that fundamental properties can be conserved. We show that convergence to 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, supporting the theoretical findings.An open-source implementation and the video will be made public upon publication.

Autotuning Symbolic Optimization Fabrics for Trajectory Generation

“…In our prior work on optimization fabrics, the framework was first applied to mobile manipulation and generalized to more dynamic environments. [5].…”

“…We compare the autotuned parameters with seven random parameter sets from the search space and a manually tuned parameter set that we obtained through expertise in previous works like [5]. In this experiment, tuning and testing are performed on the test scenario reaching-in-ring.…”

“…As the structure of the resulting trajectory generation methods remains unchanged across all time steps, it can be composed before runtime, thus saving computational costs during executing. Optimization fabrics, but also their predecessor Riemannian Motion Policies (RMPs), have shown impressive results for several manipulator applications, including dynamic and crowded environments [3]- [5]. However, despite their Fig.…”

“…In this section, we very briefly introduce the concepts required for trajectory generation with optimization fabrics. For a more in-depth introduction to optimization fabrics and its foundations in differential geometry, the reader is referred to [3], [5], [11].…”