Dynamic Optimization Fabrics for Motion Generation

TL;DR

This paper extends optimization fabrics to dynamic and non-holonomic robots, demonstrating their ability to guarantee trajectory convergence and obstacle avoidance with high scalability and real-time performance.

Contribution

It generalizes the optimization fabric framework to dynamic scenarios, providing theoretical guarantees and empirical validation for high-frequency motion planning.

Findings

Achieves up to 500 Hz replanning with a 7-DOF robotic arm.

Shows comparable trajectories to model predictive control with better scalability.

Validates approach on robots including a mobile manipulator avoiding moving humans.

Abstract

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.