Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations
Ken-Joel Simmoteit, Philipp Schillinger, Leonel Rozo
TL;DR
The paper tackles safe and robust execution of learned robot skills under unknown and cluttered environments by fusing neural contractive dynamical systems with implicit geometric representations. It introduces the Signed Distance Field Diffeomorphic Transform (SDT), comprising a contractive base dynamics, an implicit distance field, a barrier, and two contraction-preserving diffeomorphic transforms (SDDC and SDC) to achieve obstacle avoidance without compromising contraction guarantees. It develops novel obstacle-avoidance metrics (RFC and VM) and validates the approach across LASA trajectories and real kitchen tasks, showing smooth, contraction-preserving modulation and competitive or superior performance against state-of-the-art baselines. Real-world experiments with a 7-DoF Panda demonstrate safety and robustness when interacting with objects like a dishwasher, including the need to extend the robot’s SDF with the grasped object. The work highlights practical implications for deploying contractive robot skills in dynamic, cluttered environments and outlines avenues for handling concave and dynamic obstacles, as well as potential integration with control barrier functions.
Abstract
Ensuring safety and robustness of robot skills is becoming crucial as robots are required to perform increasingly complex and dynamic tasks. The former is essential when performing tasks in cluttered environments, while the latter is relevant to overcome unseen task situations. This paper addresses the challenge of ensuring both safety and robustness in dynamic robot skills learned from demonstrations. Specifically, we build on neural contractive dynamical systems to provide robust extrapolation of the learned skills, while designing a full-body obstacle avoidance strategy that preserves contraction stability via diffeomorphic transforms. This is particularly crucial in complex environments where implicit scene representations, such as Signed Distance Fields (SDFs), are necessary. To this end, our framework called Signed Distance Field Diffeomorphic Transform, leverages SDFs and flow-based diffeomorphisms to achieve contraction-preserving obstacle avoidance. We thoroughly evaluate our framework on synthetic datasets and several real-world robotic tasks in a kitchen environment. Our results show that our approach locally adapts the learned contractive vector field while staying close to the learned dynamics and without introducing highly-curved motion paths, thus outperforming several state-of-the-art methods.