Safety-Critical Dynamic Motion Generation for Manipulators Using Differentiable Distance Fields in Configuration Space
Xuemin Chi, Jihao Huang, Yiming Li, Bolun Dai, Zhitao Liu, Sylvain Calinon
AI summary
Problem
Existing safety-critical controllers for high-dimensional manipulators rely solely on positional data, ignoring obstacle velocities and leading to inadequate reactive safety in dynamic environments.
Approach
The authors formulate time-varying control barrier and Lyapunov functions using differentiable configuration space distance fields to map obstacle dynamics into joint space, unifying them in a real-time quadratic programming framework.
Key results
- Develops TVCBFs using differentiable distance fields to capture obstacle position and velocity in joint space
- Constructs a singularity-free TVCLF for dynamic whole-body reaching tasks
- Integrates safety, stability, and physical constraints into a unified real-time QP controller
- Validates superior reactive safety and tracking performance on planar arms and a 7-axis Franka robot
Why it matters
Provides a computationally efficient, safety-guaranteed control paradigm for high-frequency robotic manipulation in unpredictable, dynamic settings.
Abstract
Generating collision-free motions in dynamic en- vironments is a challenging problem for high-dimensional robotics, particularly under real-time constraints. Control Bar- rier Functions (CBFs), widely utilized in safety-critical con- trol, have shown significant potential for motion generation. However, for high-dimensional robot manipulators, existing QP formulations and CBF-based methods rely on positional infor- mation, overlooking higher-order derivatives such as velocities. This limitation may lead to reduced success rates, decreased performance, and inadequate safety constraints. To address this, we construct time-varying CBFs (TVCBFs) that consider dy- namic obstacles. Our approach leverages recent developments on distance fields for articulated manipulators, a differentiable representation that enables the mapping of objects’ position and velocity into the robot’s joint space, offering a comprehensive understanding of the system’s interactions. This allows the ma- nipulator to be treated as a point-mass system thus simplifying motion generation tasks. Additionally, we introduce a time- varying control Lyapunov function (TVCLF) to enable whole- body contact motions. Our approach integrates the TVCBFs, TVCLF, and manipulator physical constraints within a unified QP framework. We validate our method through simulations and comparisons with state-of-the-art approaches, demonstrat- ing its effectiveness on a 7-axis Franka arm in real-world experiments. Source codes, experimental data and videos are available on the project webpage: https://sites.google. com/view/sdfcdf-tvcbfs-qp.