# Safe Dynamic Motion Generation in Configuration Space Using Differentiable Distance Fields

arXiv: https://arxiv.org/abs/2412.16456 · HTML: https://mlsanity.com/paper/2412.16456/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2024.

## Built on by (most cited first, 2 of 2)

- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [From Fields to Splats: A Cross-Domain Survey of Real-Time Neural Scene Representations](https://mlsanity.com/paper/2509.23555/) (2025)

## Abstract (arXiv)

Generating collision-free motions in dynamic environments is a challenging problem for high-dimensional robotics, particularly under real-time constraints. Control Barrier Functions (CBFs), widely utilized in safety-critical control, have shown significant potential for motion generation. However, for high-dimensional robot manipulators, existing QP formulations and CBF-based methods rely on positional information, 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 velocity conditions for 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 manipulator 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 TVCBF, TVCLF, and manipulator physical constraints within a unified QP framework. We validate our method through simulations and comparisons with state-of-the-art approaches, demonstrating its effectiveness on a 7-axis Franka robot in real-world experiments.