Safe Dynamic Motion Generation in Configuration Space Using Differentiable Distance Fields
Xuemin Chi, Yiming Li, Jihao Huang, Bolun Dai, Zhitao Liu, Sylvain Calinon
TL;DR
The paper tackles safe, real-time motion generation for high-dimensional manipulators operating in dynamic environments by introducing velocity-aware safety via time-varying control barrier functions (TVCBFs) and a time-varying control Lyapunov function (TVCLF) within a unified QP framework. It leverages differentiable distance fields to map obstacle dynamics into configuration space, enabling a velocity-informed safety constraint and a singularity-free path to target via the configuration-distance $d_c(p_g,q)$. The key contributions include TVCLF design in configuration space, TVCBF development with both SDF and configuration-space distance representations, and cohesive QP formulations that respect joint limits and physical constraints; validated through 2D planar and 7-DOF Franka experiments showing improved safety and responsiveness over state-of-the-art baselines. This approach enables robust, real-time, whole-body manipulation in dynamic environments and lays groundwork for extensions to MPC-based planning and more complex manipulation tasks in configuration space.
Abstract
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.