# Configuration Space Distance Fields for Manipulation Planning

arXiv: https://arxiv.org/abs/2406.01137 · HTML: https://mlsanity.com/paper/2406.01137/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2024.

## Built on by (most cited first, 12 of 12)

- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations](https://mlsanity.com/paper/2504.18860/) (2025)
- [OREN: Octree Residual Network for Real-Time Euclidean Signed Distance Mapping](https://mlsanity.com/paper/2510.18999/) (2025)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Physics-Informed Eikonal Caging for Whole-Arm Manipulation Planning](https://mlsanity.com/paper/2606.22143/) (2026)
- [From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs](https://mlsanity.com/paper/2607.19306/) (2026)
- [Data-augmented Learning of Geodesic Distances in Irregular Domains through Soner Boundary Conditions](https://mlsanity.com/paper/2503.04579/) (2025)
- [Efficient Construction of Implicit Surface Models From a Single Image for Motion Generation](https://mlsanity.com/paper/2509.20681/) (2025)
- [Inspection Planning Primitives with Implicit Models](https://mlsanity.com/paper/2510.07611/) (2025)
- [PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles](https://mlsanity.com/paper/2511.15522/) (2025)
- [Can Explicit Physical Feasibility Benefit VLA Learning? An Empirical Study](https://mlsanity.com/paper/2604.17896/) (2026)
- [RAM: Reachability Across Morphologies](https://mlsanity.com/paper/2606.09108/) (2026)

## Abstract (arXiv)

The signed distance field is a popular implicit shape representation in robotics, providing geometric information about objects and obstacles in a form that can easily be combined with control, optimization and learning techniques. Most often, SDFs are used to represent distances in task space, which corresponds to the familiar notion of distances that we perceive in our 3D world. However, SDFs can mathematically be used in other spaces, including robot configuration spaces. For a robot manipulator, this configuration space typically corresponds to the joint angles for each articulation of the robot. While it is customary in robot planning to express which portions of the configuration space are free from collision with obstacles, it is less common to think of this information as a distance field in the configuration space. In this paper, we demonstrate the potential of considering SDFs in the robot configuration space for optimization, which we call the configuration space distance field. Similarly to the use of SDF in task space, CDF provides an efficient joint angle distance query and direct access to the derivatives. Most approaches split the overall computation with one part in task space followed by one part in configuration space. Instead, CDF allows the implicit structure to be leveraged by control, optimization, and learning problems in a unified manner. In particular, we propose an efficient algorithm to compute and fuse CDFs that can be generalized to arbitrary scenes. A corresponding neural CDF representation using multilayer perceptrons is also presented to obtain a compact and continuous representation while improving computation efficiency. We demonstrate the effectiveness of CDF with planar obstacle avoidance examples and with a 7-axis Franka robot in inverse kinematics and manipulation planning tasks.