We propose NUDGE (Nudge Update via Differentiable GEometry), a training-free obstacle-avoidance procedure that can be incorporated in any robot policy based on diffusion or flow matching, including diffusion policies and vision-language-action models. Our work injects gradients from a signed distance field, a function returning each point's distance to the nearest obstacle, into the policy at inference time to steer it away from obstacles. It supports any common action parameterization, from absolute or relative joint poses to end-effector poses, through a differentiable joint-trajectory decoder. Experiments show that NUDGE preserves the policy's task distribution and runs reactively in real time.
Figures & tables
Fig. 1: NUDGE provides zero-shot collision avoidance for generative robot policies at inference time. (a) From a live point cloud, NUDGE computes a signed distance field in real time to react to scene changes, injects its gradient into the policy’s denoising loop, and steers the predicted action chunk away from obstacles. (b) We fine-tuned a π0 policy for a table-cleaning task, where the policy learns to model the contact and task distribution from demonstrations. Top: the unguided baseline collides with the pool noodle. Middle & Bottom: NUDGE avoids the obstacle at the extra cost of only 2.5 ms per action chunk.
Action representation
Notation
Decoder qt+i=Di(A;qt)
Joint pose
ai=qitgt
qt+i=ai
Joint delta
ai=Δqi
qt+i=qt+∑j=1iaj
EEF pose
ai=Tiee
qt+i=IK(ai;qt+i−1)
EEF delta
ai=ΔTiee
qt+i=IK(Ttee⋅∏j=1iaj;qt+i−1)
TABLE I: Action-space decoders
Goal
Collision
Manifold
Method
Success ↑
Reach ↑
Coll. Ep. ↓
Coll. Rate ↓
On-Sphere ↑
Sphere Err. (cm) ↓
Vanilla
37.0%
82.0%
54.0%
16.4%
84.3%
2.78
Post-Projection
25.0%
29.0%
14.5%
4.7%
56.4%
4.84
OmniGuide [ 37 ]
39.0%
81.0%
52.0%
15.98%
84.9%
2.71
RAIL [ 4 ]
37.5%
37.5%
0.0%
0.00%
82.9%
2.73
NUDGE, ρk=0.01
42.0%
73.0%
47.0%
13.8%
80.5%
3.00
TABLE II: Sphere-manifold results
Fig. 2: Collision-query geometry: NUDGE’s whole-body spheres versus OmniGuide’s EEF point and four wrist probe.
Fig. 3: Left. The robot trajectory from start to goal with end-effort constrained on the sphere manifold. Right. Failure modes on the sphere constraint task: collides with the obstacle and pushes the end-effector off the learned task manifold.
Fig. 4: One- and three-obstacle LIBERO-Object scenes with matched initial robot/object poses and camera view. We note that the additional obstacles may make a collision-free grasp infeasible.
Unguided
OmniGuide
RAIL
NUDGE
Task
SR ↑
CR ↓
SR ↑
CR ↓
SR ↑
CR ↓
SR ↑
CR ↓
One obstacle
Can
50
5.70
60
15.19
10
0.00
100
0.00
Cheese
40
6.56
40
17.25
0
0.00
60
9.71
Dressing
20
4.55
40
0.09
0
0.00
40
0.00
BBQ
0
4.72
10
2.22
0
0.00
10
0.03
TABLE III: LIBERO-Object results
Fig. 5: Top: Denoising visualization for a single action chunk. The policy predicts a 50 -step chunk of joint deltas. The actions are mapped to end-effector pose and rendered in a color spectrum across denoising steps, from random noise at t=10 down to the final denoised chunk at t=0 . The environment is shown as a voxel map. Bottom, left: Real-world setup; the obstacle is a pool noodle. Bottom, middle and right: Final action chunk at t=0 for the unguided baseline and NUDGE, respectively. The baseline is unaware of the obstacle and collides with it. NUDGE pushes the chunk away from the obstacle.
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles · Department of Computer Science, University of California, Los Angeles
School of Mechanical Engineering, Kyung Hee University, Yongin, Republic of Korea. · Advanced Institute of Convergence Technology (AICT), Suwon, Republic of Korea.