cs.ROSep 18, 2026

Stochastic Neural Signed Swept Volume for Real-time Chance-Constrained Trajectory Optimization

Authors: Qingyi Chen, Kevin Zhang, Lucas Chen, Zachary Kingston

Organizations: Department of Computer Science, Purdue University, West Lafayette, IN, USA

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Abstract

Collision-free motion planning requires reliable collision models from sensed environments and validation of states along a continuous trajectory. To make this tractable, most planners check for collision at discrete states along continuous trajectories against a single determinized model of the environment, introducing a trade-off between safety and computational efficiency. While continuous collision checking approaches that approximate the swept volume of the robot exist, they are computationally expensive or overly conservative. Data-driven approaches can learn the swept volume; however, these neural models are susceptible to approximation errors and are therefore often limited to serving as coarse filters for downstream collision checkers. In this work, we propose to learn a signed distance function of the swept volume as a probabilistic field, enabling quantification of epistemic uncertainty, incorporation of perception noise, and eventual integration into a chance-constrained trajectory optimization framework. We demonstrate our approach on challenging high-dimensional manipulation problems with significant sensor noise, both in simulation and on real hardware.

Figures & tables

Figure 1: Our method uses a learned swept volume model to formulate continuous collision-avoidance constraints for uncertainty-aware motion planning. The figure shows reconstructed neural swept volumes for the three robots. Within each group, the columns show the predicted swept volume (blue), the ground-truth swept volume (white), and an overlay visualization.
Figure 2: Ground-truth swept-volume SDF computation via spherical representations. The blue region depicts the swept volume of a moving sphere. Solid black dots mark query points; green arrows indicate their signed distances to the swept-volume boundary. In (b), the red arrows show the incorrect distance produced by the naive formulation at an interior point, which measure distance to an individual sphere boundary rather than to the boundary of the union.
RobotLossMean Error ↓\downarrowMean StdCoverage
α=1\alpha=1α=2\alpha=2α=3\alpha=3
PandaNLL3.44.478.496.599.4
MSE4.75.873.491.296.5
UR5NLL3.74.981.497.699.5
MSE4.45.372.290.896.4
FetchNLL4.25.585.997.999.5
Table I : Learning and uncertainty quantification performance of the probabilistic (NLL) and deterministic (MSE) swept-volume SDF models across three robots. Mean error and std are in unit [mm].
  σp=0\sigma_{p}=0 mσp=0.01\sigma_{p}=0.01 mσp=0.02\sigma_{p}=0.02 m
TaskMethodSR ↑\uparrowCR ↓\downarrowTime ↓\downarrowLen ↓\downarrowSR ↑\uparrowCR ↓\downarrowTime ↓\downarrowLen ↓\downarrowSR ↑\uparrowCR ↓\downarrowTime ↓\downarrowLen ↓\downarrow
Bookshelf (small)RRT-Connect2575–4.2 ±\pm 0.72771–4.6 ±\pm 0.93356–4.6 ±\pm 0.8
SV (MSE)32681.0 ±\pm 0.74.7 ±\pm 1.337611.0 ±\pm 0.64.9 ±\pm 1.138511.0 ±\pm 0.65.0 ±\pm 1.4
SV (NLL)35651.0 ±\pm 0.75.3 ±\pm 1.539591.0 ±\pm 0.65.6 ±\pm 1.446431.0 ±\pm 0.66.4 ±\pm 1.8
Bookshelf (tall)RRT-Connect3367–4.5 ±\pm 0.63763–4.6 ±\pm 0.64058–4.7 ±\pm 0.7
SV (MSE)43571.5 ±\pm 0.94.6 ±\pm 0.743571.5 ±\pm 0.94.8 ±\pm 0.941571.6 ±\pm 0.95.1 ±\pm 1.1
Table II: RRT-Connect trajectory refinement results on MBM under different perception-noise levels σp\sigma_{p} . SR: success rate [%], CR: collision rate [%], Time: planning time [s], Len: path length. Best and second best per column within each task. Planning time and path length are unranked: both swept-volume variants share the same optimization budget, and shorter paths here reflect less conservative avoidance rather than better performance.
Figure 3: Example planned trajectory in the Cage (red) environment and the corresponding learned swept volume reconstruction (transparent blue). The robot motion is shown sequentially from left to right and top to bottom.
 σp=0\sigma_{p}=0 mσp=0.01\sigma_{p}=0.01 mσp=0.02\sigma_{p}=0.02 m
MethodSR ↑\uparrowCR ↓\downarrowTime ↓\downarrowLen ↓\downarrowSR ↑\uparrowCR ↓\downarrowTime ↓\downarrowLen ↓\downarrowSR ↑\uparrowCR ↓\downarrowTime ↓\downarrowLen ↓\downarrow
Straight-line1783–4.8 ±\pm 1.11783–4.8 ±\pm 1.11783–4.8 ±\pm 1.1
CuRobo32320.9 ±\pm 0.75.2 ±\pm 1.532270.9 ±\pm 0.85.8 ±\pm 1.924311.0 ±\pm 0.95.1 ±\pm 1.3
RRT-Connect60400.5 ±\pm 0.67.8 ±\pm 3.854463.0 ±\pm 1.95.1 ±\pm 2.032681.8 ±\pm 1.85.4 ±\pm 2.0
CCIKOPT ( α\alpha =0)16711.7 ±\pm 3.34.0 ±\pm 0.811013.8 ±\pm 4.54.5 ±\pm 1.06013.9 ±\pm 4.24.9 ±\pm 0.8
CCIKOPT ( α\alpha =1)16711.5 ±\pm 3.34.0 ±\pm 0.810117.3 ±\pm 5.64.5 ±\pm 1.07013.8 ±\pm 4.15.7 ±\pm 2.2
Table III: Static obstacle planning results under different perception-noise levels σp\sigma_{p} . Swept Volume (SV) indicates our approach. SR: success rate [%], CR: collision rate [%], Time: planning time [s], Len: path length. Best and second best per column.
Figure 4: An illustrative comparison of the paths planned from start (orange) to goal (green). Only the obstacles (red) near the planned trajectory are visualized for clarity of presentation. Left: MSE-trained model. The red arrow marks a collision. The learned swept volume for the colliding segment (transparent blue) under-approximates the true occupied region, causing a collision. Right : NLL-trained model with a 1σ1\sigma uncertainty buffer. Accounting for predictive uncertainty yields a more conservative swept-volume estimate and a collision-free trajectory in critical regions.
MethodHzSR ↑\uparrowCR ↓\downarrowTime [ms] ↓\downarrowLen ↓\downarrow
DRP [ 29 ]1555449 ±\pm 43.3 ±\pm 0.3
4064369 ±\pm 43.7 ±\pm 0.3
10071299 ±\pm 34.3 ±\pm 0.5
CuRobo [ 26 ]1502457 ±\pm 130–
4001656 ±\pm 91–
SV (MSE)15703028 ±\pm 142.9 ±\pm 0.4
Table IV : Dynamic obstacle planning results. Hz: replanning rate, SR: success rate [%], CR: collision rate [%], Time: planning time [ms], Len: path length. Best and second best per column.
Figure 5: Snapshots of our method successfully planning the robot (solid white) toward the goal (transparent green) among dynamic obstacles (red). Historical robot and obstacle trajectories are visualized with transparency, with more recent states rendered more opaque.
Figure 6: Real-world dynamic obstacle avoidance on a Franka robot. Snapshots from left to right show the process of the robot avoiding moving foam pool noodles to reach its goal (transparent).
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