U-OBCA: Uncertainty-Aware Optimization-Based Collision Avoidance via Wasserstein Distributionally Robust Chance Constraints

Zehao Wang; Yuxuan Tang; Han Zhang; Jingchuan Wang; Weidong Chen

cs.ROMar 5, 2026

U-OBCA: Uncertainty-Aware Optimization-Based Collision Avoidance via Wasserstein Distributionally Robust Chance Constraints

Authors: Zehao Wang, Yuxuan Tang, Han Zhang, Jingchuan Wang, Weidong Chen

Organizations: School of Automation and Intelligent Sensing, Shanghai Jiao Tong University and Institute of Medical Robotics, Shanghai Jiao Tong University, Shanghai 200240, China. · Key Laboratory of System Control and Information Processing, Ministry of Education of China, and Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, China.

Abstract

Uncertainties arising from localization error, trajectory prediction errors of the moving obstacles and environmental disturbances pose significant challenges to robot's safe navigation. Existing uncertainty-aware planners often approximate polygon-shaped robots and obstacles using simple geometric primitives such as circles or ellipses. Though computationally convenient, these approximations substantially shrink the feasible space, leading to overly conservative trajectories and even planning failure in narrow environments. In addition, many such methods rely on specific assumptions about noise distributions, which may not hold in practice and thus limit their performance guarantees. To address these limitations, we extend the Optimization-Based Collision Avoidance (OBCA) framework to an uncertainty-aware formulation, termed U-OBCA. The proposed method explicitly accounts for the collision risk between polygon-shaped robots and obstacles by formulating OBCA-based chance constraints, and hence avoiding geometric simplifications and reducing unnecessary conservatism. These probabilistic constraints are further tightened into deterministic nonlinear constraints under mild distributional assumptions, which can be solved efficiently by standard numerical optimization solvers. The proposed approach is validated through theoretical analysis, numerical simulations and real-world experiments. The results demonstrate that U-OBCA significantly mitigates the conservatism in trajectory planning and achieves higher navigation efficiency compared to existing baseline methods, particularly in narrow and cluttered environments.

Figures & tables

Panel of Figure 1 — Fig. 1: Motivation: collision risk assessment between polygonal shapes under pose uncertainty.

Panel of Figure 2 — Fig. 2: The distance between the vehicle and the obstacle.

Panel of Figure 3 — Fig. 3: The simulation results in the parallel parking scenario.

Methods	Cost	Collision Num	Success Rate
U-OBCA $(\alpha=0.01)$	37.18	32	97.1%
U-OBCA $(\alpha=0.1)$	10.54	178	87.0%
OBCA [ 21 ]	10.32	3210	1.4%

TABLE I: Simulation results comparison of different methods in parking scenario

Methods	Success Rate (%)	Finishing Time (s)	Mean Cost Value	Min Distance (m)	Mean Computation Time (s)
U-OBCA	97	11.887 $\pm$ 0.956	197.423 $\pm$ 49.518	0.174 $\pm$ 0.069	0.114 $\pm$ 0.071
OBCA [ 21 ]	35	11.679 $\pm$ 0.839	181.757 $\pm$ 41.100	0.043 $\pm$ 0.045	0.109 $\pm$ 0.049
RCA [ 2 ]	84	13.446 $\pm$ 2.994	232.375 $\pm$ 85.929	0.558 $\pm$ 0.503	0.066 $\pm$ 0.044
LCC [ 6 ]	82	13.338 $\pm$ 3.061	232.247 $\pm$ 109.238	0.316 $\pm$ 0.177	0.089 $\pm$ 0.059
ECC [ 7 ]	82	13.616 $\pm$ 3.212	246.505 $\pm$ 110.087	0.561 $\pm$ 0.251	0.085 $\pm$ 0.063
RC [ 10 ]	84	12.884 $\pm$ 2.966	226.178 $\pm$ 99.326	0.367 $\pm$ 0.114	0.088 $\pm$ 0.138

TABLE II: Simulation result comparison of the different methods in random corridor scenarios

Panel of Figure 6 — Fig. 4: The simulation results in the narrow corridor scenario.

Fig. 6: Software architecture of the experimental platform.

Fig. 7: Detection and trajectory prediction results using the algorithm in [ 33 ] .

	Expectation	Variance
$x$	$-5.27\times 10^{-3}~\mathrm{m}$	$7.28\times 10^{-4}~\mathrm{m}^{2}$
$y$	$-3.22\times 10^{-3}~\mathrm{m}$	$3.17\times 10^{-4}~\mathrm{m}^{2}$
$\theta$	$3.70\times 10^{-2}~\mathrm{deg}$	$5.89\times 10^{-2}~\mathrm{deg}^{2}$

TABLE III: Estimated expectation and variance of the smart wheelchair’s localization error

Variance	Pose 1	Pose 2	Pose 3	Pose 4	Pose 5	Pose 6	Pose 7	Pose 8
Round obstacle $x$ ( $\times 10^{-4}~\mathrm{m}^{2}$ )	10.37	8.75	9.38	11.33	11.05	9.29	8.93	10.02
Round obstacle $y$ ( $\times 10^{-4}~\mathrm{m}^{2}$ )	5.22	4.70	4.23	4.78	4.95	4.44	4.02	4.68
Polygon obstacle $x$ ( $\times 10^{-4}~\mathrm{m}^{2}$ )	15.85	13.21	11.03	13.68	14.45	13.89	14.58	16.67
Polygon obstacle $y$ ( $\times 10^{-4}~\mathrm{m}^{2}$ )	4.07	4.19	4.22	4.72	5.11	4.80	5.02	5.78
Polygon obstacle $\theta$ ( $\times 10^{-2}~\mathrm{deg}^{2}$ )	10.22	8.31	11.67	10.38	15.92	11.28	9.73	10.69

TABLE IV: Estimated variances of static obstacle pose perception error

Fig. 8: An example of predicted pose error for a polygon-shaped obstacle at pose 3.

Variance	Pose 1	Pose 2	Pose 3	Pose 4
$x$ (Round) ( $\times k\times 10^{-4}~\mathrm{m}^{2}$ )	6.72	6.37	5.63	5.45
$y$ (Round) ( $\times k\times 10^{-4}~\mathrm{m}^{2}$ )	8.28	9.17	8.35	8.97
$x$ (Polygon) ( $\times k\times 10^{-4}~\mathrm{m}^{2}$ )	6.92	6.60	6.54	7.20
$y$ (Polygon) ( $\times k\times 10^{-4}~\mathrm{m}^{2}$ )	12.32	11.64	9.58	10.62
$\theta$ (Polygon) ( $\times 10^{-2}~\mathrm{deg}^{2}$ )	10.17	8.37	9.52	9.21

TABLE V: Estimated variances of moving obstacle predicted pose error

Panel of Figure 14 — Fig. 9: The experiment scenario of narrow corridor.

Panel of Figure 15 — Fig. 10: Comparison of the navigation finishing time and the minium distance to obstacles between methods.

Panel of Figure 16 — Fig. 11: The experiment scenario of the parking experiment.

Methods	Finishing Time (s)	Mean Cost	Mean Computation Time (ms)	Mean Distance (m)	Min Distance (m)
U-OBCA	32.44	267.08	557.98	1.37	0.30
RCA [ 2 ]	42.23	324.32	427.75	1.73	0.69
LCC [ 6 ]	42.16	337.09	435.62	1.70	0.69
ECC [ 7 ]	40.33	302.67	467.88	1.72	0.68
RC [ 10 ]	40.43	311.16	493.28	1.95	0.72
DRCC [ 17 ]	40.35	296.08	478.02	1.83	0.67

TABLE VI: Comparison of different methods in real world narrow corridor navigation scenarios

Finishing Time (s)	Mean Computation Time (ms)	Min distance (m)
7.96	400.13	0.17

TABLE VII: U-OBCA experiment results in real world parking scenarios

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Elizabeth Dietrich, Liam M. Imagawa, Hanna Krasowski +3

University of California, Berkeley, USA · Norwegian University of Science and Technology, Trondheim, Norway

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Oct 7, 2026

Adaptive Risk-Certified Event-Triggered Replanning for Dynamic Navigation

Safe navigation in dynamic environments requires robots to plan under obstacle predictions whose errors are uncertain, non-stationary, and can induce rare but safety-critical failures. Existing control-barrier-function safety filters can reject immediately unsafe controls, but they provide little guidance on when the current finite-horizon planning mode itself is becoming unsafe as prediction uncertainty evolves. We propose Conformal Event-Triggered Risk-Certified Replanning (CERT-Replan), a framework that uses calibrated barrier risk as an early-warning signal for replanning. CERT-Replan calibrates horizon-indexed obstacle-prediction residuals online and uses the resulting uncertainty radii to evaluate dynamic-obstacle safety margins. A one-step safety filter protects the next applied control, while a horizon-level risk monitor evaluates the upper-tail CVaR of predicted barrier-violation losses along the current MPC rollout. When this risk exceeds an allocated budget, CERT-Replan rejects the current planning mode and selects a lower-risk alternative, such as a different speed profile, corridor, or homotopy class, rather than repeatedly correcting the same nominal plan. In a non-stationary benchmark, CERT-Replan achieves an

83.3\%

collision reduction relative to the safety-filter-only baseline \textcolor{black}{and a

77.8\%

reduction relative to simple replanning triggers}, while reducing average safety-filter intervention by

32.4\%

. \textcolor{black}{With Trajectron++, CERT-Replan achieves

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collision-free operation. Hardware experiments and onboard runtime profiling demonstrate computational feasibility.}

Richie R. Suganda, Bin Hu

Department of Electrical Engineering and Computer University of Houston Houston, TX 77004, USA · Department of Engineering Technology University of Houston Houston, TX 77004, USA

Risk-Aware Path Planning Safe Motion Planning Motion Planning Dynamic Obstacle Avoidance

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Jul 3, 2026

Hope for the Best, Prepare for the Worst: Occlusion-Aware Contingency Planning for Autonomous Vehicles

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Truls Nyberg, Anna Gautier, Jana Tumova

KTH Royal Institute of Technology · Traton AB · Chalmers University of Technology +1

Collision Avoidance Occlusion Reasoning Safe Motion Planning Autonomous Driving Planning

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