Source-linked AI summary
DRO-EDL-MPC: Evidential Deep Learning-Based Distributionally Robust Model Predictive Control for Safe Autonomous Driving
Hyeongchan Ham, Heejin Ahn
TL;DR
Autonomous-driving control must account for perception uncertainty from both noisy data and uncertain models. This paper constructs evidential-distribution ambiguity sets and integrates a distributionally robust safety constraint into MPC. In CARLA, the method adapts conservativeness across perception-confidence conditions and is reported to be more computationally efficient than W-DRO-CVaR.
Problem
The paper addresses how to maintain safe motion planning when perception uncertainty varies, including out-of-distribution uncertainty that point estimates do not handle.
Source: B. Results · p. 7, §VI · p. 8Method
The method uses evidential-distribution cumulative probability to form an uncertainty-adaptive ambiguity set and incorporates its DR-EDL-CVaR constraint into computationally tractable MPC.
Source: §I · p. 2Results
The method is reported as the only approach that is less conservative under confident perception and more conservative under uncertain perception, with 5% failure under uncertain perception and 5 times the computational efficiency of W-DRO-CVaR.
Source: B. Results · pp. 7–8Takeaways & Limitations
The reported CARLA experiments show safe motion in out-of-distribution scenarios without additional training while retaining low conservativeness in in-distribution scenarios.
Source: §VI · p. 8The framework assumes independent Gaussian target distributions, which may not hold in complex real-world environments.
Source: B. EDL-based Ambiguity Set and Safety… · p. 4
Abstract
from arXiv · showhide
Safety is a critical concern in motion planning for autonomous vehicles. Modern autonomous vehicles rely on neural network-based perception, but making control decisions based on these inference results poses significant safety risks due to inherent uncertainties. To address this challenge, we present a distributionally robust optimization (DRO) framework that accounts for both aleatoric and epistemic perception uncertainties using evidential deep learning (EDL). Our approach introduces a novel ambiguity set formulation based on evidential distributions that dynamically adjusts the conservativeness according to perception confidence levels. We integrate this uncertainty-aware constraint into model predictive control (MPC), proposing the DRO-EDL-MPC algorithm with computational tractability for autonomous driving applications. Validation in the CARLA simulator demonstrates that our approach maintains efficiency under high perception confidence while enforcing conservative constraints under low confidence.
I. INTRODUCTION
Perception uncertainty can propagate through autonomous-driving decisions, arising from both noisy data and limited model knowledge. The paper develops an EDL-based ambiguity set and integrates its distributionally robust safety constraint into tractable MPC for static-obstacle motion planning.
I. INTRODUCTION
- Perception uncertainty includes data noise and limited training knowledge, and can propagate through the autonomous-driving decision pipeline.Source: §I · p. 1
- Existing DRO ambiguity sets can remain overly conservative or fail to adapt when robotics sampling is capped, while prior EDL methods have limitations under highly uncertain predictions.Source: §I · pp. 1–2
- The proposed ambiguity set uses evidential-distribution cumulative probability to provide probabilistic semantics and adjust its size to model uncertainty.Source: §I · p. 2
- DRO-EDL-MPC incorporates the DR-EDL-CVaR safety constraint and is validated in CARLA for safety under varied perception uncertainty.Source: §I · p. 2
II. PROBLEM FORMULATION
- The formulation plans ego-vehicle motion around static obstacles using a distributionally robust CVaR constraint against the worst-case distribution in an ambiguity set.Source: §II · pp. 2–3
- The obstacle is assumed constant during MPC prediction; handling dynamic obstacles is left to future work.Source: §II · p. 3
III. EDL-BASED SAFETY CONSTRAINT
The method uses evidential deep learning to represent uncertainty in obstacle-position estimates, then constructs an ambiguity set from that evidential distribution. The resulting worst-case CVaR constraint accounts for data and model uncertainty, with conservativeness adapting to perception confidence.
A. EDL-based Perception
- EDL models each obstacle-position coordinate with a Gaussian likelihood and a Normal Inverse-Gamma posterior over its mean and variance parameters.Source: A. EDL-based Perception · p. 3
- The evidential distribution captures model uncertainty, while a normal realization represents data uncertainty; the implementation assumes independent obstacle-position coordinates.Source: B. EDL-based Ambiguity Set and Safety… · p. 3, A. EDL-based Perception · p. 3
B. EDL-based Ambiguity Set and Safety Constraint
- The ambiguity set contains Gaussian distributions whose parameters lie within an evidential-distribution confidence region, with the true target distribution inside under the stated Gaussian-target and well-trained-EDL assumptions.Source: B. EDL-based Ambiguity Set and Safety… · p. 3
- At a fixed confidence level, dispersed evidence under high model uncertainty expands the ambiguity set, while concentrated evidence under low uncertainty contracts it.Source: B. EDL-based Ambiguity Set and Safety… · p. 3
- DR-EDL-CVaR applies CVaR at confidence level ϵ to data uncertainty and worst-case optimization over the ambiguity set at confidence level η to model uncertainty.Source: B. EDL-based Ambiguity Set and Safety… · p. 3
- The formulation assumes independent Gaussian target distributions, an assumption that may not hold in complex real-world environments.Source: B. EDL-based Ambiguity Set and Safety… · p. 4
IV. SOLUTION
The solution replaces the evidential ambiguity set with a conservative rectangular surrogate and identifies its worst-case obstacle distribution. Standardized, precomputed extrema make this identification computationally tractable.
A. Identification of the worst-case obstacle distribution
- The surrogate ambiguity set is introduced because finding the closed-form worst-case loss over the original set is nontrivial.The surrogate enables calculation of the worst-case loss.Source: A. Identification of the worst-case… · p. 4
- A rectangular region of Gaussian means and variances encloses the evidential contour, making the surrogate ambiguity set more conservative.Its cumulative evidential probability exceeds the confidence threshold η_i.Source: A. Identification of the worst-case… · p. 4
- For ego positions inside the unsafe interval, the surrogate worst case uses the minimum variance; for distant positions, it uses the maximum variance.The corresponding worst-case distributions are shown for the close and distant cases in Fig. 3.Source: Figure 3 · p. 4, A. Identification of the worst-case… · p. 5
- The worst-case distribution can be identified directly within the surrogate set rather than by optimizing over the loss distribution.The rectangular surrogate encloses the evidential contour, yielding a conservative solution.Source: A. Identification of the worst-case… · pp. 4–5
- The extrema defining the surrogate set are computed offline using standardized NIG contours and stored in a lookup table indexed by shape parameter.At execution time, the perception model’s NIG parameters query the table without computation overhead, and the extrema are transformed back to the original distribution.Source: A. Identification of the worst-case… · p. 5
B. Conservative constraint for tractable MPC
The section replaces position-dependent worst-case constraints with a continuous conservative constraint for MPC. It encodes uncertainty by enlarging an obstacle and proves the resulting feasible set is conservative relative to the original constraint.
B. Conservative constraint for tractable MPC
- The original safety constraints vary with the ego position, including whether a coordinate lies inside the unsafe interval.This position dependence motivates the conservative reformulation.Source: B. Conservative constraint for… · pp. 5–6
- The conservative reformulation avoids the mixed-integer variables required by a Big-M formulation and is continuous with respect to the ego state.The Big-M approach can be computationally expensive and numerically unstable.Source: B. Conservative constraint for… · p. 5
- The constructed obstacle ξEDL incorporates the uncertainty margin h_i into its size while retaining the estimated obstacle’s heading and speed.Its enlarged radius makes its safety loss at least that of the intermediate obstacle.Source: B. Conservative constraint for… · p. 6
- The reformulation’s feasible set is contained in the original feasible set, so satisfying the new constraint also satisfies the original constraint.The proof establishes G ⊆ F and that g(x) ≤ 0 is more conservative than f(x) ≤ 0.Source: B. Conservative constraint for… · p. 6
C. DRO-EDL-MPC Algorithm
DRO-EDL-MPC integrates the tractable distributionally robust constraint into MPC and applies the first optimal control input at each step. Theorem 1 states that the resulting MPC solution is feasible for the original MPC problem.
C. DRO-EDL-MPC Algorithm
- Theorem 1 states that the solution of the DRO-EDL-MPC problem is feasible for the original MPC problem.The proof links the reformulated constraint to the distributionally robust safety constraint.Source: C. DRO-EDL-MPC Algorithm · p. 6
- At execution time, the algorithm predicts NIG parameters, queries precomputed values, computes ξEDL, solves the MPC problem, and applies the first optimal control input.The process repeats after the ego vehicle’s next state is determined.Source: C. DRO-EDL-MPC Algorithm · p. 6
- The standardized solutions for confidence thresholds are precomputed and stored in memory before execution.The algorithm constructs the lookup table over α ∈ [1.01, 10.00].Source: C. DRO-EDL-MPC Algorithm · p. 6
V. EXPERIMENTS
The CARLA validation is intended to demonstrate less conservative behavior under confident perception and more conservative behavior under an uncertain environment.
V. EXPERIMENTS
- The CARLA validation demonstrates less conservative behavior under confident perception and more conservative behavior under an uncertain environment.The supplied passage states this validation objective but gives no numerical result.Source: §V · p. 6
A. Experiment Settings
DRO-EDL-CVaR adjusts conservativeness to perception confidence, balancing efficiency in confident scenarios with stronger protection under uncertainty. CARLA experiments also examine multiple and occluded obstacles, while the conclusion identifies dynamic real-world obstacles as future work.
A. Experiment Settings
- The experiments compare in-distribution car perception with out-of-distribution motorcycle perception, using a LiDAR height shift in the latter, and evaluate methods over 100 runs.The perception model uses MEDL-U trained on KITTI cars; the uncertain motorcycle case is outside that training class.Source: A. Experiment Settings · pp. 6–7
B. Results
- In confident scenarios, DR-EDL-CVaR uses a small ambiguity set, with slightly greater distance and cost than CVaR, while remaining less conservative and achieving higher success than W-DRO-CVaR.All methods had no collisions; W-DRO-CVaR had low success and Moment-Based EDL also had low success, while Single-Estimate and CVaR reached destinations in every run.Source: B. Results · p. 7, Table I · p. 7
- Under uncertain perception, DR-EDL-CVaR achieved the highest success rate, but failed in 5% of cases when extremely uncertain observations made the controller overly conservative and stuck.Single-Estimate and CVaR had high collision rates; W-DRO-CVaR and DR-EDL-CVaR had significantly lower rates, while Moment-Based EDL was inapplicable.Source: B. Results · p. 7, Table I · p. 7
- The method alone adapts from less conservative behavior under confident perception to more conservative behavior under uncertainty, and is reported 5 times more computationally efficient than W-DRO-CVaR.The paper reports computational efficiency comparable to simpler approaches.Source: Table I · p. 7, B. Results · p. 8
C. Multiple Obstacles
- In occluded-obstacle scenarios, partial hiding of a rear obstacle increases the adaptive safety boundary; the method also extends to multiple obstacles.The paper reports a clear advantage in the occluded-obstacle case.Source: Figure 6 · p. 7, C. Multiple Obstacles · p. 8
VI. CONCLUSION
- The conclusion describes DRO-EDL-MPC as tractable motion planning based on an upper bound of distributionally robust safety loss and NIG standardization; future work targets multiple dynamic obstacles in real-world settings.The conclusion reports safe motion in out-of-distribution scenarios without additional training and low conservativeness in in-distribution scenarios.Source: §VI · p. 8
A. Properties of the Value-at-Risk
The supplied passage fragments introduce VaR properties for a normal random variable and describe the construction of a transformed variable used in the derivation.
A. Properties of the Value-at-Risk
- Lemma 2 considers a normal random variable X with mean µ and variance σ^2, and a threshold ϵ in [0, 1).Source: A. Properties of the Value-at-Risk · p. 9
- The derivation also introduces k(µ) as Var_ϵ[Y], noting that it depends on σ but is treated as constant.Source: A. Properties of the Value-at-Risk · p. 9
- For Y = −|X|, the passage defines its density and cumulative distribution, then identifies VaR_ϵ[Y] as the y satisfying F_Y(y) = ϵ.Source: A. Properties of the Value-at-Risk · p. 9
B. Properties of the Conditional Value-at-Risk
The supplied fragments state selected properties of Conditional Value-at-Risk for normal variables and show a standardization step in the derivation.
B. Properties of the Conditional Value-at-Risk
- The passage states that CVaR_ϵ[−|X|] decreases monotonically with |µ|.Source: B. Properties of the Conditional… · p. 10
- For µ < 0 and VaR_ϵ[X] < 0, the passage states −|µ| + δ·σ > CVaR_ϵ[−|X|].Source: B. Properties of the Conditional… · p. 10
- The proof standardizes X as Z = (X − µ)/σ and expresses interval endpoints a(µ) and b(µ) in standardized coordinates.Source: B. Properties of the Conditional… · p. 10