DRO-EDL-MPC Algorithm for Safe Autonomous Driving

• DRO-EDL-MPC integrates evidential deep learning to quantify and adapt to both aleatoric and epistemic uncertainties in perception.
• The method employs a distributionally robust MPC framework that dynamically adjusts ambiguity sets based on the confidence of obstacle state estimates.
• Experimental validation in CARLA demonstrates its ability to balance safety and efficiency, reducing conservativeness compared to traditional robust MPC approaches.

DRO-EDL-MPC denotes an evidential deep learning-based distributionally robust model predictive control algorithm for safe autonomous driving. It combines an evidential perception module, which represents obstacle-state uncertainty through evidential distributions, with a distributionally robust MPC layer that enforces safety against the worst-case distribution in an uncertainty-aware ambiguity set. In the formulation reported in "DRO-EDL-MPC: Evidential Deep Learning-Based Distributionally Robust Model Predictive Control for Safe Autonomous Driving" (Ham et al., 8 Jul 2025), the central design objective is to account simultaneously for aleatoric and epistemic perception uncertainty while avoiding the excessive conservativeness associated with static ambiguity radii.

1. Problem formulation and conceptual scope

The algorithm is posed for an ego vehicle that must reach a goal while avoiding obstacles using an onboard perception stack that estimates environment states. The motivating difficulty is that neural perception is uncertain for two distinct reasons: data and sensor noise induce aleatoric uncertainty, while limited training coverage and out-of-distribution inputs induce epistemic uncertainty. The formulation treats both as safety-relevant because control decisions based on a single obstacle estimate can produce collisions, while risk-neutral probabilistic constraints can neglect model uncertainty, and static ambiguity radii can remain overly conservative even when perception is confident (Ham et al., 8 Jul 2025).

The pipeline is organized in three layers. First, evidential deep learning infers a posterior over obstacle states. Second, that posterior induces an ambiguity set with explicit probabilistic semantics through a confidence parameter. Third, MPC solves a receding-horizon control problem under a distributionally robust risk constraint. The robust safety condition is expressed through a distributionally robust conditional value-at-risk constraint,

$$\max_{P \in \mathcal{D}(\eta \mid m)} \operatorname{CVaR}_\epsilon[l(x_t,s)] \le 0,$$

where $\mathcal{D}(\eta \mid m)$ is the ambiguity set determined by evidential parameters $m$, and $l(x_t,s)$ is a collision-avoidance loss.

This organization makes the method adaptive in a specific sense. When the evidential posterior is concentrated, the ambiguity set contracts and the controller behaves similarly to a low-conservativeness planner. When the posterior is dispersed, the ambiguity set expands and the controller tightens safety margins. This suggests that the algorithm is designed not as a uniformly conservative robust MPC, but as a confidence-modulated robustification of motion planning.

2. Evidential uncertainty model

The perception model represents the obstacle center position $c_s \in \mathbb{R}^{n_c}$ through evidential regression with a Normal-Inverse-Gamma posterior. For each axis $i=1,\dots,n_c$, the observation model and evidential posterior are

$$c_{s,i} \mid (\mu_i,\sigma_i^2) \sim \mathcal{N}(\mu_i,\sigma_i^2),$$

$$\mu_i \mid \sigma_i^2 \sim \mathcal{N}(\nu_i,\sigma_i^2/\lambda_i), \qquad \sigma_i^2 \sim \operatorname{Inv\text{-}Gamma}(\alpha_i,\beta_i),$$

with evidential parameters $m_i=(\nu_i,\lambda_i,\alpha_i,\beta_i)$ and $\alpha_i>1$ (Ham et al., 8 Jul 2025). Assuming axis-wise independence, the obstacle center is modeled as Gaussian with mean vector $\mathcal{D}(\eta \mid m)$0 and diagonal covariance $\mathcal{D}(\eta \mid m)$1.

The decomposition of uncertainty is explicit. The expected observation variance,

$\mathcal{D}(\eta \mid m)$2

captures aleatoric uncertainty, while

$\mathcal{D}(\eta \mid m)$3

captures epistemic uncertainty. The Bayesian predictive distribution for each coordinate is Student-$\mathcal{D}(\eta \mid m)$4 with mean $\mathcal{D}(\eta \mid m)$5, degrees of freedom $\mathcal{D}(\eta \mid m)$6, and scale proportional to $\mathcal{D}(\eta \mid m)$7. Concentrated evidential posteriors, characterized in the paper by large $\mathcal{D}(\eta \mid m)$8 and $\mathcal{D}(\eta \mid m)$9, correspond to high confidence; dispersed posteriors correspond to low confidence and later induce broader ambiguity sets.

The autonomous-driving instantiation uses MEDL-U as the evidential module for 3D bounding boxes from LiDAR and camera, taking YOLOv8 2D detections as input. Training is performed on the KITTI car class, while out-of-distribution motorbike scenarios are used to elicit epistemic uncertainty (Ham et al., 8 Jul 2025). A common misunderstanding is to equate evidential deep learning exclusively with Dirichlet classification models. In this algorithm, EDL is instantiated for continuous regression, not classification, and only the obstacle center $m$0 is treated as stochastic.

3. Ambiguity sets and distributionally robust safety

The safety loss is defined from an inflated-circle collision model. With ego state $m$1, obstacle state $m$2, and radii $m$3, $m$4, the loss is

$m$5

and safety requires $m$6 (Ham et al., 8 Jul 2025). This loss is then embedded in a robust CVaR constraint, so the controller protects against adverse tails of the perception-induced state distribution rather than only its mean.

The ambiguity set is derived directly from the evidential posterior. For a cumulative probability threshold $m$7, the paper defines an axis-wise set $m$8 consisting of Gaussian parameters $m$9 inside the $l(x_t,s)$0-credible region of the NIG posterior, and then forms

$l(x_t,s)$1

Its key semantic property is probabilistic: with confidence $l(x_t,s)$2, the true lower-order Gaussian data-uncertainty distribution lies inside the evidential credible set (Ham et al., 8 Jul 2025). Under fixed $l(x_t,s)$3, low-confidence evidence enlarges the set automatically, while high-confidence evidence contracts it.

Exact optimization over the NIG credible contours is computationally expensive, so the paper introduces a surrogate rectangular superset. For each axis, extrema $l(x_t,s)$4 are computed over the NIG contour, yielding intervals $l(x_t,s)$5 and $l(x_t,s)$6 and thus a tractable surrogate set $l(x_t,s)$7 that conservatively encloses the original ambiguity set. To make this practical online, the NIG is standardized to a canonical form, credible contours are precomputed offline by numerical integration and Brent’s root-finding, and online extrema are recovered through the mappings

$l(x_t,s)$8

This design is central to the algorithm’s claim of computational tractability for autonomous driving.

4. MPC formulation and deterministic reformulation

The control layer uses a discrete-time vehicle model

$l(x_t,s)$9

where $c_s \in \mathbb{R}^{n_c}$0 is a nominal kinematic bicycle model and $c_s \in \mathbb{R}^{n_c}$1 is learned online with Gaussian Process Regression using the last $c_s \in \mathbb{R}^{n_c}$2 samples; uncertainty propagation inside the prediction horizon uses the Unscented Transform (Ham et al., 8 Jul 2025). Over a horizon $c_s \in \mathbb{R}^{n_c}$3, the controller minimizes

$c_s \in \mathbb{R}^{n_c}$4

with

$c_s \in \mathbb{R}^{n_c}$5

subject to dynamics, state and input constraints, and robust safety constraints. In the reported experiments, $c_s \in \mathbb{R}^{n_c}$6, $c_s \in \mathbb{R}^{n_c}$7, and $c_s \in \mathbb{R}^{n_c}$8.

A direct encoding of the worst-case DR-EDL-CVaR constraint leads to piecewise structure. The paper avoids mixed-integer formulations by converting the ambiguity-set geometry into a deterministic inflated obstacle. After deriving axis-wise bounds using folded-normal CVaR properties, it defines

$c_s \in \mathbb{R}^{n_c}$9

sets the inflated obstacle center to the evidential location parameter,

$i=1,\dots,n_c$0

and inflates the obstacle attribute elementwise,

$i=1,\dots,n_c$1

The resulting deterministic constraint,

$i=1,\dots,n_c$2

is shown to imply feasibility of the original distributionally robust CVaR constraint (Ham et al., 8 Jul 2025).

The online procedure therefore consists of acquiring LiDAR and camera observations, running evidential perception to obtain NIG parameters, updating the GPR dynamics residual model, recovering the ambiguity-set extrema from precomputed lookup tables, constructing $i=1,\dots,n_c$3, and solving the deterministic MPC with the inflated-obstacle constraint. The implementation uses FORCES Pro, and the paper reports typical runtimes on the order of $i=1,\dots,n_c$4–$i=1,\dots,n_c$5 ms per MPC iteration, with approximately a $i=1,\dots,n_c$6 speedup over a Wasserstein-DRO-CVaR formulation on the loss distribution (Ham et al., 8 Jul 2025).

5. Validation in CARLA

Validation is conducted in the CARLA simulator with an ego vehicle equipped with LiDAR and camera. Perception uses YOLOv8 for 2D boxes and MEDL-U for 3D bounding boxes with NIG uncertainties. Two regimes are considered: an in-distribution setting with a car obstacle and matched LiDAR mounting, and an out-of-distribution setting with a motorcycle obstacle and altered LiDAR height. Uncertainty is modeled only for the ground-plane obstacle center $i=1,\dots,n_c$7, with $i=1,\dots,n_c$8 and height ignored for avoidance (Ham et al., 8 Jul 2025).

The reported comparisons include Single-Estimate MPC, CVaR MPC without ambiguity sets, Wasserstein-DRO-CVaR on the loss distribution, Moment-Based EDL, and the proposed DR-EDL-CVaR controller. Performance is evaluated over $i=1,\dots,n_c$9 runs using collision rate, success rate, average total cost over successful runs, average minimum distance to the estimated obstacle center, and average optimization time (Ham et al., 8 Jul 2025).

In the confident-perception regime, all methods avoid collisions, but their conservativeness differs. Single-Estimate remains least conservative but offers no explicit protection against model uncertainty. CVaR and especially Wasserstein-DRO-CVaR maintain larger distances, and the latter can become over-conservative and sometimes infeasible because it applies Unscented Transform machinery directly to the loss distribution. Moment-Based EDL exhibits low success because its validity requires sufficiently concentrated evidential posteriors. DR-EDL-CVaR instead yields small ambiguity sets under high confidence, attaining distances similar to Single-Estimate while preserving robust feasibility and higher success than CVaR and Wasserstein-DRO-CVaR (Ham et al., 8 Jul 2025).

In the uncertain out-of-distribution regime, the contrast becomes sharper. Single-Estimate and CVaR exhibit high collision rates because they do not protect against epistemic uncertainty. Wasserstein-DRO-CVaR and DR-EDL-CVaR both reduce collisions, but Wasserstein-DRO-CVaR is more conservative and slower, while Moment-Based EDL is inapplicable in these uncertain cases. The paper characterizes DR-EDL-CVaR as the only compared method that remains non-conservative under high confidence and conservative under low confidence, thereby simultaneously targeting safety and efficiency (Ham et al., 8 Jul 2025).

6. Relation to adjacent research, assumptions, and limitations

DRO-EDL-MPC occupies a specific point in the broader landscape of robust learning-based control. "Safe Learning MPC with Limited Model Knowledge and Data" formulates a nonlinear stochastic MPC with Wasserstein distributionally robust chance constraints, where uncertainty is quantified empirically through multi-step residual distributions and finite-sample ambiguity radii, and it explicitly states that the paper does not use Evidential Deep Learning or Bayesian neural nets (Kandel et al., 2020). By contrast, DRO-EDL-MPC derives its ambiguity set from evidential posteriors produced by perception rather than from online residual statistics, and its safety reformulation operates through an evidentially inflated obstacle (Ham et al., 8 Jul 2025).

A separate source of terminological confusion arises from "Bi-level Meta-Policy Control for Dynamic Uncertainty Calibration in Evidential Deep Learning," where "MPC" denotes a Meta-Policy Controller that dynamically tunes a KL coefficient and Dirichlet prior strengths during evidential training, and the paper states that it does not explicitly formulate that method as a DRO problem (Yang et al., 10 Oct 2025). In DRO-EDL-MPC, by contrast, MPC retains its standard control meaning of model predictive control, and EDL is used to generate uncertainty sets for planning rather than to adapt evidential training hyperparameters.

The tractability of DRO-EDL-MPC depends on several assumptions. Static obstacles are assumed over the prediction horizon. Only the obstacle center $$c_{s,i} \mid (\mu_i,\sigma_i^2) \sim \mathcal{N}(\mu_i,\sigma_i^2),$$0 is modeled as stochastic, while heading $$c_{s,i} \mid (\mu_i,\sigma_i^2) \sim \mathcal{N}(\mu_i,\sigma_i^2),$$1, speed $$c_{s,i} \mid (\mu_i,\sigma_i^2) \sim \mathcal{N}(\mu_i,\sigma_i^2),$$2, and size vector $$c_{s,i} \mid (\mu_i,\sigma_i^2) \sim \mathcal{N}(\mu_i,\sigma_i^2),$$3 are treated as single estimates. Axis-wise independence is assumed so that $$c_{s,i} \mid (\mu_i,\sigma_i^2) \sim \mathcal{N}(\mu_i,\sigma_i^2),$$4 remains diagonal. The rectangular surrogate around NIG credible contours introduces extra conservativeness, though it enables a smooth deterministic reformulation without integer variables. The method also depends critically on the calibration quality of the evidential model: under-calibrated evidence can produce under- or over-conservative behavior (Ham et al., 8 Jul 2025).

These limitations define the current scope of the algorithm. The reported formulation is designed for autonomous driving scenarios in which perception confidence should directly modulate robust constraint tightening, but it does not yet address dynamic multi-agent forecasting, full attribute uncertainty, or dense scenes with many interacting obstacles. A plausible implication is that future generalizations will need to preserve the explicit probabilistic semantics of the evidential ambiguity set while extending the tractable reformulation beyond static, axis-decoupled obstacle representations.