Stein Variational Uncertainty-Adaptive Model Predictive Control

Hrishikesh Sathyanarayan; Ian Abraham

cs.ROApr 1, 2026

Stein Variational Uncertainty-Adaptive Model Predictive Control

Authors: Hrishikesh Sathyanarayan, Ian Abraham

Organizations: Department of Mechanical Engineering, Yale University, USA · Department of Electrical Engineering, University of Sydney, Australia

Abstract

We propose a Stein variational distributionally robust controller for nonlinear dynamical systems with latent parametric uncertainty. The method is an alternative to conservative worst-case ambiguity-set optimization with a deterministic particle-based approximation of a task-dependent uncertainty distribution, enabling the controller to concentrate on parameter sensitivities that most strongly affect closed-loop performance. Our method yields a controller that is robust to latent parameter uncertainty by coupling optimal control with Stein variational inference, and avoiding restrictive parametric assumptions on the uncertainty model while preserving computational parallelism. In contrast to classical DRO, which can sacrifice nominal performance through worst-case design, we find our approach achieves robustness by shaping the control law around relevant uncertainty that are most critical to the task objective. The proposed framework therefore reconciles robust control and variational inference in a single decision-theoretic formulation for broad classes of control systems with parameter uncertainty. We demonstrate our approach on representative control problems that empirically illustrate improved performance-robustness tradeoffs over nominal, ensemble, and classical distributionally robust baselines.

Figures & tables

Fig. 1: Autonomous Racing under Vehicle Inertial Uncertainty. Here, we apply our control framework to autonomous racing, minimizing lap time under significant uncertainty in the vehicle’s mass distribution (mass and inertia). We compare our approach to state-of-the-art baselines: Ensemble Model Predictive Control [ 4 ] , classical Distributionally Robust Control [ 1 ] , and nominal Model Predictive Control. Our approach quickly adapts to task-sensitive uncertainties faster than nominal baselines, enabling fast adaptation and convergence to the objective.

Panel of Figure 2 — Fig. 2: Example Experimental Outcomes from Our Method. We demonstrate the efficacy of our approach on a two-dimensional rocket landing and cartpole swingup control tasks.

	Cartpole Swing-Up		Rocket Landing
Method	Success (%)	Time (s)	Success (%)	Time (s)
Ours	100.0	10.24 $\pm$ 2.57	90.63	5.70 $\pm$ 2.53
EMPPI	93.75	24.47 $\pm$ 13.82	68.75	5.21 $\pm$ 2.54
MPC	93.75	23.54 $\pm$ 13.84	56.25	5.52 $\pm$ 2.81
DRO	78.13	23.34 $\pm$ 13.45	68.75	5.25 $\pm$ 3.38

TABLE I: Performance comparison on cartpole swing-up and rocket landing tasks. Our method consistently achieves the highest success rates on both problems, while also exhibiting substantially faster convergence on the cartpole task (

\approx 2\times

relative speedup), at the occasional slight cost of increased completion time.

	Cartpole	Rocket	Racing
$(n_{x},\,n_{u},\,n_{\theta})$	$(4,1,2)$	$(6,2,3)$	$(5,2,2)$
$\theta$	$[m_{\mathrm{pole}},\ell_{\mathrm{pole}}]$	$[m_{\mathrm{r}},I_{\mathrm{r}},\ell_{\mathrm{COM}}]$	$[m_{\mathrm{car}},I_{\mathrm{car}}]$
$\theta^{*}$	$[0.5,\,0.75]$	$[0.1,\,0.01,\,0.7]$	$[0.1,\,0.01]$
$(\theta_{\min},\theta_{\max})$	$([0.3,\,0.3],[1.0,\,1.0])$	$([0.05,\,0.005,\,0.05],[5.0,\,2.0,\,1.0])$	$([0.05,\,10^{-5}],[0.3,\,0.5])$
$\mathbf{x}_{0}$	$[0,0,0,0]$	$[0,0.5,0,0,0,0]$	$[-2.5,-2,0,0,0]$
$\mathbf{x}_{\mathrm{des}}$	$[0,\pi,0,0]$	$[0.5,0,0,0,0,0]$	ref. spline

TABLE II: Implementation details. All ensemble-based experiments use

N=5

particles,

\gamma=0.5

, and uniform priors

\{\theta^{i}\}_{i=1}^{N}\sim\mathcal{U}(\theta_{\min},\theta_{\max})

Method	Cartpole	Rocket	Racing
Ours	$27.2\pm 2.3$	$24.8\pm 2.6$	$26.9\pm 2.3$
EMPPI	$23.1\pm 2.1$	$21.2\pm 0.5$	$21.2\pm 2.1$
MPC	$19.5\pm 1.8$	$18.3\pm 1.2$	$18.1\pm 1.2$
DRO	$22.5\pm 1.2$	$20.6\pm 2.1$	$22.7\pm 2.3$

TABLE III: Per-cycle solve times (ms, mean

\pm

std across all planning cycles of the 32 trials per task) measured on the GPU (NVIDIA GeForce RTX 3080).

Fig. 3: Autonomous Racing Lap Time Completions. We report track completion over time for the autonomous racing task under uncertainty in vehicle mass and inertia. We achieve faster and more consistent progress by reasoning over task-sensitive regions of the parameter posterior that most affect control performance.

Method	Success (%)	Time (s)
IMQ	95.0	$7.63\pm 3.41$
RBF	90.0	4.55 $\pm$ 2.19
$k(\cdot,\hat{\theta})=1$	80.0	$6.48\pm 3.55$

TABLE IV: Kernel Ablation Study. Comparison of our method for the rocket landing system using RBF, IMQ, and

k(\cdot,\hat{\theta})=1

kernels. The IMQ kernel achieves the highest success rate with slightly slower completion due to the kernel’s prevention of mode collapse and preservation of particle diversity for more reliable inference.

Model Predictive Control

Model Predictive Control optimizes future actions with a system model, repeatedly applying the first action as new information arrives.

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Distributionally Robust Control via Stein Variational Inference for Contact-Rich Manipulation

Hrishikesh Sathyanarayan, Victor Vantilborgh, Harish Ravichandar, Tom Lefebvre+1

Yale University, New Haven, CT, USA · Ghent University, Belgium · Georgia Institute of Technology, Atlanta, GA, USA+1

Contact-Rich Robotic Manipulation Robust Control Distributionally Robust Optimization Variational Inference

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Reliable robotic manipulation requires control policies that can accurately represent and adapt to uncertainty arising from contact-rich interactions. Modern data-driven methods mitigate uncertainty through large-scale training and computation, and degrade significantly in performance with limited number of training samples. By contrast, classical model-based controllers are computationally efficient and reliable, but their limited ability to represent task-relevant uncertainty can hinder performance in contact-rich interactions. In this work, we propose to expand the capabilities of model-based manipulation control through more flexible uncertainty modeling that retains performance while exactly adapting to uncertainty. Our approach casts the manipulation problem as a distributionally robust control optimization and proposes a novel deterministic formulation based on Stein variational inference that preserves performance while explicitly modeling task-sensitive parameter uncertainty. As a result, the derived controllers are more aware of task sensitivities to uncertainty, yielding high reliability without compromising performance. Experimental results demonstrate up to 3

\times

improved robustness across a range of contact-rich manipulation tasks under broad parametric uncertainty, outperforming existing model-based control methods.

Abstract

Model Predictive Control

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