arXiv subjects

Dustin Nottage

Publications and source records attributed to Dustin Nottage.

10 recordsLinked to original sources

arXiv2026

Underwater Dead Reckoning with Deployable Situation-Triggered Covariance Scheduling

Underwater dead reckoning estimates vehicle position when vision is unavailable and external positioning cannot be assumed. A single set of filter parameters can work well in many situations, but fixed tuning may be poorly matched during turns, motion transitions, or periods when sensor measurements are less reliable. This paper presents the Situation-Triggered Calibrated Adaptive Robust Extended Kalman Filter for a BlueROV2. An onboard probabilistic trigger identifies the current motion situation while one error-state filter runs continuously. When the trigger is confident, the filter changes only to the corresponding pre-calibrated process- and measurement-noise matrices; the state estimate, covariance history, dynamics, and measurement models are not reset or replaced. The trigger, noise profiles, and a one-time Doppler velocity log yaw-alignment correction are calibrated offline using sparse AprilTag-supervised pool runs. A separate validation set selects the scheduling policy, which is then fixed before held-out testing. Across four held-out pool runs, the method reduces label-weighted mean per-run translation root-mean-square error from 0.488 m to 0.471 m relative to the same filter backbone with one global noise profile, and every held-out run favors the scheduled method. A paired bootstrap over 10-second segments gives a candidate-minus-baseline difference of -0.017 m with a 95% confidence interval of [-0.024, -0.008] m, while orientation error remains essentially unchanged. These results indicate that situation-aware covariance scheduling provides a modest but consistent vision-free dead-reckoning improvement without switching estimators or resetting the filter.

cs.RO↗

arXiv2026

LDLT L-Lipschitz Network Weight Parameterization Initialization

We analyze initialization dynamics for LDLT-based $\mathcal{L}$-Lipschitz layers by deriving the exact marginal output variance when the underlying parameter matrix $W_0\in \mathbb{R}^{m\times n}$ is initialized with IID Gaussian entries $\mathcal{N}(0,\sigma^2)$. The Wishart distribution, $S=W_0W_0^\top\sim\mathcal{W}_m(n,\sigma^2 \boldsymbol{I}_m)$, used for computing the output marginal variance is derived in closed form using expectations of zonal polynomials via James' theorem and a Laplace-integral expansion of $(\alpha \boldsymbol{I}_m+S)^{-1}$. We develop an Isserlis/Wick-based combinatorial expansion for $\operatorname{\mathbb{E}}\left[\operatorname{tr}(S^k)\right]$ and provide explicit truncated moments up to $k=10$, which yield accurate series approximations for small-to-moderate $\sigma^2$. Monte Carlo experiments confirm the theoretical estimates. Furthermore, empirical analysis was performed to quantify that, using current He or Kaiming initialization with scaling $1/\sqrt{n}$, the output variance is $0.41$, whereas the new parameterization with $10/ \sqrt{n}$ for $\alpha=1$ results in an output variance of $0.9$. The findings clarify why deep $\mathcal{L}$-Lipschitz networks suffer rapid information loss at initialization and offer practical prescriptions for choosing initialization hyperparameters to mitigate this effect. However, using the Higgs boson classification dataset, a hyperparameter sweep over optimizers, initialization scale, and depth was conducted to validate the results on real-world data, showing that although the derivation ensures variance preservation, empirical results indicate He initialization still performs better.

cs.LG↗

arXiv2025

LDLT $\mathcal{L}$-Lipschitz Network: Generalized Deep End-To-End Lipschitz Network Construction

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural networks has emerged as an essential area of research to enhance adversarial robustness and network certifiability. This paper presents a rigorous approach to the general design of $\mathcal{L}$-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. Initially, the ResNet architecture was reformulated as a cyclic tridiagonal LMI, and closed-form constraints on network parameters were derived to ensure $\mathcal{L}$-Lipschitz continuity; however, using a new $LDL^\top$ decomposition approach for certifying LMI feasibility, we extend the construction of $\mathcal{L}$-Lipchitz networks to any other nonlinear architecture. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained residual networks and other hierarchical architectures. Cholesky decomposition is also used for efficient parameterization. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. The $LDL^\top$ formulation is shown to be a tight relaxation of the SDP-based network, maintaining full expressiveness and achieving 3\%-13\% accuracy gains over SLL Layers on 121 UCI data sets.

cs.LG↗

arXiv2025

Safety Monitor for Off-Road Planning with Uncertainty Bounded Bekker Costs

Reliable off-road autonomy requires operational constraints so that behavior stays predictable and safe when soil strength is uncertain. This paper presents a runtime assurance safety monitor that collaborates with any planner and uses a Bekker-based cost model with bounded uncertainty. The monitor builds an upper confidence traversal cost from a lightweight pressure sinkage model identified in field tests and checks each planned motion against two limits: maximum sinkage and rollover margin. If the risk of crossing either limit is too high, the monitor switches to a certified fallback that reduces vehicle speed, increases standoff from soft ground, or stops on firmer soil. This separation lets the planner focus on efficiency while the monitor keeps the vehicle within clear safety limits on board. Wheel geometry, wheel load estimate, and a soil raster serve as inputs, which tie safety directly to vehicle design and let the monitor set clear limits on speed, curvature, and stopping at run time. The method carries uncertainty analytically into the upper confidence cost and applies simple intervention rules. Tuning of the sinkage limit, rollover margin, and risk window trades efficiency for caution while keeping the monitor light enough for embedded processors. Results from a simulation environment spanning loam to sand include intervention rates, violation probability, and path efficiency relative to the nominal plan, and a benchtop static loading check provides initial empirical validation.

eess.SY↗

arXiv2025

Hybrid Terrain-Aware Path Planning: Integrating VD-RRT* Exploration and VD-D* Lite Repair

Autonomous ground vehicles operating off-road must plan curvature-feasible paths while accounting for spatially varying soil strength and slope hazards in real time. We present a continuous state--cost metric that combines a Bekker pressure--sinkage model with elevation-derived slope and attitude penalties. The resulting terrain cost field is analytic, bounded, and monotonic in soil modulus and slope, ensuring well-posed discretization and stable updates under sensor noise. This metric is evaluated on a lattice with exact steering primitives: Dubins and Reeds--Shepp motions for differential drive and time-parameterized bicycle arcs for Ackermann steering. Global exploration is performed using Vehicle-Dynamics RRT$^{*}$, while local repair is managed by Vehicle-Dynamics D$^{*}$ Lite, enabling millisecond-scale replanning without heuristic smoothing. By separating the terrain--vehicle model from the planner, the framework provides a reusable basis for deterministic, sampling-based, or learning-driven planning in deformable terrain. Hardware trials on an off-road platform demonstrate real-time navigation across soft soil and slope transitions, supporting reliable autonomy in unstructured environments.

cs.RO↗

arXiv2025

APECS: Adaptive Personalized Control System Architecture

This paper presents the Adaptive Personalized Control System (APECS) architecture, a novel framework for human-in-the-loop control. An architecture is developed which defines appropriate constraints for the system objectives. A method for enacting Lipschitz and sector bounds on the resulting controller is derived to ensure desirable control properties. An analysis of worst-case loss functions and the optimal loss function weighting is made to implement an effective training scheme. Finally, simulations are carried out to demonstrate the effectiveness of the proposed architecture. This architecture resulted in a 4.5% performance increase compared to the human operator and 9% to an unconstrained feedforward neural network trained in the same way.

eess.SY↗

arXiv2025

L-Lipschitz Gershgorin ResNet Network

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural networks has emerged as an essential area of research for enhancing adversarial robustness and network certifiability. This paper uses a rigorous approach to design $\mathcal{L}$-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. The ResNet architecture was reformulated as a pseudo-tri-diagonal LMI with off-diagonal elements and derived closed-form constraints on network parameters to ensure $\mathcal{L}$-Lipschitz continuity. To address the lack of explicit eigenvalue computations for such matrix structures, the Gershgorin circle theorem was employed to approximate eigenvalue locations, guaranteeing the LMI's negative semi-definiteness. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained networks and a compositional framework for managing recursive systems within hierarchical architectures. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. However, a limitation was identified in the Gershgorin-based approximations, which over-constrain the system, suppressing non-linear dynamics and diminishing the network's expressive capacity.

cs.LG↗

arXiv2025

1-Lipschitz Network Initialization for Certifiably Robust Classification Applications: A Decay Problem

This paper discusses the weight parametrization of two standard 1-Lipschitz network architectures, the Almost-Orthogonal-Layers (AOL) and the SDP-based Lipschitz Layers (SLL). It examines their impact on initialization for deep 1-Lipschitz feedforward networks, and discusses underlying issues surrounding this initialization. These networks are mainly used in certifiably robust classification applications to combat adversarial attacks by limiting the impact of perturbations on the classification output. Exact and upper bounds for the parameterized weight variance were calculated assuming a standard Normal distribution initialization; additionally, an upper bound was computed assuming a Generalized Normal Distribution, generalizing the proof for Uniform, Laplace, and Normal distribution weight initializations. It is demonstrated that the weight variance holds no bearing on the output variance distribution and that only the dimension of the weight matrices matters. Additionally, this paper demonstrates that the weight initialization always causes deep 1-Lipschitz networks to decay to zero.

cs.LG↗

arXiv2024

Cooperative Modular Manipulation with Numerous Cable-Driven Robots for Assistive Construction and Gap Crossing

Soldiers in the field often need to cross negative obstacles, such as rivers or canyons, to reach goals or safety. Military gap crossing involves on-site temporary bridges construction. However, this procedure is conducted with dangerous, time and labor intensive operations, and specialized machinery. We envision a scalable robotic solution inspired by advancements in force-controlled and Cable Driven Parallel Robots (CDPRs); this solution can address the challenges inherent in this transportation problem, achieving fast, efficient, and safe deployment and field operations. We introduce the embodied vision in Co3MaNDR, a solution to the military gap crossing problem, a distributed robot consisting of several modules simultaneously pulling on a central payload, controlling the cables' tensions to achieve complex objectives, such as precise trajectory tracking or force amplification. Hardware experiments demonstrate teleoperation of a payload, trajectory following, and the sensing and amplification of operators' applied physical forces during slow operations. An operator was shown to manipulate a 27.2 kg (60 lb) payload with an average force utilization of 14.5\% of its weight. Results indicate that the system can be scaled up to heavier payloads without compromising performance or introducing superfluous complexity. This research lays a foundation to expand CDPR technology to uncoordinated and unstable mobile platforms in unknown environments.

cs.RO↗

arXiv2023

In Situ Soil Property Estimation for Autonomous Earthmoving Using Physics-Infused Neural Networks

A novel, learning-based method for in situ estimation of soil properties using a physics-infused neural network (PINN) is presented. The network is trained to produce estimates of soil cohesion, angle of internal friction, soil-tool friction, soil failure angle, and residual depth of cut which are then passed through an earthmoving model based on the fundamental equation of earthmoving (FEE) to produce an estimated force. The network ingests a short history of kinematic observations along with past control commands and predicts interaction forces accurately with average error of less than 2kN, 13% of the measured force. To validate the approach, an earthmoving simulation of a bladed vehicle is developed using Vortex Studio, enabling comparison of the estimated parameters to pseudo-ground-truth values which is challenging in real-world experiments. The proposed approach is shown to enable accurate estimation of interaction forces and produces meaningful parameter estimates even when the model and the environmental physics deviate substantially.

cs.RO↗