arXiv subjects

Mohit Singh

Publications and source records attributed to Mohit Singh.

At least 19 recordsLinked to original sources

arXiv2026

Design and Attitude Control of an Underwater Quadruped Robot

Legged robots are versatile on land, but their use in underwater environments remains limited. Extending quadruped locomotion to water enables amphibious mobility with applications in inspection, environmental monitoring and disaster response. This paper presents the design, modeling, and experimental validation of a reproducible underwater quadruped robot. The robot is built around custom waterproof motor housings machined from polyoxymethylene plastic, which use off-the-shelf O-rings and dynamic shaft seals. A simplified model is derived to describe the dynamics of this underwater legged system, capturing how drag forces on spherical end effectors transmit torque to the floating base. Building on this model, a closed-loop attitude controller is developed using an error formulation defined on the special orthogonal group SO(3). The controller is evaluated both in simulation and experimentally in a water tank, where the robot tracks desired orientation setpoints in roll, pitch and yaw.

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arXiv2026

If it is Good Then Drop it -- a Spiteful Poisson Process for Submodular Maximization

We study the problem of maximizing a general and not necessarily monotone submodular function subject to a matroid independence constraint. This problem has a rich history, with multiple algorithms using both discrete and continuous methods. Recently, [Ganz-Rozenman, Kulik, Schwartz and Singh STOC `26] presented a novel hybrid approach based on a Poisson process that aims to combine the strengths of both discrete and continuous methods for the special case of the problem where the submodular function is monotone. Our main result is a new Poisson process based hybrid algorithm that works for both non-monotone and monotone submodular functions, achieving an approximation of $ \frac{1}{e}$ for the former and $1-\frac{1}{e}$ for the latter. The algorithm always maintains a feasible set and at random times governed by the Poisson process it performs a single element swap based on a best response set. The new idea is that our algorithm is spiteful as it can purposefully discard an element that is in both the current set and the best response set. Surprisingly, this spiteful step does not harm the approximation our algorithm achieves for monotone submodular functions but is necessary for the non-monotone case. As applications, we obtain fast approximation algorithms for maximizing non-monotone submodular function subject to a general matroid independence constraint as well as faster algorithms for a partition matroid.

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arXiv2026

IBPA: Real-time Free-form Manifold Mesh Reconstruction via Incremental Ball Pivoting with Integrated Hole Detection

Both Remotely Operated underwater Vehicles (ROVs) and Autonomous Underwater Vehicles (AUVs) are frequently deployed to acquire geometric bathymetric data. However, it is often discovered post-survey that the acquired data coverage is incomplete. Given the high operational cost associated with underwater deployments, it is essential to incrementally visualize surface coverage in real-time to support informed decision-making by both the operators of ROVs and the AUVs during data collection. In addition, traditional incremental surface reconstruction methods, such as Digital Terrain Models (DTMs), are inherently limited in expressiveness: they represent surfaces as height fields, allows only one elevation value per $(x, y)$ coordinate and thus cannot capture overhangs or vertical structures. To overcome these limitations, we adapt the original Ball Pivoting Algorithm (BPA) into an incremental, real-time, and free-form surface reconstruction method, referred to as Incremental BPA (IBPA). Our method incrementally constructs an orientable, manifold mesh from streaming point cloud data without imposing assumptions regarding point cloud overlap or spatial distribution. Furthermore, we introduce a hole detection mechanism that identifies and highlights incomplete mesh regions. Compared to existing approaches, our method supports more complex surface topologies without prior structural assumptions. The source code of our reference implementation is available: https://github.com/Mauhing/Incremental-BPA

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arXiv2026

Philosopher and Prophet Inequalities for Divisible Items

We study online welfare maximization with divisible resources. A sequence of $n$ players arrive one by one; upon arrival, each player draws a valuation function over $m$ divisible items from a known distribution, reveals this valuation, and must be allocated an irrevocable fractional bundle subject to unit supply constraints. While online welfare maximization has been extensively studied for indivisible items and combinatorial valuations, much less is known when the resources are divisible and players have multi-dimensional concave valuations. We give approximation algorithms for monotone concave valuations satisfying diminishing returns. Our main result is a $2/3$-approximation to the optimal online policy, also known as the philosopher benchmark. The algorithm is guided by a low-dimensional concave relaxation of the online benchmark and rounds it via a new single-item capped online contention resolution scheme. This Capped-OCRS problem allocates to each realized type no more than its prescribed fractional bundle while preserving a $2/3$-fraction of that bundle in expectation. Its analysis uses a submartingale potential for the remaining side, we show that computing the optimal online policy is #P-hard even for a single divisible item. We also obtain a tight prophet inequality against the offline hindsight optimum. We show that a fixed-price auction with one linear per-unit price for each original divisible item achieves a $1/2$-approximation to the offline/prophet benchmark. The prices are obtained by aggregating Aumann--Shapley supporting prices, a continuous analogue of supporting prices for submodular/XOS set functions, and yield simple item prices rather than copy-dependent prices arising from discretization. The factor $1/2$ for the prophet benchmark is information-theoretically tight even for one item with linear valuations.

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arXiv2026

BEVIO: Efficient Bird's-Eye-View based Sparse-Update Visual-Inertial Odometry for Lunar Day-Night Navigation

Visual-Inertial Odometry (VIO) provides smooth, high-rate state estimates and has been widely used for robotic navigation in both terrestrial and planetary applications. However, its performance is typically dependent on the frequency of visual updates, which is a challenge for planetary rovers operating under extreme resource constraints and low frame rates. This work investigates enabling reliable VIO with very sparse visual updates for lunar rover applications, addressing both day and night-time operations where feature associations become especially difficult under self-illumination conditions. We propose a Bird's Eye View (BEV)-based image matching scheme that remains robust to larger inter-frame motions and more reliable feature matching despite significant visual appearance changes. We extensively evaluate our proposed approach, BEVIO, through high-fidelity photorealistic lunar and real-time robotic experiments conducted using a half-scale lunar rover, in a long-term day-night deployment at Plaster City, CA, USA. The results demonstrate that our method enables reliable day and nighttime self-illuminated traverses at visual update rates as low as 0.25 Hz, underscoring its suitability for navigation on power- and compute-limited lunar rovers.

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arXiv2026

Optimal Spectral Design with Prior Information

We study a class of spectral design problems in which a prior positive semidefinite information matrix is updated by a sum of rank-one matrices constructed from chosen design vectors subject to a bound on their Euclidean norm. The objective of a spectral design problem is any symmetric convex function of the eigenvalues of the updated information matrix. This framework unifies classical optimal experimental design criteria, including A-, D-, and E-optimality. It also arises in model-based derivative-free optimization, where sampling directions determine the conditioning and accuracy of regression models. Although the objective is symmetric and convex in the eigenvalues, the optimization problem with design vectors/matrix as decision variables is nonconvex, and optimal solutions of their convex relaxations may not be feasible for the spectral design problem. We use tight eigenvalue relaxations to obtain a convex reformulation, and we apply the Schur--Horn theorem to construct a simple polynomial-time algorithm for solving the spectral design problem. We illustrate the optimal spectral designs computed by our algorithm. Moreover, a small set of numerical experiments shows the potential of spectral designs for derivative-free optimization.

math.OC↗

arXiv2026

A Poisson Process for Submodular Maximization

We study the problem of maximizing a monotone submodular function subject to a matroid independence constraint. For more than a decade, a rich body of work has studied this problem. Initially, a tight approximation of $ (1-\frac{1}{e})$ was given using the continuous greedy algorithm [Calinescu-Chekuri-Pal-Vondr{\'a}k STOC`2008] and later non-oblivious local search techniques were able to match this tight approximation guarantee [Filmus-Ward FOCS`2012] and [Buchbinder-Feldman FOCS`2024]. We propose a new and remarkably simple approach to this problem that is based on a stochastic Poisson process. Our approach matches the tight $ (1-\frac{1}{e})$ approximation guarantee and it differs from the known two techniques since it does not require discretization or rounding while performing very few single element swaps. We also present applications of our approach and obtain fast algorithms for submodular welfare maximization, and for the general and separable assignment problems.

cs.DS↗

arXiv2026

Stochastic Function Certification with Correlations

We study the Stochastic Boolean Function Certification (SBFC) problem, where we are given $n$ Bernoulli random variables $\{X_e: e \in U\}$ on a ground set $U$ of $n$ elements with joint distribution $p$, a Boolean function $f: 2^U \to \{0, 1\}$, and an (unknown) scenario $S = \{e \in U: X_e = 1\}$ of active elements sampled from $p$. We seek to probe the elements one-at-a-time to reveal if they are active until we can certify $f(S) = 1$, while minimizing the expected number of probes. Unlike most previous results that assume independence, we study correlated distributions $p$ and give approximation algorithms for several classes of functions $f$. When $f(S)$ is the indicator function for whether $S$ is the spanning set of a given matroid, our problem reduces to finding a basis of active elements of a matroid by probing elements. We give a non-adaptive $O(\log n)$-approximation algorithm for arbitrary distributions $p$, and show that this is tight up to constants unless P $=$ NP, even for partition matroids. For uniform matroids, we give constant factor $4.642$-approximation ([BBFT20]) that can be further improved to a $2$-approximation if additionally the random variables are negatively correlated for the case of $1$-uniform matroid. We also give an adaptive $O(\log k)$-approximation algorithm for SBFC for $k$-uniform matroids for the Graph Probing problem, where we seek to probe the edges of a graph one-at-a-time until we find $k$ active edges. The underlying distribution on edges arises from (hidden) independent vertex random variables, with an edge being active if at least one of its endpoints is active. This significantly improves over the information-theoretic lower bound on $\Omega(\mathrm{poly}(n))$ ([JGM19]) for adaptive algorithms for $k$-uniform matroids with arbitrary distributions.

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arXiv2026

Tightly-Coupled Radar-Visual-Inertial Odometry

Visual-Inertial Odometry (VIO) is a staple for reliable state estimation on constrained and lightweight platforms due to its versatility and demonstrated performance. However, pertinent challenges regarding robust operation in dark, low-texture, obscured environments complicate the use of such methods. Alternatively, Frequency Modulated Continuous Wave (FMCW) radars, and by extension Radar-Inertial Odometry (RIO), offer robustness to these visual challenges, albeit at the cost of reduced information density and worse long-term accuracy. To address these limitations, this work combines the two in a tightly coupled manner, enabling the resulting method to operate robustly regardless of environmental conditions or trajectory dynamics. The proposed method fuses image features, radar Doppler measurements, and Inertial Measurement Unit (IMU) measurements within an Iterated Extended Kalman Filter (IEKF) in real-time, with radar range data augmenting the visual feature depth initialization. The method is evaluated through flight experiments conducted in both indoor and outdoor environments, as well as through challenges to both exteroceptive modalities (such as darkness, fog, or fast flight), thoroughly demonstrating its robustness. The implementation of the proposed method is available at: https://github.com/ntnu-arl/radvio.

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arXiv2026

OmniPlanner: Universal Exploration and Inspection Path Planning across Robot Morphologies

Autonomous robotic systems are increasingly deployed for mapping, monitoring, and inspection in complex and unstructured environments. However, most existing path planning approaches remain domain-specific (i.e., either on air, land, or sea), limiting their scalability and cross-platform applicability. This article presents OmniPlanner, a unified planning framework for autonomous exploration and inspection across aerial, ground, and underwater robots. The method integrates volumetric exploration and viewpoint-based inspection, alongside target reach behaviors within a single modular architecture, complemented by a platform abstraction layer that captures morphology-specific sensing, traversability and motion constraints. This enables the same planning strategy to generalize across distinct mobility domains with minimal retuning. The framework is validated through extensive simulation studies and field deployments in underground mines, industrial facilities, forests, submarine bunkers, and structured outdoor environments. Across these diverse scenarios, OmniPlanner demonstrates robust performance, consistent cross-domain generalization, and improved exploration and inspection efficiency compared to representative state-of-the-art baselines.

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arXiv2026

Improved Regret Guarantees for Online Mirror Descent using a Portfolio of Mirror Maps

OMD and its variants give a flexible framework for OCO where the performance depends crucially on the choice of the mirror map. While the geometries underlying OPGD and OEG, both special cases of OMD, are well understood, it remains a challenging open question on how to construct an optimal mirror map for any given constrained set and a general family of loss functions, e.g., sparse losses. Motivated by parameterizing a near-optimal set of mirror maps, we consider a simpler question: is it even possible to obtain polynomial gains in regret by using mirror maps for geometries that interpolate between $L_1$ and $L_2$, which may not be possible by restricting to only OEG ($L_1$) or OPGD ($L_2$). Our main result answers this question positively. We show that mirror maps based on block norms adapt better to the sparsity of loss functions, compared to previous $L_p$ (for $p \in [1, 2]$) interpolations. In particular, we construct a family of online convex optimization instances in $\mathbb{R}^d$, where block norm-based mirror maps achieve a provable polynomial (in $d$) improvement in regret over OEG and OPGD for sparse loss functions. We then turn to the setting in which the sparsity level of the loss functions is unknown. In this case, the choice of geometry itself becomes an online decision problem. We first show that naively switching between OEG and OPGD can incur linear regret, highlighting the intrinsic difficulty of geometry selection. To overcome this issue, we propose a meta-algorithm based on multiplicative weights that dynamically selects among a family of uniform block norms. We show that this approach effectively tunes OMD to the sparsity of the losses, yielding adaptive regret guarantees. Overall, our results demonstrate that online mirror-map selection can significantly enhance the ability of OMD to exploit sparsity in online convex optimization.

math.OC↗

arXiv2025

Provably Small Portfolios for Multiobjective Optimization with Application to Subsidized Facility Location

Many multiobjective real-world problems, such as facility location and bus routing, become more complex when optimizing the priorities of multiple stakeholders. These are often modeled using infinite classes of objectives, e.g., $L_p$ norms over group distances induced by feasible solutions in a fixed domain. Traditionally, the literature has considered explicitly balancing `equity' (or min-max) and `efficiency' (or min-sum) objectives to capture this trade-off. However, the structure of solutions obtained by such modeling choices can be very different. Taking a solution-centric approach, we introduce the concept of provably small set of solutions $P$, called a {\it portfolio}, such that for every objective function $h(\cdot)$ in the given class $\mathbf{C}$, there exists some solution in $P$ which is an $\alpha$-approximation for $h(\cdot)$. Constructing such portfolios can help decision-makers understand the impact of balancing across multiple objectives. Given a finite set of base objectives $h_1, \ldots, h_N$, we give provable algorithms for constructing portfolios for (1) the class of conic combinations $\mathbf{C} = \{\sum_{j \in [N]}\lambda_j h_j: \lambda \ge 0\}$ and for (2) any class $\mathbf{C}$ of functions that interpolates monotonically between the min-sum efficiency objective (i.e., $h_1 + \ldots + h_N$) and the min-max equity objective (i.e., $\max_{j \in [N]} h_j$). Examples of the latter are $L_p$ norms and top-$\ell$ norms. As an application, we study the Fair Subsidized Facility Location (FSFL) problem, motivated by the crisis of medical deserts caused due to pharmacy closures. FSFL allows subsidizing facilities in underserved areas using revenue from profitable locations. We develop a novel bicriteria approximation algorithm and show a significant reduction of medical deserts across states in the U.S.

cs.DS↗

arXiv2025

UniPilot: Enabling GPS-Denied Autonomy Across Embodiments

This paper presents UniPilot, a compact hardware-software autonomy payload that can be integrated across diverse robot embodiments to enable autonomous operation in GPS-denied environments. The system integrates a multi-modal sensing suite including LiDAR, radar, vision, and inertial sensing for robust operation in conditions where uni-modal approaches may fail. UniPilot runs a complete autonomy software comprising multi-modal perception, exploration and inspection path planning, and learning-based navigation policies. The payload provides robust localization, mapping, planning, and safety and control capabilities in a single unit that can be deployed across a wide range of platforms. A large number of experiments are conducted across diverse environments and on a variety of robot platforms to validate the mapping, planning, and safe navigation capabilities enabled by the payload.

cs.RO↗

arXiv2025

Uncertainty Aware Mapping for Vision-Based Underwater Robots

Vision-based underwater robots can be useful in inspecting and exploring confined spaces where traditional sensors and preplanned paths cannot be followed. Sensor noise and situational change can cause significant uncertainty in environmental representation. Thus, this paper explores how to represent mapping inconsistency in vision-based sensing and incorporate depth estimation confidence into the mapping framework. The scene depth and the confidence are estimated using the RAFT-Stereo model and are integrated into a voxel-based mapping framework, Voxblox. Improvements in the existing Voxblox weight calculation and update mechanism are also proposed. Finally, a qualitative analysis of the proposed method is performed in a confined pool and in a pier in the Trondheim fjord. Experiments using an underwater robot demonstrated the change in uncertainty in the visualization.

cs.RO↗

arXiv2025

Ariel Explores: Vision-based underwater exploration and inspection via generalist drone-level autonomy

This work presents a vision-based underwater exploration and inspection autonomy solution integrated into Ariel, a custom vision-driven underwater robot. Ariel carries a $5$ camera and IMU based sensing suite, enabling a refraction-aware multi-camera visual-inertial state estimation method aided by a learning-based proprioceptive robot velocity prediction method that enhances robustness against visual degradation. Furthermore, our previously developed and extensively field-verified autonomous exploration and general visual inspection solution is integrated on Ariel, providing aerial drone-level autonomy underwater. The proposed system is field-tested in a submarine dry dock in Trondheim under challenging visual conditions. The field demonstration shows the robustness of the state estimation solution and the generalizability of the path planning techniques across robot embodiments.

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arXiv2025

DeepVL: Dynamics and Inertial Measurements-based Deep Velocity Learning for Underwater Odometry

This paper presents a learned model to predict the robot-centric velocity of an underwater robot through dynamics-aware proprioception. The method exploits a recurrent neural network using as inputs inertial cues, motor commands, and battery voltage readings alongside the hidden state of the previous time-step to output robust velocity estimates and their associated uncertainty. An ensemble of networks is utilized to enhance the velocity and uncertainty predictions. Fusing the network's outputs into an Extended Kalman Filter, alongside inertial predictions and barometer updates, the method enables long-term underwater odometry without further exteroception. Furthermore, when integrated into visual-inertial odometry, the method assists in enhanced estimation resilience when dealing with an order of magnitude fewer total features tracked (as few as 1) as compared to conventional visual-inertial systems. Tested onboard an underwater robot deployed both in a laboratory pool and the Trondheim Fjord, the method takes less than 5ms for inference either on the CPU or the GPU of an NVIDIA Orin AGX and demonstrates less than 4% relative position error in novel trajectories during complete visual blackout, and approximately 2% relative error when a maximum of 2 visual features from a monocular camera are available.

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arXiv2024

Online Refractive Camera Model Calibration in Visual Inertial Odometry

This paper presents a general refractive camera model and online co-estimation of odometry and the refractive index of unknown media. This enables operation in diverse and varying refractive fluids, given only the camera calibration in air. The refractive index is estimated online as a state variable of a monocular visual-inertial odometry framework in an iterative formulation using the proposed camera model. The method was verified on data collected using an underwater robot traversing inside a pool. The evaluations demonstrate convergence to the ideal refractive index for water despite significant perturbations in the initialization. Simultaneously, the approach enables on-par visual-inertial odometry performance in refractive media without prior knowledge of the refractive index or requirement of medium-specific camera calibration.

cs.RO↗

arXiv2024

Maximizing the Minimum Eigenvalue in Constant Dimension

In an instance of the minimum eigenvalue problem, we are given a collection of $n$ vectors $v_1,\ldots, v_n \subset {\mathbb{R}^d}$, and the goal is to pick a subset $B\subseteq [n]$ of given vectors to maximize the minimum eigenvalue of the matrix $\sum_{i\in B} v_i v_i^{\top} $. Often, additional combinatorial constraints such as cardinality constraint $\left(|B|\leq k\right)$ or matroid constraint ($B$ is a basis of a matroid defined on $[n]$) must be satisfied by the chosen set of vectors. The minimum eigenvalue problem with matroid constraints models a wide variety of problems including the Santa Clause problem, the E-design problem, and the constructive Kadison-Singer problem. In this paper, we give a randomized algorithm that finds a set $B\subseteq [n]$ subject to any matroid constraint whose minimum eigenvalue is at least $(1-\epsilon)$ times the optimum, with high probability. The running time of the algorithm is $O\left( n^{O(d\log(d)/\epsilon^2)}\right)$. In particular, our results give a polynomial time asymptotic scheme when the dimension of the vectors is constant. Our algorithm uses a convex programming relaxation of the problem after guessing a rescaling which allows us to apply pipage rounding and matrix Chernoff inequalities to round to a good solution. The key new component is a structural lemma which enables us to "guess'' the appropriate rescaling, which could be of independent interest. Our approach generalizes the approximation guarantee to monotone, homogeneous functions and as such we can maximize $\det(\sum_{i\in B} v_i v_i^\top)^{1/d}$, or minimize any norm of the eigenvalues of the matrix $\left(\sum_{i\in B} v_i v_i^\top\right)^{-1} $, with the same running time under some mild assumptions. As a byproduct, we also get a simple algorithm for an algorithmic version of Kadison-Singer problem.

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