arXiv subjects

Subhrajit Bhattacharya

Publications and source records attributed to Subhrajit Bhattacharya.

At least 19 recordsLinked to original sources

arXiv2026

From Ellipsoids to Midair Control of Dynamic Hitches

The ability to manipulate and interlace cables using aerial vehicles can greatly improve aerial transportation tasks. Such interlacing cables create hitches by winding two or more cables around each other, which can enclose payloads or can further develop into knots. Dynamic modeling and control of such hitches are key to mastering inter-cable interactions in the context of cable-suspended aerial manipulation. This paper introduces an ellipsoid-based kinematic model to connect the geometric nature of a hitch created by two cables and the dynamics of the hitch driven by four aerial vehicles, which reveals the control-affine form of the system. As the constraint for maintaining tension of a cable is also control-affine, we design a quadratic programming-based controller that combines Control Lyapunov and High-Order Control Barrier Functions (CLF-HOCBF-QP) to precisely track a desired hitch position and system shape while enforcing safety constraints like cable tautness. We convert desired geometric reference configurations into target robot positions and introduce a composite error into the Lyapunov function to ensure a relative degree of one to the input. Numerical simulations validate our approach, demonstrating stable, high-speed tracking of dynamic references.

cs.RO↗

arXiv2025

Distributed Optimization of Bivariate Polynomial Graph Spectral Functions via Subgraph Optimization

We study distributed optimization of finite-degree polynomial Laplacian spectral objectives under fixed topology and a global weight budget, targeting the collective behavior of the entire spectrum rather than a few extremal eigenvalues. By re-formulating the global cost in a bilinear form, we derive local subgraph problems whose gradients approximately align with the global descent direction via an SVD-based test on the $ZC$ matrix. This leads to an iterate-and-embed scheme over disjoint 1-hop neighborhoods that preserves feasibility by construction (positivity and budget) and scales to large geometric graphs. For objectives that depend on pairwise eigenvalue differences $h(\lambda_i-\lambda_j)$, we obtain a quadratic upper bound in the degree vector, which motivates a ``warm-start'' by degree-regularization. The warm start uses randomized gossip to estimate global average degree, accelerating subsequent local descent while maintaining decentralization, and realizing $\sim95\%{}$ of the performance with respect to centralized optimization. We further introduce a learning-based proposer that predicts one-shot edge updates on maximal 1-hop embeddings, yielding immediate objective reductions. Together, these components form a practical, modular pipeline for spectrum-aware weight tuning that preserves constraints and applies across a broader class of whole-spectrum costs.

math.OC↗

arXiv2025

Trace of Multi-variable Matrix Functions and its Application to Functions of Graph Spectrum

Matrix extension of a scalar function of a single variable is well-studied in literature. Of particular interest is the trace of such functions. It is known that for diagonalizable matrices, $M$, the function $g(M) = \text{Tr}(f(M)) = \sum_{j=1}^n f(\mu_j)$ (where $\{\mu_j\}_{j=1,2,\cdots,n}$ are the eigenvalues of $M$) inherits the monotonocity and convexity properties of $f$ (i.e., for $g$ to be convex, $f$ need not be operator convex -- convexity is sufficient). In this paper we formalize the idea of matrix extension of a function of multiple variables, study the monotonicity and convexity properties of the trace, and thus show that a function of form $g(M) = \sum_{j_1=1}^n \sum_{j_2=1}^n \cdots \sum_{j_m=1}^n f(\mu_{j_1}, \mu_{j_2},\cdots, \mu_{j_m})$ also inherits the monotonocity and convexity properties of the multi-variable function, $f$. We apply these results to functions of the spectrum of the weighted Laplacian matrix of undirected, simple graphs.

math.FA↗

arXiv2024

Spectrum Optimization of Dynamic Networks for Reduction of Vulnerability Against Adversarial Resonance Attacks

Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant frequency by an adversarial agent with the aim of saturating the network with the signal. Towards this goal, we develop the notion of network vulnerability, which is measured by the expected resonance amplitude on the network under a stochastically modeled adversarial attack. Assuming a second order dynamics model based on the network graph Laplacian matrix and a known stochastic model for the adversarial attack, we propose two methods for minimizing the network vulnerability through optimization of the spectrum of the network graph. We provide extensive numerical results analyzing the effects of both methods.

cs.SI↗

arXiv2023

Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks

We define the weighted combinatorial Laplacian operators on a simplicial complex and investigate their spectral properties. Eigenvalues close to zero and the corresponding eigenvectors of them are especially of our interest, and we show that they can detect almost $n$-dimensional holes in the given complex. Real-valued weights on simplices allow gradient descent based optimization, which in turn gives an efficient dynamic coverage repair algorithm for the sensor network of a mobile robot team. Using the theory of relative homology, we also extend the problem of dynamic coverage repair to environments with obstacles.

cs.RO↗

arXiv2023

Topo-Geometrically Distinct Path Computation using Neighborhood-augmented Graph, and its Application to Path Planning for a Tethered Robot in 3D

Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables, multi-robot topological exploration & coverage, and, congestion reduction for mobile robots navigation without inter-robot coordination. Existing paradigm is to use topological path planning methods that can provide optimal paths from distinct topological classes available in the underlying configuration space. However, these methods usually require non-trivial and non-universal geometrical constructions, which are prohibitively complex or expensive in 3 or higher dimensional configuration spaces with complex topology. Furthermore, topological methods are unable to distinguish between locally optimal paths that belong to the same topological class but are distinct because of genus-zero obstacles in 3D or due to high-cost or high-curvature regions. In this paper we propose an universal and generalized approach to multiple, locally-optimal path planning using the concept of a novel neighborhood-augmented graph, search-based planning in which can compute paths that are topo-geometrically distinct. This approach can find desired number of locally optimal paths in a wider variety of configuration spaces without requiring any complex pre-processing or geometric constructions. Unlike the existing topological methods, resulting optimal paths are not restricted to distinct topological classes, thus making the algorithm applicable to many other problems where locally optimal and geometrically distinct paths are of interest. We demonstrate the use of our algorithm to planning for shortest traversible paths for a tethered robot in 3D with cable-length constraint, and validate the results in simulations and real robot experimentation.

cs.RO↗

arXiv2023

Coordination-free Multi-robot Path Planning for Congestion Reduction Using Topological Reasoning

We consider the problem of multi-robot path planning in a complex, cluttered environment with the aim of reducing overall congestion in the environment, while avoiding any inter-robot communication or coordination. Such limitations may exist due to lack of communication or due to privacy restrictions (for example, autonomous vehicles may not want to share their locations or intents with other vehicles or even to a central server). The key insight that allows us to solve this problem is to stochastically distribute the robots across different routes in the environment by assigning them paths in different topologically distinct classes, so as to lower congestion and the overall travel time for all robots in the environment. We outline the computation of topologically distinct paths in a spatio-temporal configuration space and propose methods for the stochastic assignment of paths to the robots. A fast replanning algorithm and a potential field based controller allow robots to avoid collision with nearby agents while following the assigned path. Our simulation and experiment results show a significant advantage over shortest path following under such a coordination-free setup.

cs.RO↗

arXiv2023

Forming and Controlling Hitches in Midair Using Aerial Robots

The use of cables for aerial manipulation has shown to be a lightweight and versatile way to interact with objects. However, fastening objects using cables is still a challenge and human is required. In this work, we propose a novel way to secure objects using hitches. The hitch can be formed and morphed in midair using a team of aerial robots with cables. The hitch's shape is modeled as a convex polygon, making it versatile and adaptable to a wide variety of objects. We propose an algorithm to form the hitch systematically. The steps can run in parallel, allowing hitches with a large number of robots to be formed in constant time. We develop a set of actions that include different actions to change the shape of the hitch. We demonstrate our methods using a team of aerial robots via simulation and actual experiments.

cs.RO↗

arXiv2022

Multi-Agent Exploration of an Unknown Sparse Landmark Complex via Deep Reinforcement Learning

In recent years Landmark Complexes have been successfully employed for localization-free and metric-free autonomous exploration using a group of sensing-limited and communication-limited robots in a GPS-denied environment. To ensure rapid and complete exploration, existing works make assumptions on the density and distribution of landmarks in the environment. These assumptions may be overly restrictive, especially in hazardous environments where landmarks may be destroyed or completely missing. In this paper, we first propose a deep reinforcement learning framework for multi-agent cooperative exploration in environments with sparse landmarks while reducing client-server communication. By leveraging recent development on partial observability and credit assignment, our framework can train the exploration policy efficiently for multi-robot systems. The policy receives individual rewards from actions based on a proximity sensor with limited range and resolution, which is combined with group rewards to encourage collaborative exploration and construction of the Landmark Complex through observation of 0-, 1- and 2-dimensional simplices. In addition, we employ a three-stage curriculum learning strategy to mitigate the reward sparsity by gradually adding random obstacles and destroying random landmarks. Experiments in simulation demonstrate that our method outperforms the state-of-the-art landmark complex exploration method in efficiency among different environments with sparse landmarks.

cs.RO↗

arXiv2021

On Some Bounds on the Perturbation of Invariant Subspaces of Normal Matrices with Application to a Graph Connection Problem

We provide upper bounds on the perturbation of invariant subspaces of normal matrices measured using a metric on the space of vector subspaces of $\mathbb{C}^n$ in terms of the spectrum of both the unperturbed \& perturbed matrices, as well as, spectrum of the unperturbed matrix only. The results presented give tighter bounds than the Davis-Khan $\sinΘ$ theorem. We apply the result to a graph perturbation problem.

math.SP↗

arXiv2021

Training Robust Graph Neural Networks with Topology Adaptive Edge Dropping

Graph neural networks (GNNs) are processing architectures that exploit graph structural information to model representations from network data. Despite their success, GNNs suffer from sub-optimal generalization performance given limited training data, referred to as over-fitting. This paper proposes Topology Adaptive Edge Dropping (TADropEdge) method as an adaptive data augmentation technique to improve generalization performance and learn robust GNN models. We start by explicitly analyzing how random edge dropping increases the data diversity during training, while indicating i.i.d. edge dropping does not account for graph structural information and could result in noisy augmented data degrading performance. To overcome this issue, we consider graph connectivity as the key property that captures graph topology. TADropEdge incorporates this factor into random edge dropping such that the edge-dropped subgraphs maintain similar topology as the underlying graph, yielding more satisfactory data augmentation. In particular, TADropEdge first leverages the graph spectrum to assign proper weights to graph edges, which represent their criticality for establishing the graph connectivity. It then normalizes the edge weights and drops graph edges adaptively based on their normalized weights. Besides improving generalization performance, TADropEdge reduces variance for efficient training and can be applied as a generic method modular to different GNN models. Intensive experiments on real-life and synthetic datasets corroborate theory and verify the effectiveness of the proposed method.

cs.LG↗

arXiv2021

Pursuer Assignment and Control Strategies in Multi-agent Pursuit-Evasion Under Uncertainties

We consider a pursuit-evasion problem with a heterogeneous team of multiple pursuers and multiple evaders. Although both the pursuers (robots) and the evaders are aware of each others' control and assignment strategies, they do not have exact information about the other type of agents' location or action. Using only noisy on-board sensors the pursuers (or evaders) make probabilistic estimation of positions of the evaders (or pursuers). Each type of agent use Markov localization to update the probability distribution of the other type. A search-based control strategy is developed for the pursuers that intrinsically takes the probability distribution of the evaders into account. Pursuers are assigned using an assignment algorithm that takes redundancy (i.e., an excess in the number of pursuers than the number of evaders) into account, such that the total or maximum estimated time to capture the evaders is minimized. In this respect we assume the pursuers to have clear advantage over the evaders. However, the objective of this work is to use assignment strategies that minimize the capture time. This assignment strategy is based on a modified Hungarian algorithm as well as a novel algorithm for determining assignment of redundant pursuers. The evaders, in order to effectively avoid the pursuers, predict the assignment based on their probabilistic knowledge of the pursuers and use a control strategy to actively move away from those pursues. Our experimental evaluation shows that the redundant assignment algorithm performs better than an alternative nearest-neighbor based assignment algorithm.

cs.RO↗

arXiv2021

Landmark-based Distributed Topological Mapping and Navigation in GPS-denied Urban Environments Using Teams of Low-cost Robots

In this paper, we address the problem of autonomous multi-robot mapping, exploration and navigation in unknown, GPS-denied indoor or urban environments using a swarm of robots equipped with directional sensors with limited sensing capabilities and limited computational resources. The robots have no a priori knowledge of the environment and need to rapidly explore and construct a map in a distributed manner using existing landmarks, the presence of which can be detected using onboard senors, although little to no metric information (distance or bearing to the landmarks) is available. In order to correctly and effectively achieve this, the presence of a necessary density/distribution of landmarks is ensured by design of the urban/indoor environment. We thus address this problem in two phases: 1) During the design/construction of the urban/indoor environment we can ensure that sufficient landmarks are placed within the environment. To that end we develop a filtration-based approach for designing strategic placement of landmarks in an environment. 2) We develop a distributed algorithm using which a team of robots, with no a priori knowledge of the environment, can explore such an environment, construct a topological map requiring no metric/distance information, and use that map to navigate within the environment. This is achieved using a topological representation of the environment (called a Landmark Complex), instead of constructing a complete metric/pixel map. The representation is built by the robot as well as used by them for navigation through a balance between exploration and exploitation. We use tools from homology theory for identifying "holes" in the coverage/exploration of the unknown environment and hence guiding the robots towards achieving a complete exploration and mapping of the environment.

cs.RO↗

arXiv2020

Inter-cluster Transmission Control Using Graph Modal Barriers

In this paper we consider the problem of transmission across a graph and how to effectively control/restrict it with limited resources. Transmission can represent information transfer across a social network, spread of a malicious virus across a computer network, or spread of an infectious disease across communities. The key insight is to assign proper weights to bottleneck edges of the graph based on their role in reducing the connection between two or more strongly-connected clusters within the graph. Selectively reducing the weights (implying reduced transmission rate) on the critical edges helps limit the transmission from one cluster to another. We refer to these as barrier weights and their computation is based on the eigenvectors of the graph Laplacian. Unlike other work on graph partitioning and clustering, we completely circumvent the associated computational complexities by assigning weights to edges instead of performing discrete graph cuts. This allows us to provide strong theoretical results on our proposed methods. We also develop approximations that allow low complexity distributed computation of the barrier weights using only neighborhood communication on the graph.

cs.SI↗

arXiv2019

Multi-Robot Path Deconfliction through Prioritization by Path Prospects

This work deals with the problem of planning conflict-free paths for mobile robots in cluttered environments. Since centralized, coupled planning algorithms are computationally intractable for large numbers of robots, we consider decoupled planning, in which robots plan their paths sequentially in order of priority. Choosing how to prioritize the robots is a key consideration. State-of-the-art prioritization heuristics, however, do not model the coupling between a robot's mobility and its environment. In this paper, we propose a prioritization rule that can be computed online by each robot independently, and that provides consistent, conflict-free path plans. Our innovation is to formalize a robot's path prospects to reach its goal from its current location. To this end, we consider the number of homology classes of trajectories, and use this as a prioritization rule in our decentralized path planning algorithm, whenever any robots enter negotiation to deconflict path plans. This prioritization rule guarantees a partial ordering over the robot set. We perform simulations that compare our method to five benchmarks, and show that it reaches the highest success rate (w.r.t. completeness), and that it strikes the best balance between makespan and flowtime objectives.

cs.RO↗

arXiv2017

Path Homotopy Invariants and their Application to Optimal Trajectory Planning

We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on subsets of the Euclidean plane in the robotics literature. The problem of finding optimal trajectories in different homotopy classes in more general configuration spaces (or even characterizing the homotopy classes of such trajectories) can be difficult. In this paper we propose automated solutions to this problem in several general classes of configuration spaces by constructing presentations of fundamental groups and giving algorithms for solving the \emph{word problem} in such groups. We present explicit results that apply to knot and link complements in 3-space, discuss how to extend to cylindrically-deleted coordination spaces of arbitrary dimension, and also present results in the coordination space of robots navigating on an Euclidean plane.

cs.RO↗

arXiv2017

Approximate Structure Construction Using Large Statistical Swarms

In this paper we describe a novel local algorithm for large statistical swarms using "harmonic attractor dynamics", by means of which a swarm can construct harmonics of the environment. This in turn allows the swarm to approximately reconstruct desired structures in the environment. The robots navigate in a discrete environment, completely free of localization, being able to communicate with other robots in its own discrete cell only, and being able to sense or take reliable action within a disk of radius $r$ around itself. We present the mathematics that underlie such dynamics and present initial results demonstrating the proposed algorithm.

cs.RO↗

arXiv2016

A Search Algorithm for Simplicial Complexes

We present the `Basic S*' algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, $G$, which is constructed as a discrete representation of an underlying configuration space (a larger "continuous" space/manifold typically of dimension greater than one), we consider the Rips complex, $\mathcal{R}(G)$, associated with it. Such a complex, and hence shortest paths in it, represent the underlying metric space more closely than what the graph does. While discrete graph representations of continuous spaces is convenient for motion planning in configuration spaces of robotic systems, the metric induced in them by the ambient configuration space is significantly different from the metric of the configuration space itself. We remedy this problem using the simplicial complex representation. Our algorithm requires only an abstract graph, $G=(V,E)$, and a cost/length function, $d:E\rightarrow \mathbb{R}_+$, as inputs, and no global information such as an embedding or a global coordinate chart is required. The complexity of the Basic S* algorithm is comparable to that of Dijkstra's search, but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent/approximate the geodesic paths in the original metric space significantly more closely.

cs.DM↗