arXiv subjects

Sivakumar Rathinam

Publications and source records attributed to Sivakumar Rathinam.

At least 19 recordsLinked to original sources

arXiv2026

Longitudinal-Motion-Aware Lateral Control for Autonomous Vehicles: A Robust Nonlinear Control Framework

As autonomous vehicles (AVs) operate in increasingly dynamic traffic conditions, lateral control must be performed while longitudinal speed and acceleration vary. Yet many existing lateral controllers rely on constant-speed or operating-point-based assumptions, which can degrade performance during transient longitudinal maneuvers. Moreover, most methods assume precisely known vehicle parameters, despite real-world parametric uncertainties. To address these limitations, this paper presents a longitudinal-motion-aware robust nonlinear lateral control framework for AVs. It first derives a tracking error model that depends on varying longitudinal speed and acceleration. Using this model, feedback linearization is employed to obtain a linear input-output relation for lateral error tracking while embedding longitudinal motion into the control law. The resulting internal dynamics are then analyzed to ensure overall system stability. To address parameter uncertainty, two robust control designs with distinct implementation trade-offs are proposed: (i) a Lyapunov redesign (LR) approach inspired by sliding mode control, and (ii) an incremental nonlinear dynamic inversion (INDI) method. Both are rigorously analyzed and proven to ensure ultimate boundedness, with key robustness-tuning parameters explicitly identified. Simulations demonstrate enhanced tracking accuracy, consistent performance across varying speeds and accelerations, and robustness to model uncertainties, while also examining the effects of the robustness-related parameters. Real-vehicle tests further confirm real-time implementation and practical path-tracking performance on actual hardware.

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arXiv2026

Privacy-Preserving Decentralized Cooperative Localization with Range-Only Measurements: A Convex Optimization Based Approach

Cooperative localization using range-based measurements is critical for multi-robot systems operating in GPS-denied and unstructured environments. However, traditional cooperative approaches require sharing explicit spatial coordinates across the network, presenting a severe security vulnerability in privacy-sensitive missions. While recent literature has explored privacy-preserving alternatives, these methods typically rely on accuracy-degrading noise injection or computationally prohibitive cryptographic protocols. To overcome these limitations, we propose a novel, natively privacy-preserving Decentralized Cooperative Localization (DCL) framework based on convex optimization. Discarding probabilistic noise models, we assume strictly bounded measurement noise and formulate the localization problem via Semi-Definite Programming (SDP) to compute a Maximum-Volume Inscribed Ellipsoid (MVE). Our approach introduces novel intersection-plane constraints derived from landmark measurements to significantly tighten individual spatial bounds. To incorporate inter-robot range measurements securely, we uniquely decompose coupling constraints into localized Linear Matrix Inequalities (LMIs). Agents achieve fleet-wide spatial consensus by iteratively exchanging only abstract dual variables, completely avoiding the transmission of explicit primal position estimates. Extensive 3D Monte Carlo simulations demonstrate that our DCL framework outperforms existing SDP-based localization method in accuracy, while guaranteeing operational privacy and maintaining highly scalable, parallelizable computation.

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arXiv2026

Two-Phase Bilevel Search for the Moving-Target Traveling Salesman Problem with Moving Obstacles

The Moving-Target Traveling Salesman Problem (MT-TSP) seeks a minimum cost trajectory for an agent that departs from a static depot, visits a set of moving targets, each within one of their assigned time windows, and returns to the depot. In this article, we study the Moving-Target Traveling Salesman Problem with Moving Obstacles (MT-TSP-MO), a generalization of the MT-TSP where the agent trajectory must avoid moving obstacles. We present a Mixed-Integer Conic Programming (MICP) formulation that can be solved using off-the-shelf solvers, as well as a fast and scalable Two-Phase Bilevel Search (TPBS) algorithm that computes high-quality feasible solutions for the problem. We evaluate our approaches against an existing baseline algorithm on a broad range of problem instances with up to 40 targets and 40 obstacles. The results demonstrate that both the proposed methods significantly outperform the baseline with respect to success rates, solution costs, and computation time.

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arXiv2026

An Exact Algorithm for Load-Dependent Traveling Salesman Problem for Unmanned Aerial Vehicle Package Delivery

In this article, we present a novel formulation for the load-dependent traveling salesman problem (LD-TSP), in which travel cost (or energy expended) depends on the vehicle's current load. This problem is relevant for package delivery and urban air mobility, where vehicles must transport and drop cargo at specified locations. The challenge lies in modeling the cost, which varies with both route sequence and onboard load. Our key contributions are: (i) formulating an energy dissipation model and proving energy expenditure depends linearly on vehicle mass and distance; and (ii) formulating a mixed-integer nonlinear programming formulation and providing a novel relaxation to obtain a mixed-integer linear program. Extensive numerical results show that optimal solutions for most instances with up to 50 targets are obtained within one minute. For unsolved instances within a 10-minute limit, optimality gaps are under 13%, highlighting the formulation's tightness. We further benchmark our approach against three proposed baseline formulations and another algorithm from a related problem, and demonstrate that our formulation outperforms all baselines.

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arXiv2026

Optimal Solutions for the Moving Target Vehicle Routing Problem via Branch-and-Price with Relaxed Continuity

The Moving Target Vehicle Routing Problem (MT-VRP) seeks trajectories for several agents that intercept a set of moving targets, subject to speed, time window, and capacity constraints. We introduce an exact algorithm, Branch-and-Price with Relaxed Continuity (BPRC), for the MT-VRP. The main challenge in a branch-and-price approach for the MT-VRP is the pricing subproblem, which is complicated by moving targets and time-dependent travel costs between targets. Our key contribution is a new labeling algorithm that solves this subproblem by means of a novel dominance criterion tailored for problems with moving targets. Numerical results on instances with up to 25 targets show that our algorithm finds optimal solutions more than an order of magnitude faster than a baseline based on previous work, showing particular strength in scenarios with limited agent capacities.

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arXiv2026

Optimal Solutions for the Moving Target Vehicle Routing Problem with Obstacles via Lazy Branch and Price

The Moving Target Vehicle Routing Problem with Obstacles (MT-VRP-O) seeks trajectories for several agents that collectively intercept a set of moving targets. Each target has one or more time windows where it must be visited, and the agents must avoid static obstacles and satisfy speed and capacity constraints. We introduce Lazy Branch-and-Price with Relaxed Continuity (Lazy BPRC), which finds optimal solutions for the MT-VRP-O. Lazy BPRC applies the branch-and-price framework for VRPs, which alternates between a restricted master problem (RMP) and a pricing problem. The RMP aims to select a sequence of target-time window pairings (called a tour) for each agent to follow, from a limited subset of tours. The pricing problem adds tours to the limited subset. Conventionally, solving the RMP requires computing the cost for an agent to follow each tour in the limited subset. Computing these costs in the MT-VRP-O is computationally intensive, since it requires collision-free motion planning between moving targets. Lazy BPRC defers cost computations by solving the RMP using lower bounds on the costs of each tour, computed via motion planning with relaxed continuity constraints. We lazily evaluate the true costs of tours as-needed. We compute a tour's cost by searching for a shortest path on a Graph of Convex Sets (GCS), and we accelerate this search using our continuity relaxation method. We demonstrate that Lazy BPRC runs up to an order of magnitude faster than two ablations.

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arXiv2026

Parallel, Asymptotically Optimal Algorithms for Moving Target Traveling Salesman Problems

The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the agent are present, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The idea behind IRG is to alternate between randomly sampling a set of agent configuration-time points, corresponding to interceptions of targets, and finding a sequence of interception points by solving a generalized TSP (GTSP). This alternation asymptotically converges to the optimum. We introduce two parallel algorithms within the IRG framework. The first algorithm, IRG-PGLNS, solves GTSPs using PGLNS, our parallelized extension of state-of-the-art solver GLNS. The second algorithm, Parallel Communicating GTSPs (PCG), solves GTSPs for several sets of points simultaneously. We present numerical results for three MT-TSP variants: one where intercepting a target only requires coming within a particular distance, another where the agent is a variable-speed Dubins car, and a third where the agent is a robot arm. We show that IRG-PGLNS and PCG converge faster than a baseline based on prior work. We further validate our framework with physical robot experiments.

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arXiv2026

COLREGs Compliant Collision Avoidance and Grounding Prevention for Autonomous Marine Navigation

Maritime Autonomous Surface Ships (MASS) are increasingly regarded as a promising solution to address crew shortages, improve navigational safety, and improve operational efficiency in the maritime industry. Nevertheless, the reliable deployment of MASS in real-world environments remains a significant challenge, particularly in congested waters where the majority of maritime accidents occur. This emphasizes the need for safe and regulation-aware motion planning strategies for MASS that are capable of operating under dynamic maritime conditions. This paper presents a unified motion planning method for MASS that achieves real time collision avoidance, compliance with International Regulations for Preventing Collisions at Sea (COLREGs), and grounding prevention. The proposed work introduces a convex optimization method that integrates velocity obstacle-based (VO) collision constraints, COLREGs-based directional constraints, and bathymetry-based grounding constraints to generate computationally efficient, rule-compliant optimal velocity selection. To enhance robustness, the classical VO method is extended to consider uncertainty in the position and velocity estimates of the target vessel. Unnavigable shallow water regions obtained from bathymetric data, which are inherently nonconvex, are approximated via convex geometries using a integer linear programming (ILP), allowing grounding constraints to be incorporated into the motion planning. The resulting optimization generates optimal and dynamically feasible input velocities that meet collision avoidance, regulatory compliance, kinodynamic limits, and grounding prevention requirements. Simulation results involving multi-vessel encounters demonstrate the effectiveness of the proposed method in producing safe and regulation-compliant maneuvers, highlighting the suitability of the proposed approach for real time autonomous maritime navigation.

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arXiv2026

A Robust Simulation Framework for Verification and Validation of Autonomous Maritime Navigation in Adverse Weather and Constrained Environments

Maritime Autonomous Surface Ships (MASS) have emerged as a promising solution to enhance navigational safety, operational efficiency, and long-term cost effectiveness. However, their reliable deployment requires rigorous verification and validation (V\&V) under various environmental conditions, including extreme and safety-critical scenarios. This paper presents an enhanced virtual simulation framework to support the V\&V of MASS in realistic maritime environments, with particular emphasis on the influence of weather and bathymetry on autonomous navigation performance. The framework incorporates a high-fidelity environmental modeling suite capable of simulating adverse weather conditions such as rain, fog, and wave dynamics. The key factors that affect weather, such as rain and visibility, are parameterized to affect sea-state characteristics, perception, and sensing systems, resulting in position and velocity uncertainty, reduced visibility, and degraded situational awareness. Furthermore, high-resolution bathymetric data from major U.S. ports are integrated to enable depth-aware navigation, grounding prevention capabilities, and evaluation of vessel controllability in shallow or confined waterways. The proposed framework offers extensive configurability, enabling systematic testing in a wide spectrum of maritime conditions, including scenarios that are impractical or unsafe to replicate in real-world trials, thus supporting the V\&V of MASS.

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arXiv2026

Cyclic Modulation Control of Multi-Conflict Connected Automated Traffic

Multi-conflict traffic is ubiquitous. Connected Automated Vehicles (CAVs) offer unprecedented opportunities to enhance safety, reduce emissions, and increase throughput through precise coordination and automation. However, existing CAV strategies remain confined to specialized scenarios, such as highway on-ramp merging or single-lane roundabouts, and traditional traffic signals sacrifice efficiency for safety via rigid phasing and all-red intervals. In this paper, we present Cyclic Modulation Control of Multi-Conflict Connected Automated Traffic (CMAT), a unified, geometry-agnostic framework that embeds each conflict point into a repeating sequence of "micro-phases". Vehicles dynamically form platoons with demand-responsive sizes and negotiate time slots for occupying conflict points, enabling collision-free traversal and high intersection utilization. CMAT aims to minimize delay, guarantee safety, and accommodate arbitrary merging, diverging, and crossing patterns without manual retuning. We formalize CMAT as a mixed-integer linear programming model constructed on a directed graph abstracted from the physical intersection layout. The performance of CMAT is evaluated across a suite of multi-conflict tests, including simple two-way crossings, four-leg intersections, complex connected intersections. The results demonstrate substantial reductions in delay and significant throughput improvements compared with state-of-the-art CAV coordination methods and traditional signal timing strategies.

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arXiv2025

A Path Planning Algorithm for a Hybrid UAV Traveling in Noise Restricted Zones

This paper presents an integrated approach for efficient path planning and energy management in hybrid unmanned aerial vehicles (HUAVs) equipped with dual fuel-electric propulsion systems. These HUAVs operate in environments that include noise-restricted zones, referred to as quiet zones, where only electric mode is permitted. We address the problem by parameterizing the position of a point along the side of the quiet zone using its endpoints and a scalar parameter, transforming the problem into a variant of finding the shortest path over a graph of convex sets. We formulate this problem as a mixed-integer convex program (MICP), which can be efficiently solved using commercial solvers. Additionally, a tight lower bound can be obtained by relaxing the path-selection variable. Through extensive computations across 200 instances over four maps, we show a substantial improvement in computational efficiency over a state-of-the-art method, achieving up to a 100-fold and 10-fold decrease in computation time for calculating the lower bound and the exact solution, respectively. Moreover, the average gap between the exact cost and the lower bound was approximately 0.24%, and the exact cost was 1.05% lower than the feasible solution from the state-of-the-art approach on average, highlighting the effectiveness of our method. We also extend our approach to plan the HUAV route to visit a set of targets and return to its starting location in environments with quiet zones, yielding a Traveling Salesman Problem (TSP). We employ two methodologies to solve the TSP: one where the SOC at each target is discretized, and another where it is assumed to be the minimum allowable level upon departure. A comparative analysis reveals the second method achieves a cost within 1.02% of the first on average while requiring significantly less computational time.

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arXiv2025

A Complete and Bounded-Suboptimal Algorithm for a Moving Target Traveling Salesman Problem with Obstacles in 3D

The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting position. Each target moves with a constant velocity within its time windows, and the agent has a speed limit no smaller than any target's speed. We present FMC*-TSP, the first complete and bounded-suboptimal algorithm for the MT-TSP-O, and results for an agent whose configuration space is $\mathbb{R}^3$. Our algorithm interleaves a high-level search and a low-level search, where the high-level search solves a generalized traveling salesman problem with time windows (GTSP-TW) to find a sequence of targets and corresponding time windows for the agent to visit. Given such a sequence, the low-level search then finds an associated agent trajectory. To solve the low-level planning problem, we develop a new algorithm called FMC*, which finds a shortest path on a graph of convex sets (GCS) via implicit graph search and pruning techniques specialized for problems with moving targets. We test FMC*-TSP on 280 problem instances with up to 40 targets and demonstrate its smaller median runtime than a baseline based on prior work.

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arXiv2025

$A^*$ for Graphs of Convex Sets

We present a novel algorithm that fuses the existing convex-programming based approach with heuristic information to find optimality guarantees and near-optimal paths for the Shortest Path Problem in the Graph of Convex Sets (SPP-GCS). Our method, inspired by $A^*$, initiates a best-first-like procedure from a designated subset of vertices and iteratively expands it until further growth is neither possible nor beneficial. Traditionally, obtaining solutions with bounds for an optimization problem involves solving a relaxation, modifying the relaxed solution to a feasible one, and then comparing the two solutions to establish bounds. However, for SPP-GCS, we demonstrate that reversing this process can be more advantageous, especially with Euclidean travel costs. In other words, we initially employ $A^*$ to find a feasible solution for SPP-GCS, then solve a convex relaxation restricted to the vertices explored by $A^*$ to obtain a relaxed solution, and finally, compare the solutions to derive bounds. We present numerical results to highlight the advantages of our algorithm over the existing approach in terms of the sizes of the convex programs solved and computation time.

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arXiv2025

A Mixed-Integer Conic Program for the Multi-Agent Moving-Target Traveling Salesman Problem

The Moving-Target Traveling Salesman Problem (MT-TSP) seeks a shortest path for an agent that starts at a stationary depot, visits a set of moving targets exactly once, each within one of their respective time windows, and returns to the depot. In this paper, we introduce a new Mixed-Integer Conic Program (MICP) formulation for the Multi-Agent Moving-Target Traveling Salesman Problem (MA-MT-TSP), a generalization of the MT-TSP involving multiple agents. Our approach begins by restating the current state-of-the-art MICP formulation for MA-MT-TSP as a Nonconvex Mixed-Integer Nonlinear Program (MINLP), followed by a novel reformulation into a new MICP. We present computational results demonstrating that our formulation outperforms the state-of-the-art, achieving up to two orders of magnitude reduction in runtime, and over 90% improvement in optimality gap.

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arXiv2025

Heuristic Search for Path Finding with Refuelling

This paper considers a generalization of the Path Finding (PF) problem with refuelling constraints referred to as the Gas Station Problem (GSP). Similar to PF, given a graph where vertices are gas stations with known fuel prices, and edge costs are the gas consumption between the two vertices, GSP seeks a minimum-cost path from the start to the goal vertex for a robot with a limited gas tank and a limited number of refuelling stops. While GSP is polynomial-time solvable, it remains a challenge to quickly compute an optimal solution in practice since it requires simultaneously determine the path, where to make the stops, and the amount to refuel at each stop. This paper develops a heuristic search algorithm called Refuel A$^*$ (RF-A$^*$) that iteratively constructs partial solution paths from the start to the goal guided by a heuristic while leveraging dominance rules for pruning during planning. RF-A$^*$ is guaranteed to find an optimal solution and often runs 2 to 8 times faster than the existing approaches in large city maps with several hundreds of gas stations.

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arXiv2025

A Mixed-Integer Conic Program for the Moving-Target Traveling Salesman Problem based on a Graph of Convex Sets

This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once within their assigned time-windows, and returns to the depot. The formulation relies on the key idea that when the targets move along lines, their trajectories become convex sets within the space-time coordinate system. The problem then reduces to finding the shortest path within a graph of convex sets, subject to some speed constraints. We compare our formulation with the current state-of-the-art Mixed Integer Conic Program (MICP) solver for the MT-TSP. The experimental results show that our formulation outperforms the MICP for instances with up to 20 targets, with up to two orders of magnitude reduction in runtime, and up to a 60\% tighter optimality gap. We also show that the solution cost from the convex relaxation of our formulation provides significantly tighter lower bounds for the MT-TSP than the ones from the MICP.

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arXiv2024

C*: A New Bounding Approach for the Moving-Target Traveling Salesman Problem

We introduce a new bounding approach called Continuity* C*, which provides optimality guarantees for the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relaxes the continuity constraints on the agent's tour by partitioning the targets' trajectories into smaller segments. This allows the agent to arrive at any point within a segment and depart from any point in the same segment when visiting each target. This formulation enables us to pose the bounding problem as a Generalized Traveling Salesman Problem (GTSP) on a graph, where the cost of traveling along an edge requires solving a new problem called the Shortest Feasible Travel (SFT). We present various methods for computing bounds for the SFT problem, leading to several variants of C*. We first prove that the proposed algorithms provide valid lower-bounds for the MT-TSP. Additionally, we provide computational results to validate the performance of all C* variants on instances with up to 15 targets. For the special case where targets move along straight lines, we compare our C* variants with a mixed-integer Second Order Conic Program (SOCP) based method, the current state-of-the-art solver for the MT-TSP. While the SOCP-based method performs well on instances with 5 and 10 targets, C* outperforms it on instances with 15 targets. For the general case, on average, our approaches find feasible solutions within approximately 4.5% of the lower-bounds for the tested instances.

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arXiv2024

Heterogeneous Min-Max Multi-Vehicle Multi-Depot Traveling Salesman Problem: Heuristics and Computational Results

In this paper, a heuristic for a heterogeneous min-max multi-vehicle multi-depot traveling salesman problem is proposed, wherein heterogeneous vehicles start from given depot locations and need to cover a given set of targets. In the considered problem, vehicles can be structurally heterogeneous due to different vehicle speeds and/or functionally heterogeneous due to different vehicle-target assignments originating from different sensing capabilities of vehicles. The proposed heuristic for the considered problem has three stages: an initialization stage to generate an initial feasible solution, a local search stage to improve the incumbent solution by searching through different neighborhoods, and a perturbation/shaking stage, wherein the incumbent solution is perturbed to break from a local minimum. In this study, three types of neighborhood searches are employed. Furthermore, two different methods for constructing the initial feasible solution are considered, and multiple variations in the neighborhoods considered are explored in this study. The considered variations and construction methods are evaluated on a total of 128 instances generated with varying vehicle-to-target ratios, distribution for generating the targets, and vehicle-target assignment and are benchmarked against the best-known heuristic for this problem. Two heuristics were finally proposed based on the importance provided to objective value or computation time through extensive computational studies.

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