arXiv subjects

Arshiya Taj Abdul

Publications and source records attributed to Arshiya Taj Abdul.

6 recordsLinked to original sources

arXiv2026

cuNRTO: GPU-Accelerated Nonlinear Robust Trajectory Optimization

Robust trajectory optimization enables autonomous systems to operate safely under uncertainty by computing control policies that satisfy the constraints for all bounded disturbances. However, these problems often lead to large Second Order Conic Programming (SOCP) constraints, which are computationally expensive. In this work, we propose the CUDA Nonlinear Robust Trajectory Optimization (cuNRTO) framework by introducing two dynamic optimization architectures that have direct application to robust decision-making and are implemented on CUDA. The first architecture, NRTO-DR, leverages the Douglas-Rachford (DR) splitting method to solve the SOCP inner subproblems of NRTO, thereby significantly reducing the computational burden through parallel SOCP projections and sparse direct solves. The second architecture, NRTO-FullADMM, is a novel variant that further exploits the problem structure to improve scalability using the Alternating Direction Method of Multipliers (ADMM). Finally, we provide GPU implementations of the proposed methodologies using custom CUDA kernels for SOC projection steps and cuBLAS GEMM chains for feedback gain updates. We validate the performance of cuNRTO through simulated experiments on unicycle, quadcopter, and Franka manipulator models, demonstrating speedups of up to 139.6$\times$. More details are available at https://cunrto.github.io.

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arXiv2026

Distributed Covariance Steering via Non-Convex ADMM for Large-Scale Multi-Agent Systems

This paper studies the problem of steering large-scale multi-agent stochastic linear systems between Gaussian distributions under probabilistic collision avoidance constraints. We introduce a family of \textit{distributed covariance steering (DCS)} methods based on the Alternating Direction Method of Multipliers (ADMM), each offering different trade-offs between conservatism and computational efficiency. The first method, Full-Covariance-Consensus (FCC)-DCS, enforces consensus over both the means and covariances of neighboring agents, yielding the least conservative safe solutions. The second approach, Partial-Covariance-Consensus (PCC)-DCS, leverages the insight that safety can be maintained by exchanging only partial covariance information, reducing computational demands. The third method, Mean-Consensus (MC)-DCS, provides the most scalable alternative by requiring consensus only on mean states. Furthermore, we establish novel convergence guarantees for distributed ADMM with iteratively linearized non-convex constraints, covering a broad class of consensus optimization problems. This analysis proves convergence to stationary points for PCC-DCS and MC-DCS, while the convergence of FCC-DCS follows from standard ADMM theory. Simulations in 2D and 3D multi-agent environments verify safety, illustrate the trade-offs between methods, and demonstrate scalability to thousands of agents.

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arXiv2025

Scaling Robust Optimization for Swarms: A Distributed Perspective

This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall short in addressing uncertainties that are deterministic in nature or simply lack probabilistic data. To ensure safety under such scenarios, we employ the concept of robust constraints that must hold for all possible uncertainty realizations lying inside a bounded set. Nevertheless, standard robust optimization approaches become intractable due to the large number or non-convexity of the constraints involved in safe multi-agent control. To address this, we introduce novel robust reformulations that significantly reduce complexity without compromising safety. The applicability of the framework is further broadened to address both deterministic and stochastic uncertainties by incorporating robust chance constraints and distribution steering techniques. To achieve scalability, we derive a distributed approach based on the Alternating Direction Method of Multipliers (ADMM), supported by a convergence study that accounts for the underlying non-convexity. In addition, computational complexity bounds highlighting the efficiency of the proposed frameworks against standard approaches are presented. Finally, the robustness and scalability of the framework is demonstrated through extensive simulation results across diverse scenarios, including environments with nonconvex obstacles and up to 246 agents.

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arXiv2025

Nonlinear Robust Optimization for Planning and Control

This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with respect to all possible realizations of the disturbances within prescribed uncertainty sets. To address this problem, we introduce a bi-level optimization algorithm. The outer level employs a trust-region successive convexification approach which relies on linearizing the nonlinear dynamics and robust constraints. The inner level involves solving the resulting linearized robust optimization problems, for which we derive tractable convex reformulations and present an Augmented Lagrangian method for efficiently solving them. To further enhance the robustness of our methodology on nonlinear systems, we also illustrate that potential linearization errors can be effectively modeled as unknown disturbances as well. Simulation results verify the applicability of our approach in controlling nonlinear systems in a robust manner under unknown disturbances. The promise of effectively handling approximation errors in such successive linearization schemes from a robust optimization perspective is also highlighted.

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arXiv2025

Scaling Robust Optimization for Multi-Agent Robotic Systems: A Distributed Perspective

This paper presents a novel distributed robust optimization scheme for steering distributions of multi-agent systems under stochastic and deterministic uncertainty. Robust optimization is a subfield of optimization which aims to discover an optimal solution that remains robustly feasible for all possible realizations of the problem parameters within a given uncertainty set. Such approaches would naturally constitute an ideal candidate for multi-robot control, where in addition to stochastic noise, there might be exogenous deterministic disturbances. Nevertheless, as these methods are usually associated with significantly high computational demands, their application to multi-agent robotics has remained limited. The scope of this work is to propose a scalable robust optimization framework that effectively addresses both types of uncertainties, while retaining computational efficiency and scalability. In this direction, we provide tractable approximations for robust constraints that are relevant in multi-robot settings. Subsequently, we demonstrate how computations can be distributed through an Alternating Direction Method of Multipliers (ADMM) approach towards achieving scalability and communication efficiency. All improvements are also theoretically justified by establishing and comparing the resulting computational complexities. Simulation results highlight the performance of the proposed algorithm in effectively handling both stochastic and deterministic uncertainty in multi-robot systems. The scalability of the method is also emphasized by showcasing tasks with up to hundreds of agents. The results of this work indicate the promise of blending robust optimization, distribution steering and distributed optimization towards achieving scalable, safe and robust multi-robot control.

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arXiv2025

Deep Distributed Optimization for Large-Scale Quadratic Programming

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue to grow, the development of efficient and reliable QP algorithms is becoming increasingly vital. In this context, this paper introduces a novel deep learning-aided distributed optimization architecture designed for tackling large-scale QP problems. First, we combine the state-of-the-art Operator Splitting QP (OSQP) method with a consensus approach to derive DistributedQP, a new method tailored for network-structured problems, with convergence guarantees to optimality. Subsequently, we unfold this optimizer into a deep learning framework, leading to DeepDistributedQP, which leverages learned policies to accelerate reaching to desired accuracy within a restricted amount of iterations. Our approach is also theoretically grounded through Probably Approximately Correct (PAC)-Bayes theory, providing generalization bounds on the expected optimality gap for unseen problems. The proposed framework, as well as its centralized version DeepQP, significantly outperform their standard optimization counterparts on a variety of tasks such as randomly generated problems, optimal control, linear regression, transportation networks and others. Notably, DeepDistributedQP demonstrates strong generalization by training on small problems and scaling to solve much larger ones (up to 50K variables and 150K constraints) using the same policy. Moreover, it achieves orders-of-magnitude improvements in wall-clock time compared to OSQP. The certifiable performance guarantees of our approach are also demonstrated, ensuring higher-quality solutions over traditional optimizers.

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