arXiv subjects

Rajpal Singh

Publications and source records attributed to Rajpal Singh.

6 recordsLinked to original sources

arXiv2026

SACK : Safe Active Continual Koopman Learning for Uncertain Systems with Contractive Guarantees

Koopman operator theory provides a powerful framework for representing nonlinear dynamics through a linear operator acting on lifted observables, enabling the use of linear control techniques for nonlinear systems. However, Koopman models are typically learned from data and often degrade in performance under model uncertainty and distributional shifts between training and deployment. Although several works have explored online adaptation to address this issue, many rely on neural network-based updates that introduce significant computational overhead and lack formal safety guarantees, limiting their suitability for real-time and safety-critical robotic applications. In this work, we propose SACK, a unified framework for continual adaptive Koopman learning that enables safe and efficient online refinement of learned models during task execution. A Koopman model is first learned offline and subsequently refined online through a contractive adaptation law, which provides theoretical convergence guarantees under distributional shifts and model uncertainty. To improve data efficiency and accelerate model refinement, the adaptation mechanism is integrated with an active learning strategy that drives the system to collect informative data while accomplishing task objectives. The resulting control problem is formulated as a nonconvex optimization problem incorporating both active learning objectives and safety constraints. We further derive theoretical bounds on model approximation error and show how these bounds can be incorporated within a robust Model Predictive Control (MPC) framework to provide formal safety guarantees. To reduce conservatism in practice, we also introduce a conformal prediction-based tightening mechanism that calibrates safety margins online from observed residuals. Extensive simulation and experimental studies demonstrate efficacy of the proposed scheme.

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arXiv2026

Generalized Momenta-Based Koopman Formalism for Robust Control of Euler-Lagrangian Systems

This paper presents a novel Koopman operator formulation for Euler Lagrangian dynamics that employs an implicit generalized momentum-based state space representation, which decouples a known linear actuation channel from state dependent dynamics and makes the system more amenable to linear Koopman modeling. By leveraging this structural separation, the proposed formulation only requires to learn the unactuated dynamics rather than the complete actuation dependent system, thereby significantly reducing the number of learnable parameters, improving data efficiency, and lowering overall model complexity. In contrast, conventional explicit formulations inherently couple inputs with the state dependent terms in a nonlinear manner, making them more suitable for bilinear Koopman models, which are more computationally expensive to train and deploy. Notably, the proposed scheme enables the formulation of linear models that achieve superior prediction performance compared to conventional bilinear models while remaining substantially more efficient. To realize this framework, we present two neural network architectures that construct Koopman embeddings from actuated or unactuated data, enabling flexible and efficient modeling across different tasks. Robustness is ensured through the integration of a linear Generalized Extended State Observer (GESO), which explicitly estimates disturbances and compensates for them in real time. The combined momentum-based Koopman and GESO framework is validated through comprehensive trajectory tracking simulations and experiments on robotic manipulators, demonstrating superior accuracy, robustness, and learning efficiency relative to state of the art alternatives.

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arXiv2026

Deep Robust Koopman Learning from Noisy Data

Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However, real-world data is often noisy, making it difficult to obtain an accurate and unbiased approximation of the Koopman operator. The Koopman operator generated from noisy datasets is typically corrupted by noise-induced bias that severely degrades prediction and downstream tracking performance. In order to address this drawback, this paper proposes a novel autoencoder-based neural architecture to jointly learn the appropriate lifting functions and the reduced-bias Koopman operator from noisy data. The architecture initially learns the Koopman basis functions that are consistent for both the forward and backward temporal dynamics of the system. Subsequently, by utilizing the learned forward and backward temporal dynamics, the Koopman operator is synthesized with a reduced bias making the method more robust to noise compared to existing techniques. Theoretical analysis is used to demonstrate significant bias reduction in the presence of training noise. Dynamics prediction and tracking control simulations are conducted for multiple serial manipulator arms, including performance comparisons with leading alternative designs, to demonstrate its robustness under various noise levels. Experimental studies with the Franka FR3 7-DoF manipulator arm are further used to demonstrate the effectiveness of the proposed approach in a practical setting.

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arXiv2024

Adaptive Koopman Embedding for Robust Control of Complex Nonlinear Dynamical Systems

The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through data-driven methods, these algorithms often exhibit limitations in generalizability beyond the distribution captured by training data and are not robust to changes in the nominal system dynamics induced by intrinsic or environmental factors. To overcome these limitations, this study presents an adaptive Koopman architecture capable of responding to the changes in system dynamics online. The proposed framework initially employs an autoencoder-based neural network that utilizes input-output information from the nominal system to learn the corresponding Koopman embedding offline. Subsequently, we augment this nominal Koopman architecture with a feed-forward neural network that learns to modify the nominal dynamics in response to any deviation between the predicted and observed lifted states, leading to improved generalization and robustness to a wide range of uncertainties and disturbances compared to contemporary methods. Extensive tracking control simulations, which are undertaken by integrating the proposed scheme within a Model Predictive Control framework, are used to highlight its robustness against measurement noise, disturbances, and parametric variations in system dynamics.

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arXiv2024

Control Barrier Functions in Dynamic UAVs for Kinematic Obstacle Avoidance: A Collision Cone Approach

Unmanned aerial vehicles (UAVs), specifically quadrotors, have revolutionized various industries with their maneuverability and versatility, but their safe operation in dynamic environments heavily relies on effective collision avoidance techniques. This paper introduces a novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles. We propose a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision. By showing that the proposed constraint is a valid CBF for quadrotors, we are able to leverage its real-time implementation via Quadratic Programs (QPs), called the CBF-QPs. Validation includes PyBullet simulations and hardware experiments on Crazyflie 2.1, demonstrating effectiveness in static and moving obstacle scenarios. Comparative analysis with literature, especially higher order CBF-QPs, highlights the proposed approach's less conservative nature. Simulation and Hardware videos are available here: https://tayalmanan28.github.io/C3BF-UAV/

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arXiv2024

A Collision Cone Approach for Control Barrier Functions

This work presents a unified approach for collision avoidance using Collision-Cone Control Barrier Functions (CBFs) in both ground (UGV) and aerial (UAV) unmanned vehicles. We propose a novel CBF formulation inspired by collision cones, to ensure safety by constraining the relative velocity between the vehicle and the obstacle to always point away from each other. The efficacy of this approach is demonstrated through simulations and hardware implementations on the TurtleBot, Stoch-Jeep, and Crazyflie 2.1 quadrotor robot, showcasing its effectiveness in avoiding collisions with dynamic obstacles in both ground and aerial settings. The real-time controller is developed using CBF Quadratic Programs (CBF-QPs). Comparative analysis with the state-of-the-art CBFs highlights the less conservative nature of the proposed approach. Overall, this research contributes to a novel control formation that can give a guarantee for collision avoidance in unmanned vehicles by modifying the control inputs from existing path-planning controllers.

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