arXiv subjects

Maruthi R. Akella

Publications and source records attributed to Maruthi R. Akella.

6 recordsLinked to original sources

arXiv2025

Non-Gaussian Distribution Steering in Nonlinear Dynamics with Conjugate Unscented Transformation

In highly nonlinear systems such as the ones commonly found in astrodynamics, Gaussian distributions generally evolve into non-Gaussian distributions. This paper introduces a method for effectively controlling non-Gaussian distributions in nonlinear environments using optimized linear feedback control. This paper utilizes Conjugate Unscented Transformation to quantify the higher-order statistical moments of non-Gaussian distributions. The formulation focuses on controlling and constraining the sigma points associated with the uncertainty quantification, which would thereby reflect the control of the entire distribution and constraints on the moments themselves. This paper develops an algorithm to solve this problem with sequential convex programming, and it is demonstrated through a two-body and three-body example. The examples show that individual moments can be directly controlled, and the moments are accurately approximated for non-Gaussian distributions throughout the controller's time horizon in nonlinear dynamics.

eess.SY↗

arXiv2023

Semi-global Exponential Stability for Dual Quaternion Based Rigid-Body Tracking Control

Semi-Global Exponential Stability (SGES) is proved for the combined attitude and position rigid body motion tracking problem, which was previously only known to be asymptotically stable. Dual quaternions are used to jointly represent the rotational and translation tracking error dynamics of the rigid body. A novel nonlinear feedback tracking controller is proposed and a Lyapunov based analysis is provided to prove the semi-global exponential stability of the closed-loop dynamics. Our analysis does not place any restrictions on the reference trajectory or the feedback gains. This stronger SGES result aids in further analyzing the robustness of the rigid body system by establishing Input-to-State Stability (ISS) in the presence of time-varying additive and bounded external disturbances. Motivated by the fact that in many aerospace applications, stringent adherence to safety constraints such as approach path and input constraints is critical for overall mission success, we present a framework for safe control of spacecraft that combines the proposed feedback controller with Control Barrier Functions. Numerical simulations are provided to verify the SGES and ISS results and also showcase the efficacy of the proposed nonlinear feedback controller in several non-trivial scenarios including the Mars Cube One (MarCO) mission, Apollo transposition and docking problem, Starship flip maneuver, collision avoidance of spherical robots, and the rendezvous of SpaceX Dragon 2 with the International Space Station.

eess.SY↗

arXiv2022

Feedback Strategies for Hypersonic Pursuit of a Ground Evader

In this paper, we present a game-theoretic feedback terminal guidance law for an autonomous, unpowered hypersonic pursuit vehicle that seeks to intercept an evading ground target whose motion is constrained in a one-dimensional space. We formulate this problem as a pursuit-evasion game whose saddle point solution is in general difficult to compute onboard the hypersonic vehicle due to its highly nonlinear dynamics. To overcome this computational complexity, we linearize the nonlinear hypersonic dynamics around a reference trajectory and subsequently utilize feedback control design techniques from Linear Quadratic Differential Games (LQDGs). In our proposed guidance algorithm, the hypersonic vehicle computes its open-loop optimal state and input trajectories off-line and prior to the commencement of the game. These trajectories are then used to linearize the nonlinear equations of hypersonic motion. Subsequently, using this linearized system model, we formulate an auxiliary two-player zero-sum LQDG which is effective in the neighborhood of the given reference trajectory and derive its feedback saddle point strategy that allows the hypersonic vehicle to modify its trajectory online in response to the target's evasive maneuvers. We provide numerical simulations to showcase the performance of our proposed guidance law.

eess.SY↗

arXiv2021

Riemannian Trust-Region based Adaptive Kalman filter with unknown noise Covariance matrices

The problem of adaptive Kalman filtering for a discrete observable linear time-varying system with unknown noise covariance matrices is addressed in this paper. The measurement difference autocovariance method is used to formulate a linear least squares cost function containing the measurements and the process and measurement noise covariance matrices. Subsequently, a Riemannian trust-region optimization approach is designed to minimize the least squares cost function and ensure symmetry and positive definiteness for the estimates of the noise covariance matrices. The noise covariance matrix estimates, under sufficient excitation of the system, are shown to converge to their unknown true values. Saliently, the exponential stability and convergence guarantees for the proposed adaptive Kalman filter to the optimal Kalman filter with known noise covariance matrices is shown to be achieved under the relatively mild assumptions of uniform observability and uniform controllability. Numerical simulations on a linear time-varying system demonstrate the effectiveness of the proposed adaptive filtering algorithm.

eess.SY↗

arXiv2021

Real-Time, Flight-Ready, Non-Cooperative Spacecraft Pose Estimation Using Monocular Imagery

A key requirement for autonomous on-orbit proximity operations is the estimation of a target spacecraft's relative pose (position and orientation). It is desirable to employ monocular cameras for this problem due to their low cost, weight, and power requirements. This work presents a novel convolutional neural network (CNN)-based monocular pose estimation system that achieves state-of-the-art accuracy with low computational demand. In combination with a Blender-based synthetic data generation scheme, the system demonstrates the ability to generalize from purely synthetic training data to real in-space imagery of the Northrop Grumman Enhanced Cygnus spacecraft. Additionally, the system achieves real-time performance on low-power flight-like hardware.

cs.CV↗

arXiv2014

Stabilizing Controllers for Multi-Input, Singular Control Gain Systems

This paper proposes a new methodology for design of a stabilizing control law for multi-input linear systems with time-varying, singular gains on the control. The results presented here assume the control gain to satisfy persistence of excitation which is a necessary condition for existence of stabilizing controllers in the presence of unstable drift. This work involves a novel persistence filter construction and provides a significant extension to the authors' previous result on stabilization of single-input linear systems with time-varying singular gains. An application to underactuated spacecraft stabilization is shown which illustrates the interesting features of the time-varying control design in stabilization of nonlinear dynamical systems. Finally, the development of an observer counterpart of these results is presented in the presence of multiple-outputs subject to singular measurement gains.

math.OC↗