arXiv subjects

Ravi N Banavar

Publications and source records attributed to Ravi N Banavar.

7 recordsLinked to original sources

arXiv2025

Numerical Integrators for Mechanical Systems on Lie Groups

Retraction maps are known to be the seed for all numerical integrators. These retraction maps-based integrators can be further lifted to tangent and cotangent bundles, giving rise to structure-preserving integrators for mechanical systems. We explore the particular case where the configuration space of our mechanical system is a Lie group with certain symmetries. Here, the integrator simplifies based on the property that the tangent and cotangent bundles of Lie groups are trivializable. Finally, we present a framework for designing numerical integrators for Euler- Poincare and Lie-Poisson type equations.

math.NA↗

arXiv2022

A Unified Framework for Consensus and Synchronization on Lie Groups admitting a Bi-Invariant Metric

For a finite number of agents evolving on a Euclidean space and linked to each other by a connected graph, the Laplacian flow that is based on the inter-agent errors, ensures consensus or synchronization for both first and second-order dynamics. When such agents evolve on a circle (the Kuramoto oscillator), the flow that depends on the sinusoid of the inter-agent error angles generalizes the same. In this work, it is shown that the Laplacian flow and the Kuramoto oscillator are special cases of a more general theory of consensus on Lie groups that admit bi-invariant metrics. Such a theory not only enables generalization of these consensus and synchronization algorithms to Lie groups but also provide insight on to the abstract group theoretic and differential geometric properties that ensures convergence in Euclidean space and the circle.

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arXiv2021

Geometric PID Controller for Stabilization of Nonholonomic Mechanical Systems on Lie Groups

The PID controller is an elegant and versatile controller for set point tracking in double integrator systems of which mechanical systems evolving on Euclidean space constitute a large class. But since mechanical systems are typically constrained interconnections of rigid bodies whose configuration space is $SE(3)$, which is not even topologically Euclidean, a geometric PID controller has been developed for mechanical systems evolving on Lie groups. In this work, we extend the framework to such systems which have nonholonomic constraints. It encompasses many practically applicable mechanical systems encountered in robotics as robots are constrained interconnections of rigid bodies where the constraints could either be holonomic or nonholonomic.

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arXiv2019

Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

The Wheeled Inverted Pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway. Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discrete-time constrained optimal control problem. Further, we describe a nonlinear continuous-time model with parameters for designing a closed loop LQ-controller. A dual control architecture is implemented in which the designed optimal trajectory is then provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQ-controller in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme.

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arXiv2019

Robust Attitude Tracking for Aerobatic Helicopters: A Geometric Approach

This paper highlights the significance of the rotor dynamics in control design for small-scale aerobatic helicopters, and proposes two singularity free robust attitude tracking controllers based on the available states for feedback. 1. The first, employs the angular velocity and the flap angle states (a variable that is not easy to measure) and uses a backstepping technique to design a robust compensator (BRC) to \textbf{\textit{actively}} suppress the disturbance induced tracking error. 2. The second exploits the inherent damping present in the helicopter dynamics leading to a structure preserving, \textbf{\textit{passively}} robust controller (SPR), which is free of angular velocity and flap angle feedback. The BRC controller is designed to be robust in the presence of two types of uncertainties: structured and unstructured. The structured disturbance is due to uncertainty in the rotor parameters, and the unstructured perturbation is modeled as an exogenous torque acting on the fuselage. The performance of the controller is demonstrated in the presence of both types of disturbances through numerical simulations. In contrast, the SPR tracking controller is derived such that the tracking error dynamics inherits the natural damping characteristic of the helicopter. The SPR controller is shown to be almost globally asymptotically stable and its performance is evaluated experimentally by performing aggressive flip maneuvers. Throughout the study, a nonlinear coupled rotor-fuselage helicopter model with first order flap dynamics is used.

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arXiv2017

The Principal Fiber Bundle Structure of the Gimbal-Spacecraft System

The gimbal-spacecraft system, that consists of a variable speed control moment gyro (VSCMG) mounted inside a spacecraft, has been employed as an actuator for the attitude control of a spacecraft and has been much studied in the aerospace control community. Employing a Newtonian approach, the equations of motion are derived, and further study focusses on singularity issues and control law synthesis. While the geometric mechanics community has studied many mechanical systems of engineering interest, including spinning rotors (or momentum wheels) that are used as actuators, there has not been a particular effort to model and control the gimbal-spacecraft system in a geometric framework. This article serves two purposes: it presents the gimbal-spacecraft system in a geometric mechanics framework, and in particular, highlights the connection form, that could form the basis for future control design, and secondly, the exposition is of a tutorial nature whereby the willing reader, with minimal prerequisites, is introduced to the tools of differential geometry in this context.

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arXiv2016

Circular orbit spacecraft control at the L4 point using Lyapunov functions

The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body problem (CRTBP). Incorporating the requirements of a fixed radius orbit and a desired angular momentum, a Lyapunov function is constructed and the requisite analysis is performed to obtain a controller. Asymptotic stability is proved in a defined region around the L4 point using LaSalle's principle.

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