Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

This paper presents a geometric finite-time inner-outer loop control strategy for slung payload transportation using a quadrotor. The underactuated nature of the quadrotor in conjunction with the cable connection makes it impossible to simultaneously and arbitrarily track the load position, cable direction and the quadrotor’s attitude. By exploiting the differential flatness of the system dynamics, it is possible to arbitrarily control the load position, with the cable direction and quadrotor attitude remaining dependent on the trajectory and controller dynamics. A two-loop feedback control strategy is proposed comprising an inner-loop control law addressing quadrotor attitude tracking within finite time, and an outer-loop controller addressing the stabilization of the cable direction and position tracking of the payload trajectory. The control laws are expressed in a coordinate-free setting and are singularity-free. We include the effects of unmodeled dynamics on the load system and design an adaptive estimator to estimate and reject such uncertainties. The performance and robustness of the feedback laws is demonstrated through numerical simulations and experimental results. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.

Department of Electrical Engineering

World University root node

Nonlinear Dynamics

Geometric finite-time inner-outer loop trajectory tracking control strategy for quadrotor slung-load transportation

The Poincaré representation of equations of motion provides a global characterization of the dynamics of a rigid body subjected to external torques. We use this representation to obtain the global dynamics of a spherical robot with three independent internal rotors rolling on a plane. The robot is subjected to nonholonomic constraints arising out of pure rolling motion. The dynamics of the system is obtained by projecting the kinematic vector fields on the constrained distribution using the nonholonomic affine connection. The rotor torques are incorporated into the dynamics by way of the total angular momentum of the robot about the point of contact. © 2018 IEEE.

2018 Indian Control Conference, ICC 2018 - Proceedings

Poincaré representation of the equations of motion of a spherical robot actuated by internal rotors

The purpose of this article is to illustrate the role of connections and symmetries in the Wheeled Inverted Pendulum (WIP) mechanism—an underactuated system with rolling constraints—popularized commercially as the Segway, and thereby arrive at a set of simpler dynamical equations that could serve as the starting point for more complex feedback control designs. The first part of the article views the nonholonomic constraints enforced by the rolling assumption as defining an Ehresmann connection on a fiber bundle. The resulting equations are the reduced Euler Lagrange equations, which are identical to the Lagrange–d’Alembert equations of motion. In the second part, we explore conserved quantities, in particular, nonholonomic momenta. To do so, we first introduce the notion of a symmetry group, whose action leaves both the Lagrangian and distribution invariant. We examine two symmetry groups—SE(2) and SE(2) × S1. The first group leads to the purely kinematic case while the second gives rise to nonholonomic momentum equations. © 2017, Springer Science+Business Media B.V.

Fulltext

Symmetries in the wheeled inverted pendulum mechanism

In this paper, we present the modeling and local equilibrium controllability analysis of a spherical robot. The robot consists of a spherical shell that is internally actuated by a pendulum mechanism. The rolling motion of the sphere manifests itself as a nonholonomic constraint in the modeling. We derive the dynamic model of the system using Lagrangian reduction and the variational principle. We first compute the Lagrangian and identify the symmetry with respect to a group action. The system Lagrangian and the rolling constraint are invariant with respect to the group isotropy and hence permit a reduced dynamic formulation termed as the nonholonomic 'Euler-Poincaré' equation with advected dynamics. Using Lie brackets and symmetric products of the potential and control vector fields, local configuration accessibility and local (fiber) equilibrium controllability are presented. © 2015 John Wiley & Sons, Ltd.

International Journal of Robust and Nonlinear Control

Geometric modeling and local controllability of a spherical mobile robot actuated by an internal pendulum

This paper presents tracking control laws for two different objectives of a nonholonomic system - a spherical robot - using a geometric approach. The first control law addresses orientation tracking using a modified trace potential function. The second law addresses contact position tracking using a right transport map for the angular velocity error. A special case of this is position and reduced orientation stabilization. Both control laws are coordinate free. The performance of the feedback control laws are demonstrated through simulations. © 2016

IFAC-PapersOnLine

Geometric tracking control for a nonholonomic system: a spherical robot

This paper presents a geometric framework for analysis of dynamics of flapping wing micro aerial vehicles (FWMAV) which achieve locomotion in the special Euclidean group SE(3) using internal shape changes. We review the special structure of the configuration manifold of such systems. This work addresses to extend the work in geometric locomotion to the aerial locomotion problem. Furthermore, there seems to be limited work in modelling of flapping wing bodies in a geometric framework. We derive the dynamic model of the FWMAV using Lagrangian reduction theory defined on symmetry groups. The reduction is achieved by applying Hamilton's variation principle on a reduced Lagrangian. The resultant dynamics is governed by the Euler-Poincare and Euler-Lagrange equations.

arXiv preprint arXiv:1511.

A geometric approach to the dynamics of flapping wing micro aerial vehicles: Modelling and reduction

This paper develops the equations of motion in the reduced space for the wheeled inverted pendulum, which is an underactuated mechanical system subject to nonholonomic constraints. The equations are derived from the Lagrange-d'Alembert principle using variations consistent with the constraints. The equations are first derived in the shape space, and then, a coordinate transformation is performed to get the equations of motion in more suitable coordinates for the purpose of control. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Reduced equations of motion for a wheeled inverted pendulum

This paper presents tracking control laws for two different objectives of a nonholonomic system - a spherical robot - using a geometric approach. The first control law addresses orientation tracking using a modified trace potential function. The second law addresses contact position tracking using a $right$ transport map for the angular velocity error. A special case of this is position and reduced orientation stabilization. Both control laws are coordinate free. The performance of the feedback control laws are demonstrated through simulations.

Geometric approach to tracking and stabilization for a spherical robot actuated by internal rotors

In this paper, we present local equilibrium configuration controllability analysis of a spherical robot. The robot is actuated by the principle of displacing the center of gravity of the system using an internal mechanism. The system is defined on a trivial principal fiber bundle, characterized by base body motion and the shape dynamics, and the equations of motion are in the form of the nonholonomic Euler-Poincaré equation with advected dynamics. Using Lie brackets and symmetric products of the potential and control vector fields, local configuration accessibility and local (fiber) equilibrium controllability are presented. © 2013 IEEE.

Proceedings of the IEEE Conference on Decision and Control

Local equilibrium controllability of a spherical robot actuated by a pendulum

Mechanical systems with rolling constraints form a class of nonholonomic systems. In this paper we derive the dynamic model of a spherical robot, which has been designed and realized in our laboratory, using Lagrangian reduction theory defined on symmetry groups. The reduction is achieved by applying Hamilton's variation principle on a reduced Lagrangian and then imposing the nonholonomic constraints. The equations of motion are in the Euler-Poincaré form and are equivalent to those obtained using Lagrange-d'Alembert's principle. © 2012 IFAC.