In this paper, we extend the interconnection and damping assignment passivity-based control strategy to systems subjected to nonholonomic Pfaffian constraints. The results are applied to stabilize the pitch dynamics of an underactuated mobile inverted pendulum (MIP) robot subjected to nonholonomic constraints arising out of no-slip conditions. A novel feature of this paper is that we reduce the kinetic energy partial differential equations and potential energy partial differential equation to a set of ordinary differential equations, that are explicitly solved. ©2009 IEEE.

Arun D. Mahindrakar

Department of Electrical Engineering

Interconnection and damping assignment

MOBILE INVERTED PENDULUM

NO-SLIP CONDITION

Non holonomic constraint

NONHOLONOMICS

Passivity based control

Pfaffian

PITCH DYNAMICS

Underactuated

Underactuated mechanical systems

Computational fluid dynamics

Damping

image segmentation

Partial differential equations

Passivation

Pendulums

Plasma waves

Ordinary differential equations

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Extending interconnection and damping assignment passivity-based control (IDA-PBC) to underactuated mechanical systems with nonholonomic Pfaffian constraints: The mobile inverted pendulum robot

Proceedings of the IEEE Conference on Decision and Control

The mobile inverted pendulum (MIP) is a mechanical system that presents multiple control challenges. In particular, two objectives, namely desired position control and stabilization of the unstable pendulum-like central body, need to be simultaneously met. In this brief, we propose a novel smooth time-invariant controller to achieve the twin objectives. A feature of the controller design is that it readily extends to achieve waypoint tracking, another interesting task for mobile platforms. To validate the theory developed, an MIP has been indigenously designed and fabricated. Extensive experiments on the MIP have been performed. It has been observed that the system accomplishes position stabilization as well as waypoint tracking with negligible error. © 2012 IEEE.

IEEE Transactions on Control Systems Technology

Position stabilization and waypoint tracking control of mobile inverted pendulum robot

IEEE Transactions on Robotics

Controllability and Posture Control of a Wheeled Pendulum Moving on an Inclined Plane

Velocity and position control of a wheeled inverted pendulum by partial feedback linearization

IEEE Transactions on Automatic Control

Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment

IEEE Transactions on Industrial Electronics

JOE: a mobile, inverted pendulum

Communications on Pure and Applied Mathematics

Control of nonlinear underactuated systems

Journal	Proceedings of the IEEE Conference on Decision and Control
ISSN	01912216
Open Access	No