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

Muralidharan, Vijay; Ravichandran, Maruthi T.; Mahindrakar, Arun D.

doi:10.1109/cdc.2009.5399890

Cited by 12 publications

(6 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We also formulate conditions to guarantee asymptotic stability and also show a procedure to estimate the domain of attraction. Although in one study an IDA-PBC controller was derived for a three-dimensional MIP, only the pendulum angle was stabilized (Muralidharan et al, 2009). The stability of the other states was not considered, and the procedure to solve the PDEs was different from this study.…”

Section: Introductionmentioning

confidence: 89%

Passivity-Based Nonlinear Stabilizing Control for a Mobile Inverted Pendulum

Yokoyama

Takahashi²

2011

Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics

View full text Add to dashboard Cite

Mobile inverted pendulums (MIPs) need to be stabilized at all times using a reliable control method. Previous studies were based on a linearized model or feedback linearization. In this study, interconnection and damping assignment passivity-based control (IDA-PBC) is applied. The IDA-PBC is a nonlinear control method which has been shown to be powerful in stabilizing underactuated mechanical systems. Although partial differential equations (PDEs) must be solved to derive the IDA-PBC controller and this is a difficult task in general, we show that the IDA-PBC controller for the MIP can be derived solving the PDEs. We also formulate conditions which must be satisfied to guarantee asymptotic stability and show a procedure to estimate the domain of attraction. Simulation results indicate that the IDA-PBC controller achieves fast performance theoretically ensuring a large domain of attraction. We also verify its effectiveness in experiments. In particular control performance under an impulsive disturbance to the MIP are verified. The IDA-PBC achieves as fast transient performance as a linear-quadratic regulator (LQR). In addition, we show that even when the pendulum declines quickly and largely because of the disturbance, the IDA-PBC controller is able to stabilize it whereas the LQR can not.

show abstract

Section: Introductionmentioning

confidence: 89%

Passivity-Based Nonlinear Stabilizing Control for a Mobile Inverted Pendulum

Yokoyama

Takahashi²

2011

Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics

View full text Add to dashboard Cite

show abstract

“…The first general adaptation to nonholonomic systems is found in Blankenstein (2002) considering nonholonomic systems that may be underactuated in the constrained space. Assuming that the nonholonomic systems we are interested in are fullyactuated in the constrained space, the desired dynamics can take the following form as in Muralidharan et al (2009):…”

Section: Ida-pbc For a Class Of Nonholonomic Mechanical Systemsmentioning

confidence: 99%

Distributed IDA-PBC for a Class of Nonholonomic Mechanical Systems

Tsolakis

Keviczky

2021

IFAC-PapersOnLine

View full text Add to dashboard Cite

“…The idea of shaping the energy can also be expanded to mechanical systems subject to nonholonomic constraints: Maschke and Van der Schaft [1994] stabilize nonholonomic systems by shaping the potential energy. Muralidharan et al [2009] stabilize the pitch dynamics of the WIP through IDA-PBC.…”

Section: Existing Workmentioning

confidence: 99%

“…Since the matrix C is solely defined by the Christoffel symbols ofM , the matching of the systems (6) and (7) requires, in general, additional gyroscopic forcesĴ ν, whereĴ = −Ĵ T , which are mistakently missing in Muralidharan et al [2009] for imposing the constraints before taking variations in the derivation of the equations of motion (see Bloch [2003]). …”

Section: Modelingmentioning

confidence: 99%

Energy shaping for the robust stabilization of a wheeled inverted pendulum

Delgado

Kotyczka

2015

IFAC-PapersOnLine

View full text Add to dashboard Cite

The paper deals with the robust energy-based stabilization of a wheeled inverted pendulum, which is an underactuated, unstable mechanical system subject to nonholonomic constraints. The equilibrium to be stabilized is characterized by the length of the driven path, the orientation, and the pitch angle. We use the method of Controlled Lagrangians which is applied in a systematic way, and is very intuitive, for it is physically motivated. After a detailed presentation of the model under nonholonomic constraints, we provide an elegant solution of the matching equations for kinetic and potential energy shaping for the considered systems. Simulations show the applicability and robustness of the method.

show abstract

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

Cited by 12 publications

References 9 publications

Passivity-Based Nonlinear Stabilizing Control for a Mobile Inverted Pendulum

Passivity-Based Nonlinear Stabilizing Control for a Mobile Inverted Pendulum

Distributed IDA-PBC for a Class of Nonholonomic Mechanical Systems

Energy shaping for the robust stabilization of a wheeled inverted pendulum

Contact Info

Product

Resources

About