Linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. The specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. The basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...

This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are...

This paper studies the problem of modeling and control of multiple cooperative underactuated manipulators handling a rigid object. A single underactuated manipulator is a nonholonomic system in most cases, but cooperative underactuated manipulator systems may not. We reveal holonomic property of such a system by presenting a smooth feedback controller subject to two conditions: 1) there are not...

linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. the specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. the basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...

This thesis is devoted to nonlinear control, reduction, and classification of underactuated mechanical systems. Underactuated systems are mechanical control systems with fewer controls than the number of configuration variables. Control of underactuated systems is currently an active field of research due to their broad applications in Robotics, Aerospace Vehicles, and Marine Vehicles. The exam...

This thesis is devoted to nonlinear control, reduction, and classification of underactuated mechanical systems. Underactuated systems are mechanical control systems with fewer controls than the number of configuration variables. Control of underactuated systems is currently an active field of research due to their broad applications in Robotics, Aerospace Vehicles, and Marine Vehicles. The exam...

There are many interesting mathematical problems in control theory. In this paper we will discuss problems and techniques related to underactuated systems. An underactuated system is one with fewer control inputs than degrees of freedom. Balancing a ruler on the tip of a finger is a good example of an underactuated system. This system has five degrees of freedom (three for the fingertip and two...

The control of underactuated mechanical system is very complex for the loss of its control inputs. The model of underactuated mechanical systems in a potential field is built with Lagrangian method and its structural properties are analyzed in detail. A genetic algorithm (GA)based stable control approach is proposed for the class of underactuated mechanical systems. The Lyapunov stability theor...

This paper investigates the in-hand manipulation capabilities of a compliant, underactuated planar robotic hand by treating the system as a simple, symmetric, 6-bar linkage mechanism with compliant joints. Although underactuated hands are generally not considered to be adept at dexterous tasks, we have found through past work that an underactuated manipulator can control n degrees of freedom wi...

For a class of second order underactuated mechanical systems, a robust finite time control strategy is developed in this paper. The robust finite time controller is to drive the tracking error to be zero at the fixed final time. In order to assure system stability, we present a generalized Lyapunov stability proof for the second order underactuated mechanical system. By utilizing a Lyapunov sta...