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...

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 shows how to generate underactuated manipulators by substituting nonholonomic spherical pairs for (holonomic) spherical pairs in ordinary (i.e. not underactuated) manipulators. As a case study, an underactuated manipulator, previously proposed by one of the authors, is demonstrated to be generated, through this pair substitution from an inversion of the 6-3 fully parallel manipulator...

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...

The dexterity of a manipulator with passive joints, also known as an underactuated manipulator, differs from the dexterity of a fully actuated one, even if their mechanical structures are identical. Therefore, for fault tolerance and energy saving purposes, it is important to study the dexterity of underactuated manipulators. The purpose of this work is to quantify the dexterity of underactuate...

In this report, different control techniques for underactuated systems are considered. Underactuated systems are systems that have more degrees of freedom to be controlled than independent control inputs. Several control-techniques are considered for the point-to-point control of underactuated mechanical systems. After that, a control technique is considered for tracking control of underactuate...

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...

We introduce the notion of kinematic controllability for second-order underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collision-free trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by timeoptimal time scaling. While this approach is well know...

In this report, different control techniques for underactuated systems are considered. Underactuated systems are systems that have more degrees of freedom to be controlled than independent control inputs. Several control-techniques are considered for the point-to-point control of underactuated mechanical systems. After that, a control technique is considered for tracking control of underactuate...