In this paper we develop a robust controller based on variable structure systems (VSS) control theory for the stabilization of a class of Underactuated Mechanical Systems. This controller is based on a noncollocated partial feedback linearization of the underactuated system with a particular choice of the additional control for which the design is made using the sliding mode approach. Simulatio...

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...

Inspired by the previous work of Aicardi et al.[1] a path following controller for underactuated planar vehicles is designed by adopting a polar-like kinematic model of the system. The solution proposed does not generally guarantee null asymptotic path following error, but only its boundedness below an adjustable upper threshold. However, knowledge of the path curvature is not necessary, thus r...

In this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under-actuated left invariant mechanical systems on Lie groups. We exploit the invariance of the controlled nonlinear dynamics to the group action (symmetry) to derive a set of reduced dynamics for the system. We 3rst present su4cient conditions for the controllability of the redu...

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...

This paper describes how to use backstepping to develop control laws to perform trajectory tracking for a nonlinear, underactuated surface vessel. The research extends earlier backstepping designs for underactuated vessels by explaining how to select outputs when generalized forces act on the vessel. The resulting control law can correct orientation errors to track linear trajectories and can t...

This work is focused on the position control of an underactuated brachiation mobile robot with 3 links. We present the modeling of the dynamics of the robot and introduce the application of the nonlinear model-based predictive control (NMPC) to such a system. The robot has 3 revolute joints but only one of them is actuated, i. e., the robot has less control inputs than degrees of freedom. The i...

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...