In recent works, IDA-PBC has been succesfully applied to mechanical control problems with no physical damping present. In some cases, the friction terms can be obviated without compromising stability in closed loop. However in methods that modify the kinetic energy, a controller designed for stabilizing the undamped system might loose passivity, a key property for stabilization, when damping is...

This paper addresses the position tracking control problem of an underactuated hovercraft vehicle. A nonlinear Lyapunov-based tracking controller is developed and proved to exponentially stabilize the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be a specially chosen trajectory (e.g., a trimming trajectory). ...

This paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters. It is first shown that although the system is not asymptotically stabilizable to a given configuration using a time-invariant continuous feedback, it is strongly accessible and small-time locally controllable at any equilibrium. Time-invariant discon...

In this paper we study the dynamics and kinematics of manipulators that have fewer actuators than degrees of freedom. These under{actuated manipulators arise in a number of important applications such as free{ ying space robots, hyper{redundant manipulators, manipulators with structural exibility, etc. In our analysis we decompose such under{actuated manipulators into component active and passi...

In this paper, we consider the regulation control problem for an underactuated overhead crane system. Motivated by recent passivitybased controllers for underactuated systems, we design several controllers that asymptotically regulate the planar gantry position and the payload angle. Specifically, utilizing LaSalle’s invariant set theorem, we first illustrate how a simple proportional–derivativ...

A new digital control method for a time varying sampled data system called a variable period deadbeat control is proposed to control high order nonholonomic chained systems with drift terms. This control law has a potential to avoid an excessive overshoot to prevent the trajectories close to the singular manifold of the transformation needed to obtain the chained forms. The control will be appl...

In this paper, we present the design of a robust interconnection and damping assignment controller for a rolling-balancing system known as the disk-on-disk. The underactuation feature of this system hampers the control design, and since we consider matched disturbances, the problem becomes even more challenging. To overcome this difficulty, we propose to design first a controller to stabilize t...

This paper presents an Internal Model Control (IMC) structure designed for a class of continuous linear underactuated systems. The study treats the case of Minimum Phase (MP) systems and those whose zero dynamics are not necessarily stable. The proposed IMC structure is based on a specific controller which is obtained by the realization of an approximate inverse of the model plant. It is shown ...

The development of universal grippers able to pick up unfamiliar objects of widely varying shapes and surfaces is a very challenging task. Passively compliant underactuated mechanisms are one way to obtain the gripper which could accommodate any irregular and sensitive grasping object. The purpose of the underactuation is to use the power of one actuator to drive the opening and closing motion ...

This paper presents a systematic numerical algorithm to design optimal H∞ continuous-time controllers to robustly stabilize periodic orbits for hybrid dynamical systems in the presence of discrete-time uncertainties. A parameterized set of closed-loop hybrid systems is assumed for which there exists a common periodic orbit. The algorithm is created based on an iterative sequence of optimization...