We obtain an intrinsic vector-valued symmetric bilinear form that can be associated with an underactuated constrained mechanical control system. We determine properties of the form that serve as sufficient conditions for driving a constrained mechanical system underactuated by one control to an ǫ-neighborhood of rest from an arbitrary initial configuration and velocity. We also determine proper...

Underactuated manipulators are a class of robotic mechanisms where passive joints are present. By controlling only the motion of the active joints, it is possible to control the entire system. Our goal is to develop control schemes using both classical nonlinear and modern learning techniques for underactuated manipulators. To examine the validity of the approaches, we developed an experimental...

In this paper, we propose a sliding mode controller for a robot manipulator with passive joints. A robot manipulator with passive joints which are not equipped with any actuators is a kind of underactuated system. Underactuated systems have some advantages compared to fully-actuated ones. For example, they weigh less and consume less energy because they have smaller number of components than fu...

In this paper, a stability control strategy for underactuated biped robots is proposed based on imbalance degree. The dynamic models of single-leg support of underactuated biped robots are firstly illustrated. Based on the external disturbance force strength of the system, the motion process of an underactuated biped robot is partitioned into three stages according to the imbalance degree. In d...

This paper investigates the design of composite nonlinear feedback (CNF) control law for an underactuated gantry crane system to achieve positioning and anti-swing control. First, the dynamic model of a nonlinear underactuated gantry crane system is established by using the Euler-Lagrange modeling method. Then, the CNF control law is designed for the system to improve the anti-swing performance...

Underactuated systems are those processing fewer actuators than degrees of freedom. But generally they are difficult to control. In this paper we realize crawling motion by an underactuated robot. By changing the location of the fixed point of the robot to the environment, the constraint of the system is changed. Local accessibility of the system with changing the constraints as a nonhoronomic ...

A novel strategy to design time invariant motion controllers for underactuated mobile systems is applied to the position and attitude control of an underactuated 3D vehicle. The idea consists in defining a velocity vector field such that an ideal, fully actuated system would exponentially achieve the control objective by simply following such field. Then a steering law for the given underactuat...

In this paper, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms include three classes of cascade systems, namely, nonlinear systems in strict feedback form, feedforward form, and nontriangular quadratic form (to be defined). In each case, the transformation to cascade systems is provided in closed-form. We apply ou...

This paper presents a design framework for the stabilization of a class of underactuated mechanical systems. By utilizing nonregular static state feedbacks, these systems are transformed into a class of nonlinear systems with chain structures. Then, controller design is presented by applying the backstepping design technique. The design procedure is applied to an underactuated robotic system an...