This paper deals with the inverse dynamics problem of underactuated mechanical systems subjected to execute partly specified motions. The modeling methodology focuses on a special class of differentially flat systems, represented by a group of relevant technical examples. The governing equations are obtained as index three differential-algebraic equations, and a simple numerical code for their ...

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...

In this paper, two nonlinear H∞ control techniques are used to solve the position control problem of underactuated cooperative manipulators. The first technique consists in representing the nonlinear system in a quasi-linear parameter varying form and the solution is given in terms of linear matrix inequalities. The second technique gives an explicit solution to the cooperative manipulators H∞ ...

Abstract—The problem of finding control laws for underactuated systems has attracted growing attention since these systems are characterized by the fact that they have fewer actuators than the degrees of freedom to be controlled. The acrobot, which is a planar two-link robotic arm in the vertical plane with an actuator at the elbow but no actuator at the shoulder, is a representative in underac...

This paper presents a discrete sliding mode observer (DSMO) for state estimation of a class of a second order underactuated system. The estimated states are used to implement the discrete sliding mode control (DSMC). Modified Bartoszewicz’s reaching law is used to synthesize a DSMC. A partially filled liquid container motion coupled with liquid slosh constitutes a class of second order underact...

This paper builds off of recent work on rapidly exponentially stabilizing control Lyapunov functions (RES-CLF) and control Lyapunov function based quadratic programs (CLFQP) for underactuated hybrid systems. The primary contribution of this paper is developing a robust control technique for underactuated hybrid systems with application to bipedal walking, that is able to track desired trajector...

The control of nonholonomic and underactuated systems with symmetry is illustrated by the problem of controlling a bicycle. We derive a controller which, using steering and rear-wheel torque, causes a model of a riderless bicycle to recover its balance from a near fall as well as converge to a time parameterized path in the ground plane. Our construction utilizes new results for both the deriva...

We consider the problem of feasible trajectory generation of an underactuated axi-symmetric spacecraft subject to two external torques acting on the plane normal to the symmetry axis. We derive the condition that must be satissed by an attitude history in order to be a feasible trajectory. W e then propose a methodology to generate trajectories satisfying this condition. Our approach makes use ...

Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motion of the ball. The task is nontrivial due to the discrete-continuous nature of the corresponding dynamics. This paper proposes to add an elastic element to the manipulator so the ball can be controlled in a continuous-time phase instead of an intermittent contact. ...

A control method without state feedback of the free link is proposed for swing-up and stabilization at the upright position of a flexible free link in a twolink underactuated flexible manipulator (the active first and free second links are rigid and flexible, respectively). The proposed method is based on the actuation of bifurcations produced in the second link under high-frequency excitation ...