Integrated mechanical and control design of underactuated multibody systems

Multibody systems are called underactuated if they have less control inputs than degrees of freedom, e.g. due to passive joints or body flexibility. For trajectory tracking of underactuated multibody systems often advanced modern nonlinear control techniques are necessary. The analysis of underactuated multibody systems might show that they possess internal dynamics. Feedback linearization is only possible if the internal dynamics remain bounded, i.e. the system is minimum phase. Also feed-forward control design for minimum phase systems is much easier to realize than for non-minimum phase systems. However, often the initial design of an underactuated multibody system is non-minimum phase. Therefore, in this paper a procedure for integrated mechanical and control design is proposed such that minimum phase underactuated multibody systems are obtained. Thereby an optimization-based design process is used, whereby the geometric dimensions and mass distribution of the multibody systems are altered.     

Control of underactuated mechanical systems with servo-constraints

This paper deals with a class of controlled mechanical systems in which the number of control inputs, equal to the number of desired system outputs, is smaller than the number of degrees of freedom. The related inverse dynamics control problem, i.e., the determination of control input strategy that force the underactuated system to complete the partly specified motion, is a challenging task. In the present formulation, the desired system outputs, expressed in terms of the system states, are treated as servo-constraints on the system, and the problem is viewed from the constrained motion perspective. Mixed orthogonal-tangent realization of the constraints by the available control reactions is stated, and a specialized methodology for solving the “singular” control problem is developed. The governing equations are manipulated to index three differential-algebraic equations, and a simple numerical code for solving the equations is proposed. The feedforward control law obtained as a solution to these equations can then be enhanced by a closed-loop control strategy with feedback of the actual servo-constraint violations to provide stable tracking of the reference motion in the presence of perturbations and modeling uncertainties. An overhead trolley crane executing a load-prescribed motion serves as an illustration. Some results of numerical simulations are reported.     

Correction to: Adaptive RBFNN finite-time control of normal forms for underactuated mechanical systems

Nonlinear Dynamics - The list of authors in the original publication was incomplete. The complete list of authors is shown here, including the third author, Faiçal Mnif.     

A controller for 2-DOF underactuated mechanical systems with discontinuous friction

We propose a controller for a class of 2-DOF underactuated mechanical systems with discontinuous friction in the unactuated joint. The control objective is the regulation of the unactuated variable while the position and speed of the actuated joint remain bounded. The unactuated joint is considered as a mechanical system with discontinuous friction but continuous, artificial control input given by a term depending on the actuated positions and velocities. The proposed controller guarantees the convergence of the position error of the unactuated joint to zero, and it is robust with respect to some uncertainty in the discontinuous friction coefficients. We illustrate the technique with its application to two systems.     

Tracking control for underactuated non-minimum phase multibody systems

Nonlinear Dynamics - We consider tracking control for multibody systems which are modeled using holonomic and non-holonomic constraints. Furthermore, the systems may be underactuated and contain...     

Combined open-loop and funnel control for underactuated multibody systems

Nonlinear Dynamics - We consider tracking control for multibody systems which are modeled using generalized coordinates. Utilizing the two-degree- of-freedom approach to controller design, we...     

Reduced normal forms for nonlinear control of underactuated hoisting systems

Nearly every cargo that is transported by ship is boxed in standardized containers. The land to ship and ship to land handling of containers is performed by container cranes. These cranes dominate the throughput of the containers in ports. The operators need to be well-trained and skilled because of the requirements of the task to load or unload the ships. During container handling, the crane-load system can be compared to a pendulum of rope length L and deflection f{\phi} . It is referred to as an underactuated system. Whenever the fixed point of the pendulum is displaced, the load starts oscillating. In the nonlinear dynamics literature, one finds the field of resonant coupling to transfer energy from actuated controllable modes to underactuated uncontrollable modes. This work presents a novel normal form approach in order to identify the mode coupling. The proposed method decomposes a nonlinear control system into controllable and uncontrollable subsystem. Only the normal form terms in the controllable subsystem are utilized to design a general controller. Simulation results are given to highlight the load oscillation suppression.     

Uniform ultimate boundedness for underactuated mechanical systems as mismatched uncertainty disappeared

Nonlinear Dynamics - We propose to design control for uncertain underactuated mechanical systems. The underactuated mechanical system is to follow prescribed holonomic or nonholonomic constraints....     

Sliding mode control with an extended disturbance observer for a class of underactuated system in cascaded form

Nonlinear Dynamics - A sliding mode controller based on an extended disturbance observer is investigated to control a class of underactuated system in this paper. By using strict feedback...     

Low-complexity robust tracking of high-order nonlinear systems with application to underactuated mechanical dynamics

This paper presents a low-complexity design approach with predefined transient and steady-state tracking performance for global practical tracking of uncertain high-order nonlinear systems. It is assumed that all nonlinearities and their bounding functions are unknown and the reference signal is time varying. A simple output tracking scheme consisting of nonlinearly transformed errors and positive design parameters is presented in the presence of virtual and actual control variables with high powers where the error transformation technique using time-varying performance functions is employed. Contrary to the existing results using known nonlinear bounding functions of model nonlinearities, the proposed tracking scheme can be implemented without using nonlinear bounding functions (i.e., the feedback domination design), any adaptive and function approximation techniques for estimating unknown nonlinearities. It is shown that the tracking performance of the proposed control system is ensured within preassigned bounds, regardless of high-power virtual and actual control variables. The motion tracking problem of an underactuated unstable mechanical system with unknown model parameters and nonlinearities is considered as a practical application, and simulation results are provided to show the effectiveness of the proposed theoretical result.     

Dynamic delayed feedback control for stabilizing the giant swing motions of an underactuated three-link gymnastic robot

This paper investigates the dynamics of the giant swing motions of an underactuated three-link gymnastic robot moving in a vertical plane by means of dynamic delayed feedback control (DDFC). DDFC, being one of useful methods to overcome the so-called odd number limitation in controlling a chaotic discrete-time system, is extended to control a continuous-time system such as a 3-link gymnastic robot with passive joint. Meanwhile, a way to calculate the error transfer matrix and the input matrix which are necessary for discretization is proposed, based on a Poincaré section which is defined to regard the target system as a discrete-time system. Moreover, the stability of the closed-loop system by the proposed control strategy is discussed. Furthermore, some numerical simulations are presented to show the effectiveness in controlling a chaotic motion of the 3-link gymnastic robot to a periodic giant swing motion.     

Parametrization of sets of stabilizing controllers in mechanical systems

Procedures to parametrize a set of stabilizing controllers are reviewed. These procedures are the key ones in the frequency-domain synthesis of the optimal (minimum H ₂-and H _∞-norms) controller or filter for a linear stationary system. A relationship between the parametrization procedures proposed by different authors is shown. Examples of parametrization procedures in synthesis problems (delay problems, multichannel filtering problems, etc.) are given __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 3–27, June 2008.     

Nonlinear control for teleoperation systems with time varying delay

In this paper, we introduce delay-dependent control strategies for bilateral teleoperation systems in the presence of passive and constant input forces under time varying delay. We first design teleoperation systems where the local and remote sites are coupled by position signals of the master and slave manipulator. The design also combined undelayed position and velocity signals with nonlinear adaptive control terms to deal with the parametric uncertainties associated with the dynamical model of the master and slave manipulator. Then, we develop teleoperators by delaying position and velocity signals of the master and slave manipulator. Using Lyapunov–Krasovskii function, delay-dependent stability and tracking conditions for both teleoperators are developed in the presence of symmetrical and unsymmetrical time varying delays. The stability conditions are established in the presence of passive and constant human and environment interaction forces with the master and slave manipulators. Finally, simulation results are presented to demonstrate the validity of the theoretical development of the proposed designs for real-time teleoperation applications.