Control Of Underactuated Mechanical Systems Research Articles

Passivity-based control of underactuated mechanical systems with Coulomb friction: Application to earthquake prevention

Passivity property gives a sense of energy balance. The classical definitions and theorems of passivity in dynamical systems require time invariance and locally Lipschitz functions. However, these conditions are not met in many systems. Characteristic examples are nonautonomous and discontinuous systems due to the presence of Coulomb friction. This paper presents an extended result for the negative feedback connection of two passive nonautonomous systems with set-valued right-hand side based on an invariance-like principle. Such extension is the base of a structural passivity-based control synthesis for underactuated mechanical systems with Coulomb friction. The first step consists of designing the control able to restore the passivity in the considered friction law, achieving stabilization of the system trajectories to a domain with zero velocities. Then, an integral action is included to improve the latter result and perform a tracking over a constant reference (regulation). Finally, the control is designed considering dynamics in the actuation. These control objectives are obtained using fewer control inputs than degrees of freedom, as a result of the underactuated nature of the plant. The presented control strategy is implemented in an earthquake prevention scenario, where a mature seismogenic fault represents the considered frictional underactuated mechanical system. Simulations are performed to show how the seismic energy can be slowly dissipated by tracking a slow reference, thanks to fluid injection far from the fault, accounting also for the slow dynamics of the fluid’s diffusion.

Adaptive total energy shaping of a class of manipulators

AbstractPoint‐to‐point control of underactuated mechanical systems is a challenging problem, especially if some of the system's parameters are uncertain. A popular method to stabilize underactuated manipulators is total energy shaping, in which a new Hamiltonian function is assigned to the closed‐loop system while a set of partial differential equations (PDEs) should be solved. In this study, an adaptive total energy shaping controller based on the approach called interconnection and damping assignment passivity‐based control (IDA‐PBC) for some underactuated robots is designed. The proposed method can overcome uncertainties in the dynamical parameters and also the parameters of the input mapping matrix under the satisfaction of the PDEs. The stability of the desired pose is ensured by the Lyapunov approach via suitable design of adaptation laws without the requirement for the persistence of excitation condition or other similar conditions. The results are applied to a 3‐DOF underactuated manipulator and verified by simulations.

Integral passivity‐based control of underactuated mechanical systems with state‐dependent matched disturbances

AbstractThis work investigates the energy shaping control of a class of underactuated mechanical systems subject to state‐dependent linearly parameterized matched disturbances. To this end, a new integral interconnection and damping‐assignment passivity‐based design is proposed. The controller design is developed for systems subject to either momenta‐dependent disturbances or position‐dependent disturbances or to both simultaneously. The effectiveness of the proposed approach is demonstrated with numerical simulations on three examples: an Acrobot system with nonlinear friction; a ball‐on‐beam system with constant and position‐dependent disturbances; a disk‐on‐disk system with a complete set of state‐dependent disturbances. In all examples, the proposed controller shows better performance compared to previous implementations.

An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System

In this paper, an adaptive technology and the interconnection and damping assignment passivity-based control method are combined to solve the stabilization problem for underactuated mechanical systems with uncertainties (including matched and unmatched). These uncertainties include unknown friction coefficients and unknown terms in kinetic energy and potential energy. A novel adaptive interconnection and damping assignment passivity-based control scheme is proposed and an adaptive stabilization controller is designed to make the closed-loop system locally stable. Verification is conducted on the ball and beam system. The locally asymptotic stability is demonstrated using the LaSalle’s invariance principle and approximate linearization. The effectiveness of the proposed control law is verified through numerical simulations.

Integral passivity‐based control of underactuated mechanical systems with actuator dynamics and constant disturbances

AbstractThis work investigates the energy shaping control of a class of underactuated mechanical systems with first‐order actuator dynamics and subject to both matched and unmatched constant additive disturbances. To this end, a new nonlinear control law which includes two independent integral actions is presented. The controller design is outlined for systems with first‐order actuator dynamics, and also for systems with direct actuation. The effectiveness of the proposed approach is demonstrated with numerical simulations on an inertia wheel pendulum and on a ball‐on‐beam system, both actuated by electric DC motors and subject to constant disturbances.

Energy shaping control of a class of underactuated mechanical systems with high-order actuator dynamics

In this work we present some new results on energy shaping control for underactuated mechanical systems with high-order actuator dynamics. To this end, we propose an extension of the Interconnection and damping assignment Passivity based control methodology to account for actuator dynamics. This brings the following new results: i) a potential and kinetic energy shaping and damping assignment procedure that yields two alternative controllers; ii) a potential energy shaping and damping assignment procedure for a narrower class of underactuated mechanical systems. The proposed approach is illustrated with numerical simulations on three examples: an Acrobot system with a series elastic actuator; a soft continuum manipulator actuated by electroactive polymers; a two-mass-spring system actuated by a DC motor.

Energy shaping control of underactuated mechanical systems with fluidic actuation

AbstractEnergy shaping is a remarkably effective control strategy which can be applied to a wide range of systems, including underactuated mechanical systems. However, research in this area has generally neglected actuator dynamics. While this is often appropriate, it might result in degraded performance in the case of fluidic actuation. In this work we present some new results on energy shaping control for underactuated mechanical systems for which the control action is mediated by a pressurized ideal fluid. In particular, we introduce an extended multi‐step energy shaping and damping‐assignment controller design procedure that builds upon the Interconnection‐and‐damping‐assignment Passivity‐based‐control methodology in a modular fashion to account for the pressure dynamics of the fluid. Stability conditions are assessed with a Lyapunov approach, the effect of disturbances is discussed, and the case of redundant actuators is illustrated. The proposed approach is demonstrated with numerical simulations for a modified version of the classical ball‐on‐beam example, which employs two identical cylinders, either hydraulic or pneumatic, to actuate the beam.

Data-driven passivity-based control of underactuated mechanical systems via interconnection and damping assignment

Since its introduction in the late 1980s, passivity-based control (PBC) has proven to be successful in controlling many robotic systems. The connection between stability and passivity theory is the most attractive feature of controllers designed using this methodology. However, the need to solve nonlinear partial differential equations (PDE) in closed-form has been a major challenge in applying PBC to general robotic systems. Here, we introduce a systematic approach to design controllers for a class of underactuated mechanical systems based on interconnection and damping assignment. Exploiting the universal approximation capability of neural networks, we formulate a data-driven optimisation problem that discovers solutions to the required PDEs automatically. Our approach does not destroy the passivity structure, preserving the inherent stability properties. We demonstrate the efficacy of our framework on two benchmark problems: the inertia wheel pendulum and the ball and beam system.

On closed-loop vibrational control of underactuated mechanical systems

On closed-loop vibrational control of underactuated mechanical systems

A speed regulator for a force-driven cart-pole system

In this paper, we present a speed regulator for a force-driven cart-pole system. The proposed controller allows bringing the pole towards its upright position, while the cart moves asymptotically at desired constant speed, recovering the position regulation when we assign a desired constant position of the cart. The main motivation for addressing speed regulation is to broaden the scope of control of underactuated mechanical systems, because so far, the control of this class of mechanical systems has been focused primarily on position regulation; and therefore, there is few information and results available on broader control objectives, such as speed regulation. In particular, we design a speed regulator for the cart-pole system, as this system is one of the more representative test benches of underactuated mechanical system found in many automatic control research laboratories. Another novelty is the introduction of an alternative energy shaping approach for the velocity control design of a class of underactuated mechanical systems. A complete asymptotic stability analysis based on the Lyapunov theory and the Barbashin–Krasovskii theorem is presented. Local asymptotic stability is concluded. Simulation results upon a force-driven cart-pole model illustrate the performance of the proposed controller.

Data-driven robust tracking control of underactuated mechanical systems using identified flat output and active disturbance rejection control

This paper presents a data-driven control design framework to achieve robust tracking without exploiting mathematical model of nonlinear underactuated mechanical systems (UMS). The method leverages differential flatness property of linearised systems, online estimation and compensation of disturbances by active disturbance rejection control. The differentially flat output is derived directly from measured data with unknown dynamics and parameters by the flat output identification algorithm. A reduced nominal model of UMS is proposed to simplify the process of finding flat output and trajectory planning. Technique of sparse regression is applied to identify relationships between flat output and system states, which reduce the order of the well-known extended state observer (ESO) and thereby make the ESO more effective for trajectory planning and tracking in terms of the flat output. The proposed control is validated by experimental studies of a rotary crane system in which a rest-to-rest tracking control is implemented.

ADAPTIVE WAVELETS SLIDING MODE CONTROL FOR A CLASS OF SECOND ORDER UNDERACTUATED MECHANICAL SYSTEMS

The control of underactuated mechanical systems (UMS) remains an attracting field where researchers can develop their control algorithms. To this date, various linear and nonlinear control techniques using classical and intelligent methods have been published in literature. In this work, an adaptive controller using sliding mode control (SMC) and wavelets network (WN) is proposed for a class of second-order UMS with two degrees of freedom (DOF).This adaptive control strategy takes advantage of both sliding mode control and wavelet properties. In the main result, we consider the case of un-modeled dynamics of the above-mentioned UMS, and we introduce a wavelets network to design an adaptive controller based on the SMC. The update algorithms are directly extracted by using the gradient descent method and conditions are then settled to achieve the required convergence performance.The efficacy of the proposed adaptive approach is demonstrated through an application to the pendubot.

Adaptive tracking control for underactuated mechanical systems with relative degree two

The adaptive tracking state-feedback control for underactuated mechanical systems with outputs characterized by global relative degree equal to two is addressed. A new control technique called virtual control is proposed. Fictitious control inputs and outputs are introduced to achieve full actuation: the key step is to find the reference signals for the fictitious outputs so that the resulting virtual adaptive controls are zero. The adaptive control of an underactuated three-link walking robot with unknown torso mass is designed according to the proposed control strategy. Simulations show that adaptation is crucial for stable walking.

Adaptive fractional-order fast terminal sliding mode with fault-tolerant control for underactuated mechanical systems: Application to tower cranes

We develop a robust controller for tracking a class of underactuated mechanical systems (UMSs) that considers many inconveniences, such as actuator faults, parametric uncertainties, and disturbances, by combining a fast terminal sliding mode with fractional derivatives and integrals. Despite these disadvantages and the lack of actuators, such a controller has some advantages, such as robustness, quick transient responses, finite-time convergence, and the flexibility of fractionally derivative orders. However, this control version still requires a complete knowledge of faults, parametric variations, and disturbances. Hence, to overcome these limitations, we improve the controller by integrating an adaptation estimator to approximate the necessary knowledge through an equivalently unique component. We apply the proposed controller to a Liebherr-130-HC tower crane, which is a highly underactuated system, to investigate control quality. Simulation and comparison of the results with the other control approaches, such as sliding mode control (SMC), terminal SMC, and parametric estimator-based SMC, are conducted to highlight the advantages of the proposed controller.

Gauss’s principle and tracking control of underactuated mechanical systems

Abstract Gauss’s principle of least constraint is used to derive equations of motion. The principle is then used to motivate a template for the closed loop of the (tracking) controlled system. The control law arises from minimization of the distance between the controlled model and the template in the sense of least constraint. The control template is derived and analysed for the example of a free rigid body. This leads to quite natural formulations of its controlled inertia, damping and stiffness. This template is then used to compute a controller for a quadcopter, an underactuated system. A simulation result for an aerobatic maneuver demonstrates quite good performance of the proposed controller even though there is no formal proof of stability.

Revisited adaptive sliding mode control of underactuated mechanical systems with real-time experiments

Revisited adaptive sliding mode control of underactuated mechanical systems with real-time experiments

Feed-forward control of total retrieval of the space tether from vertical position

This paper presents the results of studies of the feasibility of total and safe retrieval of a space tether of two bodies connected by an elastic, massless cable. The purpose of the research is to build up the control for the mode of the total and safe retrieval of the tether, which is one of the basic modes of its functioning. It allowed the development of the feed-forward control of the tether length or tension that provides demanded change of the angular momentum of the tether under the effect of the gravitational torque. The novelty of the research results consists also in the novel approach to the control of underactuated mechanical systems, which have the number of the control channels less than their degrees of freedom. Here the constraints on the tether angular motion relative to the pitch axis are introduced. They reduce the number of the system degrees of freedom and allow realizing the necessary mode of motion. For this control, only the remaining degree of freedom is used. The numerical simulation of the effect of the mode parameters on the tether motion is carried out for the tether in the chosen ranges of the parameters. The numerical example demonstrates the simplicity of the application of the method in practice. Plots illustrate the analysis of the results.

Revisited adaptive sliding mode control of underactuated mechanical systems with real-time experiments

Revisited adaptive sliding mode control of underactuated mechanical systems with real-time experiments

Adaptive Interconnection and Damping Assignment Passivity Based Control for Underactuated Mechanical Systems

Adaptive Interconnection and Damping Assignment Passivity Based Control for Underactuated Mechanical Systems

IDA-PBC with adaptive friction compensation for underactuated mechanical systems

In this work the control of underactuated mechanical systems with dry friction on actuated and unactuated joints is investigated. A new interconnection-and-damping-assignment passivity-based-control (IDA-PBC) design is presented, which includes the adaptive estimation of the friction forces and the introduction of a nonlinear dissipative term in the closed-loop system dynamics. As a result, the traditional IDA-PBC is complemented with an additional matching condition and the control law is augmented with a new term that accounts for the Coulomb friction forces on all joints. Two adaptive control paradigms are considered for comparison purposes and stability conditions are discussed. The control design is detailed for two demonstrative examples: the disk-on-disk system; the Acrobot system. The effectiveness of the proposed design is demonstrated with numerical simulations.