A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

An underactuated mechanical system (UMS) is a system which has fewer independent control actuators than degrees of freedom to be controlled. Control of UMS is considered as one of the most active fields of research because of its diverse engineering applications. This survey reviews UMS from its history to the state-of-the-art research on modelling, classification, control, and to some extent, provides some unique insights for bottleneck issues and future research directions.

/pdf/a-survey-of-underactuated-mechanical-systems-4tw16vhjoz.pdf

A Survey of Underactuated Mechanical Systems

The problems of speed observation and position feedback stabilization of mechanical systems are addressed in this paper. Our interest is centered on systems that can be rendered linear in the velocities via a (partial) change of coordinates. It is shown that the class is fully characterized by the solvability of a set of partial differential equations (PDEs) and strictly contains the class studied in the existing literature on linearization for speed observation or control. A reduced order globally exponentially stable observer, constructed using the immersion and invariance methodology, is proposed. The design requires the solution of another set of PDEs, which are shown to be solvable in several practical examples. It is also proven that the full order observer with dynamic scaling recently proposed by Karagiannis and Astolfi obviates the need to solve the latter PDEs. Finally, it is shown that the observer can be used in conjunction with an asymptotically stabilizing full state--feedback interconnection and damping assignment passivity--based controller preserving asymptotic stability.

/pdf/speed-observation-and-position-feedback-stabilization-of-ztgij4pesy.pdf

Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems

Cable-suspended transportation is an important way of transferring goods and materials by rotorcraft in complex and hazardous environments, where external disturbances, system uncertainties, and, especially, the underactuated characteristic bring great challenges to realize safe and smooth deliveries. In terms of the aforementioned problems, this paper presents an enhanced coupling hierarchical control scheme for both quadrotor positioning and payload swing elimination. By exploiting the cascade property of quadrotor transportation systems, we can design controllers for the inner loop and the outer one separately, provided that the growth restriction condition is well satisfied, which greatly simplifies the design procedure. As the outer loop describes the quadrotor translation and payload swing motion, our central work focuses on the controller design of this subsystem. Specifically, a generalized payload signal is introduced to increase the state coupling, based on which we construct a novel energy storage function. Consequently, an energy coupling control law is proposed, which ensures that the equilibrium point of the system is asymptotically stable by using Lyapunov techniques and LaSalle's invariance theorem. Experimental results are presented to illustrate the superior control performance, even in the presence of external disturbances and parameter uncertainties.

A Novel Energy-Coupling-Based Hierarchical Control Approach for Unmanned Quadrotor Transportation Systems

The problem of robustification of interconnection and damping assignment passivity-based control for underactuated mechanical system vis-a-vis matched, constant, and unknown disturbances is addressed in the paper. This is achieved adding an outer-loop controller to the interconnection and damping assignment passivity-based control. Three designs are proposed, with the first one being a simple nonlinear PI, while the second and the third ones are nonlinear PIDs. While all controllers ensure stability of the desired equilibrium in spite of the presence of the disturbances, the inclusion of the derivative term allows us to inject further damping enlarging the class of systems for which asymptotic stability is ensured. Numerical simulations of the Acrobot system and experimental results on the disk-on-disk system illustrate the performance of the proposed controller. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Robust IDA‐PBC for underactuated mechanical systems subject to matched disturbances

Total energy shaping is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Lagrangian or Hamiltonian structure with a desired energy function - that qualifies as Lyapunov function for the desired equilibrium. The success of the method relies on the possibility of solving two PDEs which identify the kinetic and potential energy functions that can be assigned to the closed loop. Particularly troublesome is the partial differential equation (PDE) associated to the kinetic energy which is nonlinear and inhomogeneous and the solution, that defines the desired inertia matrix, must be positive-definite. In this note, we prove that we can eliminate or simplify the forcing term in this PDE by modifying the target dynamics and introducing a change of coordinates in the original system. Furthermore, it is shown that, in the particular case of transformation to the Lagrangian coordinates, the possibility of simplifying the PDEs is determined by the interaction between the Coriolis and centrifugal forces and the actuation structure. The examples of pendulum on a cart and Furuta's pendulum are used to illustrate the results.

http://www.esi2.us.es/~jaar/Datos/Articles/lhmnlc06.pdf

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Some Remarks on Interconnection and Damping Assignment Passivity‐ Based Control of Mechanical Systems

. We consider the problem of entanglement detection in the presence of faulty, potentially malicious detectors. A common—and, as of yet, the only—approach to this problem is to perform a Bell test in order to identify nonlocality of the measured entangled state. However, there are two signiﬁcant drawbacks in this approach: the requirement to exceed a critical, and often high, detection eﬃciency, and much lower noise tolerance. In this paper, we propose an alternative approach to this problem, which is resilient to the detection loophole and is based on the standard tool of entanglement witness. We discuss how the two main techniques to detection losses, namely the discard and assignment strategies, apply to entanglement witnessing. We demonstrate using the example of a two-qubit Bell state that the critical detection eﬃciency can be signiﬁcantly reduced compared to the Bell test approach.

pdf/entanglement-witnessing-with-untrusted-detectors-3tt8g3ig.pdf

Entanglement witnessing with untrusted detectors

The detection loophole , particularly the critical detection eﬃciencies of the spatially separated measurement devices, severely limit the distances over which nonlocal quantum correlations can be sustained in state-of-the-art Bell experiments. Instead of looking for quantum strategies with marginally lower threshold requirements, we exploit the properties of loophole-free nonlocal correlations, which are experimentally attainable today, albeit at short distances, to extend them over arbitrarily large distances. Speciﬁcally, we consider Bell experiments wherein the spatially separated parties randomly choose the location of their measurement devices in addition to their measurement settings. We demonstrate that when devices close to the source are perfect and witness extremal loophole-free nonlocal correlations, such correlations can be extended to devices with almost-zero detection eﬃciency and visibility placed arbitrarily far from the source. We then derive an analytic trade-oﬀ speciﬁc to the Clauser-Horne-Shimony-Holt Bell inequality: the higher the loophole-free nonlocality close to the source, the lower the threshold requirements away from the source. We utilize this trade-oﬀ and optimal quantum strategies to estimate the critical requirements of a measurement device placed away from the source. Finally, we formulate a versatile numerical method utilizing certiﬁable randomness to measure the nonlocal behaviour of individual measurement devices and estimate their critical parameters in generic network scenarios entailing several spatially separated measurement devices.

https://www.nature.com/articles/s41534-023-00799-1.pdf

Extending loophole-free nonlocal correlations to arbitrarily large distances

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Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Some Remarks on Interconnection and Damping Assignment Passivity‐ Based Control of Mechanical Systems

Entanglement witnessing with untrusted detectors

Extending loophole-free nonlocal correlations to arbitrarily large distances