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

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Guidance And Control Of Ocean Vehicles

http://webpages.lss.supelec.fr/perso/ortega/papers/eloisa_ejc04.pdf

Interconnection and damping assignment passivity-based control: a survey

Aerial manipulation aims at combining the versatility and the agility of some aerial platforms with the manipulation capabilities of robotic arms. This letter tries to collect the results reached by the research community so far within the field of aerial manipulation, especially from the technological and control point of view. A brief literature review of general aerial robotics and space manipulation is carried out as well.

/pdf/aerial-manipulation-a-literature-review-2gq2uh3t8a.pdf

Aerial Manipulation: A Literature Review

We present a constructive tool for generation and orbital stabilization of periodic solutions for underactuated nonlinear systems. Our method can be applied to any mechanical system with a number of independent actuators smaller than the number of degrees of freedom by one. The synthesized feedback control law is nonlinear and time-dependent. It is derived from a feedback structure that explicitly uses the general or full integral of the systems zero dynamics. The control law generates a periodic solution and makes it exponentially orbitally stable.

Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach

We consider the problem of (asymptotic) stabilization of mechanical systems with underactuation degree one. A state-feedback design is derived applying the interconnection and damping assignment passivity-based control methodology. Its application relies on the possibility of solving a set of partial differential equations that identify the energy functions that can be assigned to the closed-loop. The following results are established: 1) identification - in terms of some algebraic inequalities - of a subclass of these systems for which the partial differential equations are trivially solved; 2) characterization of all systems which are feedback-equivalent to this subclass; and 3) introduction of a suitable parametrization of the assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. An additional feature of our developments is that the open-loop system need not be described by a port-controlled Hamiltonian (or Lagrangian) model, a situation that arises often in applications due to model reductions or preliminary feedbacks that destroy the structure. The new result is applied to obtain an (almost) globally stabilizing controller for the inertia wheel pendulum, a controller for the chariot with pendulum system that can swing-up the pendulum from any position in the upper half plane and stop the chariot at any desired location, and an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling. In all cases we obtain very simple and intuitive solutions that do not rely on, rather unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with desired potential and kinetic energy functions.

/pdf/interconnection-and-damping-assignment-passivity-based-4jcynay9a2.pdf

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

This paper presents the design and control of a multirotor-based aerial manipulator developed for outdoor operation. The multi-rotor has eight rotors and large payload to integrate a 7-degrees of freedom arm and to carry sensors and processing hardware needed for outdoor positioning. The arm can also carry an end-effector and sensors to perform different missions. The paper focuses on the control design and implementation aspects. A stable backstepping-based controller for the multirotor that uses the coupled full dynamic model is proposed, and an admittance controller for the manipulator arm is outlined. Several experimental tests with the aerial manipulator are also presented. In one of the experiments, the performance of the pitch attitude controller is compared to a PID controller. Other experiments of the arm controller following an object with the camera are also presented.

Control of a multirotor outdoor aerial manipulator

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

Furuta's pendulum has been an excellent benchmark for the automatic control community in the last years, providing, among others, a better understanding of model-based Nonlinear Control Techniques. Since most of these techniques are based on invariants and/or integrals of motion then, the dynamic model plays an important role. This paper describes, in detail, the successful dynamical model developed for the available laboratory pendulum. The success relies on a basic dynamical model derived from Classical Mechanics which has been augmented to compensate the non-conservative torques. Thus, the quasi-conservative “practical” model developed allows to design all the controllers as if the system was strictly conservative. A survey of all the nonlinear controllers designed and experimentally tested on the available laboratory pendulum is also reported.

/pdf/furuta-s-pendulum-a-conservative-nonlinear-model-for-theory-2za6twah9r.pdf

José Ángel Acosta

Papers

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Control of a multirotor outdoor aerial manipulator

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

Furuta's Pendulum: A Conservative Nonlinear Model for Theory and Practise

Brief paper: A constructive solution for stabilization via immersion and invariance: The cart and pendulum system