14,058 research outputs found
Differential-Flatness and Control of Quadrotor(s) with a Payload Suspended through Flexible Cable(s)
We present the coordinate-free dynamics of three different quadrotor systems
: (a) single quadrotor with a point-mass payload suspended through a flexible
cable; (b) multiple quadrotors with a shared point-mass payload suspended
through flexible cables; and (c) multiple quadrotors with a shared rigid-body
payload suspended through flexible cables. We model the flexible cable(s) as a
finite series of links with spherical joints with mass concentrated at the end
of each link. The resulting systems are thus high-dimensional with high
degree-of-underactuation. For each of these systems, we show that the dynamics
are differentially-flat, enabling planning of dynamically feasible
trajectories. For the single quadrotor with a point-mass payload suspended
through a flexible cable with five links (16 degrees-of-freedom and 12
degrees-of-underactuation), we use the coordinate-free dynamics to develop a
geometric variation-based linearized equations of motion about a desired
trajectory. We show that a finite-horizon linear quadratic regulator can be
used to track a desired trajectory with a relatively large region of
attraction
Configuration Flatness of Lagrangian Systems Underactuated by One Control
Lagrangian control systems that are differentially flat with flat outputs that only depend on configuration variables are said to be configuration flat. We provide a complete characterisation of configuration flatness for systems with n degrees of freedom and n - 1 controls whose range of control forces only depends on configuration and whose Lagrangian has the form of kinetic energy minus potential. The method presented allows us to determine if such a system is configuration flat and, if so provides a constructive method for finding all possible configuration flat outputs. Our characterisation relates configuration flatness to Riemannian geometry. We illustrate the method by two examples
Flat systems, equivalence and trajectory generation
Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft
A Test for Differential Flatness by Reduction to Single Input Systems
For nonlinear control systems (p inputs), we present a test for flatness. The method consists of making an initial guess for p-1 of the flat outputs, which may involve parameters still to be determined. A choice of functions of time for the p-1 outputs reduce the system to one with a single input. For single input systems the problem of flatness has been solved and thus leads to the identification of the last flat output, or to obstructions to flatness under the hypotheses. We demonstrate the method for a coupled rigid body in ā2 and for a single rigid body in ā3
Configuration Controllability of Simple Mechanical Control Systems
In this paper we present a definition of 'configuration controllability' for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is derived. This condition involves an object that we call the symmetric product. Of particular interest is a definition of 'equilibrium controllability' for which we are able to derive computable sufficient conditions. Examples illustrate the theory
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