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Techniques using gyroscopic forces and scalar potentials are used to create swarming behaviors for multiple agent systems. The methods result in collision avoidance between the agents as well as with obstacles.

The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identit

We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dyn

We propose a new dynamic extension of the thrust variable in the quadcopter dynamics that preserves the positive sign of the thrust. This extension not only eliminates the positive sign constraint on the thrust variable, but also leads to global chartwise feedback linearization of the quadcopter dynamics. For the latter, an atlas is first constructed on the entire state space of the quadcopter and then the dynamically extended quadcopter system is transformed to a 14-dimensional linear controlla

We derive closed-form solutions of electric fields, dielectrophoretic (DEP) forces, and time-averaged DEP forces in a parallel electrode array for three cases: first, the case of a two-phase DEP electrode array with a first-order approximate boundary condition; second, the case of a two-phase DEP electrode array with the exact boundary condition; and last, the case of a four-phase travelling wave DEP electrode array with a first-order approximate boundary condition. We also compare these analyti

We develop reduction theory for controlled Lagrangian and controlled Hamiltonian systems with symmetry. Reduction theory for these systems is needed in a variety of examples, such as a spacecraft with rotors, a heavy top with rotors, and underwater vehicle dynamics. One of our main results shows the equivalence of the method of reduced controlled Lagrangian systems and that of reduced controlled Hamiltonian systems in the case of simple mechanical systems with symmetry.

A novel method based on the techniques of differential flatness and dynamic feedback linearization is proposed to simultaneously control web tension, web transport velocity, and web displacement in the longitudinal direction in roll-to-roll web systems. Literature has mostly focused on the control of web tension and velocity, but has paid little attention to the control of web displacement. However, the control of the longitudinal displacement of web is important for register error reduction in

We study the method of controlled Lagrangians to stabilize mechanical systems connected with external forces. The basic idea is that we transform by feedback a given controlled Lagrangian system to another controlled Lagrangian system with positive definite energy and a dissipative external force such that a dissipative feedback force stabilizes the closed-loop system. We derive matching conditions for energy plus force shaping that are more general and stronger than those in the literature. We

Summary A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space , extend the system from M to the ambient space , and modify it outside M to add transversal stability to M in the final dynamics in . Controllers are designed for the final system in the ambient space . Then, their restriction to M produces controllers for the original system on M . This m

We provide some criteria for stabilizability by the energy-shaping method for the class of all controlled Lagrangian systems of two degrees of freedom and one degree of under-actuation: a necessary and sufficient condition for Lyapunov stabilizability, two sufficient conditions for asymptotic stabilizability, and a necessary and sufficient condition for exponential stabilizability. As a corollary, we show that some of the asymptotically stabilizing controllers that were designed in old literatur

Many control systems are mechanical systems. The unique feature of mechanical systems is the notion of energy, which gives much information on the stability of equilibria. Two kinds of forces are associated with the energy: dissipative force and gyroscopic force. A dissipative force is, by definition, a force which decreases the energy, and a gyroscopic force is, by definition, a force that does not change the energy. Gyroscopic forces add couplings to the dynamics. In this thesis, we develop a