Manfredi Maggiore

Necessary and sufficient graphical conditions for formation control of unicycles

The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node. A similar result is given for formation stabilization to a line and to more general geometric arrangements.

State Agreement for Continuous-Time Coupled Nonlinear Systems

Two related problems are treated in continuous time. First, the state agreement problem is studied for coupled nonlinear differential equations. The vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems. Generalizing the work of Moreau, under the assumption that the vector fields satisfy a certain subtangentiality condition, it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time. The proof uses nonsmooth analysis. Second, the rendezvous problem for kinematic point-mass mobile robots is studied when the robots’ fields of view have a fixed radius. The circumcenter control law of Ando e [IEEE Trans. Robotics Automation, 15 (1999), pp. 818-828] is shown to solve the problem. The rendezvous problem is a kind of state agreement problem, but the interaction structure is state dependent.

Control Methodology to Mitigate the Grid Impact of Wind Turbines

This paper introduces a new control topology for converter-interfaced wind turbines. Through a singular perturbation decomposition of the system dynamics, a controller is designed that isolates wind-power fluctuations from the power grid. Specifically, the controller causes the closed-loop wind turbine to behave as a simple first-order power filter, where power injected into the grid is a low-pass filtered version of the incident wind power. It is shown that a turbine hub-speed instability imposes a limit on the largest filtering time constant that may be safely implemented. A linearized analysis is used to calculate how a small filter time constant can be implemented to obtain regulation of the tip-speed ratio for the widest range of frequencies. The methodology thus offers the possibility to either deliver a filtered power at suboptimal conversion efficiency or track peak wind power. It is mathematically demonstrated that the control structure achieves the regulation of torsional dynamics and the dc-link capacitor voltage without involving the grid-side converter controls, thus eliminating the influence of those dynamics on the grid. Simulation studies are used to demonstrate the methodologys viability and explore the associated tradeoffs.

Path following for the PVTOL aircraft

This article presents a solution to the path following problem for the planar vertical take-off and landing aircraft (PVTOL) which is applicable to a class of smooth Jordan curves. Our path following methodology enjoys the two properties of output invariance of the path (i.e., if the PVTOLs centre of mass is initialized on the path and its initial velocity is tangent to the path, then the PVTOL remains on the path at all future times) and boundedness of the roll dynamics. Further, our controller guarantees that, after a finite time, the time average of the roll angle is zero, and the PVTOL does not perform multiple revolutions about its longitudinal axis.

Brief paper: Path following using transverse feedback linearization: Application to a maglev positioning system

This article presents an approach to path following control design based on transverse feedback linearization. A “transversal” controller is designed to drive the output of the plant to the path. A “tangential” controller meets application-specific requirements on the path, such as speed regulation and internal stability. This methodology is applied to a five degree-of-freedom (5-DOF) magnetically levitated positioning system. Experimental results demonstrate the effectiveness of our control design.

Virtual Holonomic Constraints for Euler–Lagrange Systems

This technical brief investigates virtual holonomic constraints for Euler-Lagrange systems with n degrees-of-freedom and n-1 controls. In our framework, a virtual holonomic constraint is a relation specifying n-1 configuration variables in terms of a single angular configuration variable. The enforcement by feedback of such a constraint induces a desired repetitive behavior in the system. We give conditions under which a virtual holonomic constraint is feasible, i.e, it can be made invariant by feedback, and it is stabilizable. We provide sufficient conditions under which the dynamics on the constraint manifold correspond to an Euler- Lagrange system. These ideas are applied to the problem of swinging up an underactuated pendulum while guaranteeing that the second link does not fall over.

On Local Transverse Feedback Linearization

Given a control-affine system and a controlled invariant submanifold, we present necessary and sufficient conditions for local feedback equivalence to a system whose dynamics transversal to the submanifold are linear and controllable. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set.

Distributed Circular Formation Stabilization for Dynamic Unicycles

This paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius, whose center is stationary but dependent on the initial conditions, and travel around the circle in a desired direction. The vehicles are required to converge to a formation on the circle, expressed by desired separations and ordering of the unicycles. The information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree. A hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation.

Reduction Principles and the Stabilization of Closed Sets for Passive Systems

In this technical note, we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space.

Path following using transverse feedback linearization: Application to a maglev positioning system

This article presents an approach to path following control design based on transverse feedback linearization. A “transversal” controller is designed to drive the output of the plant to the path. A “tangential” controller meets application-specific requirements on the path, such as speed regulation and internal stability. This methodology is applied to a five degree-of-freedom (5-DOF) magnetically levitated positioning system. Experimental results demonstrate the effectiveness of our control design.