Luca Consolini

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.

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.

A Geometric Characterization of Leader-Follower Formation Control

The paper focuses on leader-follower formations of nonholonomic mobile robots. A formation control alternative to those existing in the literature is introduced. We show that the geometry of the formation imposes a bound on the maximum admissible curvature of leader trajectory. A peculiar feature of the proposed strategy is that the followers position is not rigidly fixed with respect to the leader reference frame but varies in suitable cones centered in the leader reference frame. Our approach also applies to hierarchical multirobot formations described by rooted tree graphs. Simulation experiments confirm the effectiveness of the proposed control schemes.

Active Filter for the Removal of the DC Current Component for Single-Phase Power Lines

Nonlinear loads and grid-connected converters can cause, in addition to the generation of several current harmonics in the grid current, a dc current component injection. A dc current component can cause the magnetic core saturation of distribution power transformers. Transformers operating under saturation conditions present increased power losses, overheating, and distorted current waveforms. Since a dc current component causes a small dc voltage component drop across the parasitic resistance of the distribution grid conductors, canceling the dc voltage component at the point of common coupling (PCC) implies the compensation of the dc current component injected/absorbed by electric loads or grid-connected converters connected at the same PCC. This paper proposes a low-cost nonlinear sensor for an accurate detection, free from offset problems, of the dc voltage component present in the grid voltage. The detection of the dc voltage component was used to realize an active filter of the dc current component. The proposed solution is outlined, and then the stability issue is addressed by means of a simplified model. Experimental results confirmed that the simplified model closely approximates the real system.

On the VTOL Exact Tracking With Bounded Internal Dynamics via a PoincarÉ Map Approach

This paper considers the problem of open-loop exact tracking for the vertical takeoff and landing aircraft with respect to the nominal output. It is shown that if the norm of the acceleration of the reference curve is lower than kmg, where g is the gravity acceleration and km sime 0.2672, then there exists a special initial state such that the internal dynamics are bounded. The bounding term is directly proportional to the maximum norm of the acceleration of the reference trajectory.

Generalized bang-bang control for feedforward constrained regulation

In a behavioral framework, simple sufficient conditions for the minimum-time rest-to-rest feedforward constrained control problem are provided. The investigation of the time-optimal input-output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure. The resulting optimal input is composed of sequences of bang-bang functions and linear combinations of the modes associated to the zero dynamics. This signal behavior constitutes a generalized bang-bang control that can be fruitfully exploited for feedforward constrained regulation. Using discretization, an arbitrarily good approximation of the optimal generalized bang-bang control is found by solving a sequence of linear programming problems. Numerical examples are included

Virtual Holonomic Constraints for Euler-Lagrange Systems

Abstract This paper investigates virtual holonomic constraints for Euler-Lagrange systems with n degrees-of-freedom and n − 1 controls. The constraints have the form q1 = ϕ1 (qn), …, qn – 1 = ϕn ∓ 1 (qn), where qn is a cyclic configuration variable, so their enforcement corresponds to the stabilization of a desired oscillatory motion. We give conditions under which such a set of constraints is feasible, meaning that it can be made invariant by feedback. We show that it is possible to systematically determine feasible virtual constraints as periodic solutions of a scalar differential equation, the virtual constraint generator. Moreover, under a symmetry assumption we show that the motion on the constraint manifold is a Euler-Lagrange system with one degree-of-freedom, and use this fact to complete characterize its dynamical properties. Finally, we show that if the constraint is feasible then the virtual constraint manifold can always be stabilized using input-output feedback linearization.

On the Control of a Leader-Follower Formation of Nonholonomic Mobile Robots

This paper deals with leader-follower formations of nonholonomic mobile robots. Formalizing the problem in a geometric framework, it is proposed a controller that is alternative to those existing in the literature. It is shown that the geometry of the formation imposes a bound on the maximum admissible curvature of leader trajectory. A peculiar characteristic of the proposed strategy is that the position of the followers is not fixed with respect to the leader reference frame but varies in suitable cones. The formation geometry adapts to the followers dynamics and this allows lower control effort with respect to other approaches based on rigid formations

On a Class of Hierarchical Formations of Unicycles and Their Internal Dynamics

This paper studies a class of hierarchical formations for an ordered set of n + 1 unicycle robots: the first robot plays the role of the leader and the formation is induced through a constraint function F, so that the position and orientation of the ith robot depends only on the pose of the preceding ones. We study the dynamics of the formation with respect to the leaders reference frame by introducing the concept of reduced internal dynamics, we characterize its equilibria and provide sufficient conditions for their existence. The discovered theoretical results are applied to the case in which the constraint F induces a formation where the ith robot follows a convex combination of the positions of the previous i - 1 vehicles. In this case, we prove that if the curvature of the leaders trajectory is sufficiently small, the positions and orientations of the robots, relative to the leaders reference frame, are confined in a precise polyhedral region.

Path following of car-like vehicles using dynamic inversion

This paper focuses on a special path following task arising from the needs of vision-based autonomous guidance: a given front point of a car-like vehicle that is within the look-ahead range of a stereo vision system must follow a prespecified Cartesian path. A solution to this path following problem is provided by a new feedforward/feedback control strategy where the feedforward is determined by a dynamic generator based on exact dynamic inversion over the nominal vehicle model and the feedback is mainly issued by correcting terms proportional to the tangential and normal errors determined with respect to the vehicle’s ideal trajectory. A convergence analysis of the resulting dynamic inversion based controller is established versus a vehicle’s uncertain model defined via equation errors. Simulation examples highlighting the controller’s performances are included.