Mario Tosques

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.

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.

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.

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.

Path following for the PVTOL: A set stabilization approach

This article proposes a path following controller that regulates the center of mass of the planar vertical take-off and landing aircraft (PVTOL) to the unit circle and makes the aircraft traverse the circle in a desired direction. A static feedback controller is designed using the ideas of transverse feedback linearization, finite time stabilization and virtual constraints. No time parameterization is given to the desired motion on the unit circle. Instead, our approach relies on the nested stabilization of two sets on which the dynamics of the PVTOL exhibit desirable behavior.

A path following problem for a class of non-holonomic control systems with noise

This paper deals with a path following problem for a system affected by noise and proposes a dynamic inversion-based controller that makes use of the error between the real position and a suitable path location. An estimate of such error is given in terms of the noise bounds, showing the practical stability of the closed loop system. The results presented in this article apply to a subclass of Chaplygin control systems which includes several common mechanical systems. As an example the developed strategy has been applied to maneuver a kinematic model of a system moving in a 3-dimensional space in such a way that a point located at a positive distance from its center of geometry is driven towards a given path.

A dynamic inversion based controller for path following of car-like vehicles

Abstract 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. 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 vehicles ideal trajectory. A convergence analysis of the resulting dynamic inversion based controller is established versus a vehicles uncertain model defined via equation errors. A simulation example highlighting the controllers performances is included.

On the Existence of Small Periodic Solutions for the 2-Dimensional Inverted Pendulum on a Cart

This paper studies the problem of controlling an inverted pendulum on a cart which has to track a given curve lying on a vertical plane in such a way that the pendulum rod does not overturn. The problem is reduced to finding sufficiently small T-periodic solutions for a special type of mathematical forced pendulum equation.