António Pedro Aguiar

Trajectory-Tracking and Path-Following of Underactuated Autonomous Vehicles With Parametric Modeling Uncertainty

We address the problem of position trajectory-tracking and path-following control design for underactuated autonomous vehicles in the presence of possibly large modeling parametric uncertainty. For a general class of vehicles moving in either 2- or 3-D space, we demonstrate how adaptive switching supervisory control can be combined with a nonlinear Lyapunov-based tracking control law to solve the problem of global boundedness and convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be of a particular type (e.g., trimming trajectories) and can be any sufficiently smooth bounded curve parameterized by time. We also show how these results can be applied to solve the path-following problem, in which the vehicle is required to converge to and follow a path, without a specific temporal specification. We illustrate our design procedures through two vehicle control applications: a hovercraft (moving on a planar surface) and an underwater vehicle (moving in 3-D space). Simulations results are presented and discussed.

Dynamic positioning and way-point tracking of underactuated AUVs in the presence of ocean currents

This paper addresses the problem of dynamic positioning and way-point tracking of underactuated autonomous underwater vehicles (AUVs) in the presence of constant unknown ocean currents and parametric modelling uncertainty. A non-linear adaptive controller is proposed that steers an AUV along a sequence of way-points consisting of desired positions (x, y) in a inertial reference frame, followed by vehicle positioning at the final target point. The controller is first derived at the kinematic level assuming that the ocean current disturbance is known. An exponential observer for the current is then designed and convergence of the resulting closed-loop system trajectories is analysed. Finally, integrator backstepping and Lyapunov based techniques are used to extend the kinematic controller to the dynamic case and to deal with model parameter uncertainty. Simulation results with a dynamic model of an underactuated autonomous underwater shuttle for the transport of benthic labs are presented and discussed.

Coordinated Path-Following in the Presence of Communication Losses and Time Delays

This paper addresses the problem of steering a group of vehicles along given spatial paths while holding a desired time-varying geometrical formation pattern. The solution to this problem, henceforth referred to as the coordinated path-following (CPF) problem, unfolds in two basic steps. First, a path-following (PF) control law is designed to drive each vehicle to its assigned path, with a nominal speed profile that may be path dependent. This is done by making each vehicle approach a virtual target that moves along the path according to a conveniently defined dynamic law. In the second step, the speeds of the virtual targets (also called coordination states) are adjusted about their nominal values so as to synchronize their positions and achieve, indirectly, vehicle coordination. In the problem formulation, it is explicitly considered that each vehicle transmits its coordination state to a subset of the other vehicles only, as determined by the communications topology adopted. It is shown that the system that is obtained by putting together the PF and coordination subsystems can be naturally viewed as either the feedback or the cascade connection of the latter two. Using this fact and recent results from nonlinear systems and graph theory, conditions are derived under which the PF and the coordination errors are driven to a neighborhood of zero in the presence of communication losses and time delays. Two different situations are considered. The first captures the case where the communication graph is alternately connected and disconnected (brief connectivity losses). The second reflects an operational scenario where the union of the communication graphs over uniform intervals of time remains connected (uniformly connected in mean). To better root the paper in a nontrivial design example, a CPF algorithm is derived for multiple underactuated autonomous underwater vehicles (AUVs). Simulation results are presented and discussed.

Path-following for nonminimum phase systems removes performance limitations

We highlight an essential difference between path-following and reference-tracking for nonminimum phase systems. It is well known that in the reference-tracking, for nonminimum phase systems, there exists a fundamental performance limitation in terms of a lower bound on the L/sub 2/-norm of the tracking error, even when the control effort is free. We show that this is not the case for the less stringent path-following problem, where the control objective is to force the output to follow a geometric path without a timing law assigned to it. Furthermore, the same is true even when an additional desired speed assignment is imposed.

Position tracking of underactuated vehicles

This paper addresses the problem of position tracking for underactuated autonomous vehicles moving in either two or three-dimensional space. A nonlinear tracking controller is proposed for a general class of vehicles that yields global stability and exponential convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be of a particular type (e.g., trimming trajectories) and in fact can be any sufficiently smooth bounded curve parameterized by time. The control algorithm proposed builds upon Lyapunov techniques. To illustrate its potential, we describe two vehicle control applications: an hovercraft (moving on a planar surface) and an underwater vehicle (moving in three-dimensional space). Simulation results are presented and discussed.

Position tracking for a nonlinear underactuated hovercraft: controller design and experimental results

This paper addresses the position tracking control problem of an underactuated hovercraft vehicle. A nonlinear Lyapunov-based tracking controller is developed and proved to exponentially stabilize the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be a specially chosen (e.g., a trimming trajectory). In fact, it can be any sufficiently smooth bounded curve parameterized by time. The nonlinear controller has been experimentally validated on the Caltech Multi-Vehicle Wireless Testbed (MVWT), a platform for the development and implementation of novel single-and multiple-vehicle control designs. Experimental results are given for tracking of prescribed trajectories and for target following.

Regulation of a nonholonomic dynamic wheeled mobile robot with parametric modeling uncertainty using Lyapunov functions

Addresses the problem of regulating the dynamic model of a nonholonomic wheeled robot of the unicycle type to a point with a desired orientation. A simple controller is derived that yields global convergence of the trajectories of the closed loop system in the presence of parametric modeling uncertainty. Controller design relies on a non-smooth coordinate transformation in the original state space, followed by the derivation of a Lyapunov-based, adaptive, smooth control law in the new coordinates. Convergence to the origin is analyzed and simulation results are presented.

Coordinated path-following control for nonlinear systems with logic-based communication

We address the problem of designing decentralized feedback laws to force the outputs of decoupled nonlinear systems (agents) to follow geometric paths while holding a desired formation pattern. To this effect we propose a general framework that takes into account i) the topology of the communication links among the agents, ii) the fact that communications do not occur in a continuous manner, and iii) the cost of exchanging information. We provide conditions under which the resulting overall closed loop system is input-to-state stable and apply the methodology for two cases: agents with nonlinear dynamics in strict feedback form and a class of underactuated vehicles. Furthermore, we address explicitly the case where the communications among the agents occur with non-homogenous, possibly varying delays. A coordinated path-following algorithm is derived for multiple underactuated autonomous underwater vehicles. Simulation results are presented and discussed.

Regulation of a nonholonomic autonomous underwater vehicle with parametric modeling uncertainty using Lyapunov functions

Addresses the problem of regulating the dynamic model of a nonholonomic underactuated autonomous underwater vehicle (AUV) to a point with a desired orientation. A time-invariant discontinuous controller is proposed that yields convergence of the trajectories of the closed-loop system in the presence of parametric modeling uncertainty. Controller design relies on a non-smooth coordinate transformation in the original state space followed by the derivation of a Lyapunov-based, adaptive, smooth control law in the new coordinates. Convergence of the regulation system is analyzed and simulation results are presented.

Synchronization in multi-agent systems with switching topologies and non-homogeneous communication delays

We study the synchronization problem for n single state agents with linear continuous time dynamics. The agent states are required to synchronize and travel at a desired common speed. This problem arises naturally in the design of coordinated path-following algorithms problem [9] and in studies on the synchronization of Kuramoto oscillator networks [17]. When the desired speed is zero or there are no time delays, it has been shown in the literature that a so-called neighboring control rule makes the states synchronize asymptotically under some connectivity conditions on the union of the underlying communication graphs. We will show that when both the desired speed and the communication delay are non-zero, the behavior of the synchronization system changes significantly. We start by considering asymmetric networks and switching topologies with homogeneous time delays. We then address some issues related to the behavior of the synchronization system in the presence of heterogeneous time delays. We provide connectivity conditions under which the synchronization problem is solved and introduce synchronization laws that compensates for the effect of non-zero speed and time delays. Simulations illustrate the synchronization of three agents.