Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.

The use of Coulomb's friction law with the principles of classical rigid body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations, compliant contact models, while increasing the dimensionality of the state vector, can resolve these problems. The simplicity and efficiency of rigid body models, however, provide strong motivation for their use during those portions of a simulation when the rigid body solution is unique and stable. In this paper, we use singular perturbation analysis in conjunction with linear complementarity theory to establish conditions under which the solution predicted by the rigid body dynamic model is stable. We employ a general model of contact compliance to derive stability criteria for planar mechanical systems. In particular, we show that for cases with one sliding contact, there is always at most one stable solution. Our approach is not directly applicable to transitions between rolling and sliding where the Coulomb friction law is discontinuous. To overcome this difficulty, we introduce a smooth nonlinear friction law, which approximates Coulomb friction. Such a friction model can also increase the efficiency of both rigid body and compliant contact simulation. Numerical simulations for the different models and comparison with experimental results are also presented. 1 1

High performance robust motion control of single-rod hydraulic actuators is considered. In contmst to the double-rod hydraulic actuators studied previously, the two chambers of a single-rod hydraulic actuator have different areas. As a result, the dynamic equations describing the pressure changes in the two chambers cannot be combined into a single load pressure equation. This complicates the controller design since it not only increases the dimension of the system to be dealt with but also brings in the stability issue of the added internal dynamics. A discontinuous projection based adaptive robust controller is constructed. The controller is able to take into account not only the effect of parameter vam”ations coming from the inertia load and various hydraulic parameters but also the efiect of hardto-model nonlinearities such as uncompensated friction forces and external disturbances. Extensive experimental results are obtained for the swing motion control of a hydraulic arm. In comparison to a state-of-the-art industrial motion controller, the proposed ARC atgorithm achieves more than a magnitude reduction of tracking errors. Furthermore, during constant velocity and regulation periods, the ARC controller reduces the tmcking errors almost down to the measurement resolution level. 1

We address the problem of position trajectorytracking 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 two or three-dimensional 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 three-dimensional space). Simulations results are presented and discussed.

Explicit formulas of smooth time-varying state fced-bacim which malrc the origin of an underactuated sur-face vessel globally uniformly asymptotically stable are proposed. The construction of the feedback cxtensivdy relies on the backstepping approach. The feedbac~ constructed are time periodic functions. 1

Contraction theory is a recent tool enabling to study the stability of nonlinear systems trajectories with respect to one another, and therefore belongs to the class of incremental stability methods. In this paper, we extend the original definition of contraction theory to incorporate in an explicit manner the control input of the considered system. Such an extension, called universal contraction, is quite analogous in spirit to the well-known Input-to-State Stability (ISS). It serves as a simple formulation of incremental ISS, external stability, and detectability in a differential setting. The hierarchical combination result of contraction theory is restated in this framework, and a differential small-gain theorem is derived from results already available in Lyapunov theory.

Guaranteeing that traditional concepts of stability like uniform global exponential or asymptotic stability #UGES or UGAS# are veri#ed when using design tools based on new concepts of stability may be of signi#- cant importance. It is especially so when attempting to bridge the gap between theory and practice. This paper addresses the question of the applicabilityofcontraction theory to the design of UGES observers for ocean vehicles. A relation between the concept of exponential convergence of a contracting system and uniform global exponential stability #UGES# is #rst given. Then two contraction-based GES observers, respectively for unmanned underwater vehicles #UUV# and a class of ships, are constructed, and simulation results are provided. 1

On the contrary to Lyapunov theory, contraction theory studies system behavior independently from a specific attractor, thus leading to simpler computations when verifying exponential convergence of nonlinear systems. To check the contraction property, a condition of negativity on the Jacobian of the system has to be fulfilled. In this paper, attention is paid to results for which the negativity condition can be relaxed, i.e. the maximum eigenvalue of the Jacobian may take zero or positive values. In this issue, we present a theorem and a corollary which sufficient conditions enable to conclude when the Jacobian is not uniformly negative definite but fulfils some weaker conditions. Intended as an illustrative example, a nonlinear underwater vehicle observer, which Jacobian is not uniformly negative definite, is presented and proven to be exponentially convergent using the new criterion.

This paper addresses the state estimation of systems with perspective outputs. We derive a minimum-energy estimator which produces an estimate of the state that is “most compatible” with the dynamics, in the sense that it requires the least amount of noise energy to explain the measured outputs. Under suitable observability assumptions, the estimate converges globally asymptotically to the true value of the state in the absence of noise and disturbance. In the presence of noise, the estimate converges to a neighborhood of the true value of the state. These results are also extended to solve the estimation problem when the measured outputs are transmitted through a network. In that case, we assume that the measurements arrive at discrete-time instants, are time-delayed, noisy, and may not be complete. We show that the re-designed minimum-energy estimator preserves the same convergence properties. We apply these results to the estimation of position and orientation for a mobile robot that uses a monocular charged-coupled-device (CCD) camera mounted onboard to observe the apparent motion of stationary points. In the context of our application, the estimator can deal directly with the usual problems associated with vision systems such as noise, latency and intermittency of observations. Experimental results are presented and discussed.

We present an optimal control based algorithm for the computation of robust domains of attraction for perturbed systems. We give a sufficient condition for the continuity of the optimal value function and a characterization by Hamilton-Jacobi equations. A numerical scheme is presented and illustrated by an example.