In a point-to-point wireless fading channel, multiple transmit and receive antennas can be used to improve the reliability of reception (diversity gain) or increase the rate of communication for a fixed reliability level (multiplexing gain). In a multiple access situation, multiple receive antennas can also be used to spatially separate signals from different users (multiple access gain). Recent work has characterized the fundamental tradeoff between diversity and multiplexing gains in the point-to-point scenario. In this paper, we extend the results to a multiple access fading channel. Our results characterize the fundamental tradeoff between the three types of gain and provide insights on the capabilities of multiple antennas in a network context. 1

Abstract This paper presents a comparative evaluation of different dis-tance metrics and local planners within the context of probabilistic roadmap methods for motion planning. Both C-space andWorkspace distance metrics and local planners are considered. The study concentrates on cluttered three-dimensionalWorkspaces typical, e.g., of mechanical designs. Our results include recommendations for selecting appropriate combinationsof distance metrics and local planners for use in motion planning methods, particularly probabilistic roadmap methods. Wefind that each local planner makes some connections than none of the others do-- indicating that better connectedroadmaps will beconstructed using multiple local planners. We propose a new local planning method we call rotate-at-s that outperforms the commonstraight-line in C-space method in crowded environments. 1

The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given high-level specifications of tasks and geometric models of the robot and obstacles. The "Movers'" problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the three-dimensional Movers' problem: Given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collision-free path taking P from some initial configuration to a desired goal configuration. This paper describes an implementation of a complete algorithm (at a given resolution)for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six-dimensional configuration space (called C-space). The C-space obstacles, which characterize the physically unachievable configurations, are directly represented by six-dimensional manifolds whose boundaries are five-dimensional C-surfaces. By characterizing these surfaces and their intersections, collision-free paths may be found by the

Abstruct-Zstimating the three-dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics, such as autonomous navigation, manipulation, servo, tracking, docking, planning, and surveillance. Although “visual motion estimation” is an old problem (the first formulations date back to the beginning of the century), only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions. In this paper we formulate the visual motion estimation lproblem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold. Such a formulation has structural advantages over previous recursive schemes, since the estimation of motion is decoupled from the estimation of the structure of

Subdivision surfaces solve numerous problems related to the geometry of character and animation models. However, unlike on parametrised surfaces there is no natural choice of texture coordinates on subdivision surfaces. Existing algorithms for generating texture coordinates on non-parametrised surfaces often find solutions that are locally acceptable but globally are unsuitable for use by artists wishing to paint textures. In addition, for topological reasons there is not necessarily any choice of assignment of texture coordinates to control points that can satisfactorily be interpolated over the entire surface. We introduce a technique, pelting, for finding both optimal and intuitive texture mapping over almost all of an entire subdivision surface and then show how to combine multiple texture mappings together to produce a seamless result.

In this paper we present methods to smoothly interpolate orientations, given N rotational keyframes of an object along a trajectory. The methods allow the user to impose constraints on the rotational path, such as the angular velocity at the endpoints of the trajectory. We convert the rotations to quaternions, and then spline in that non-Euclidean space. Analogous to the mathematical foundations of flat-space spline curves, we minimize the net "tangential acceleration" of the quaternion path. We replace the flat-space quantities with curved-space quantities, and numerically solve the resulting equation with finite difference and optimization methods. 1 Introduction The problem of using spline curves to smoothly interpolate mathematical quantities in flat Euclidean spaces is a well-studied problem in computer graphics [bartels et al 87], [kochanek&bartels 84]. Many quantities important to computer graphics, however, such as rotations, lie in non-Euclidean spaces. In 1985, a method to...

We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion could always be achieved by means of trajectories of a special kind, namely, concatenations of at most five pieces, each of which is either a straight line or a circle, and (b) that these concatenations can be classified into 48 three-parameter families. We show how these results fit in a much more general framework, and can be discovered and proved by applying in a systematic way the techniques of Optimal Control Theory. It turns out that the "classical" optimal control tools developed in the 1960's, such as the Pontryagin Maximum Principle and theorems on the existence of optimal trajectories, are helpful to go part of the way and get some information on the shortest paths, but do not suffice ...

A complementarity framework is described for the modeling of certain classes of mixed continuous /discrete dynamical systems. The use of such a framework is well-known for mechanical systems with inequality constraints, but we give a more general formulation which applies for instance also to systems with relays in a feedback loop. The main theoretical results in the paper are concerned with uniqueness of smooth continuations; the solution of this problem requires the construction of a map from the continuous state to the discrete state. A crucial technical tool is the so-called linear complementarity problem (LCP); we introduce various generalizations of this problem. Specific results are obtained for Hamiltonian systems, passive systems, and linear systems.

Let X be a closed manifold with χ(X) = 0, and let f: X → S 1 be a circlevalued Morse function. We define an invariant I which counts closed orbits of the gradient of f, together with flow lines between the critical points. We show that our invariant equals a form of topological Reidemeister torsion defined by Turaev [28]. We proved a similar result in our previous paper [7], but the present paper refines this by separating closed orbits and flow lines according to their homology classes. (Previously we only considered their intersection numbers with a fixed level set.) The proof here is independent of the proof in [7], and also simpler. Aside from its Morse-theoretic interest, this work is motivated by the fact that when X is three-dimensional and b1(X)> 0, the invariant I equals a counting invariant I3(X) which was conjectured in [7] to equal the Seiberg–Witten invariant of X. Our result, together with this conjecture, implies that the Seiberg–Witten invariant equals the Turaev torsion. This was conjectured by Turaev [28] and refines the theorem of Meng and Taubes [14].

We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian network with hidden variables is the rank of the Jacobian matrix of the transformation between the parameters of the network and the parameters of the observable variables. We compute the dimensions of several networks including the naive Bayes model with a hidden root node. 1