An algorithm for cooperative probabilistic control design

This paper deals with the decentralized closed loop control in a pure probabilistic framework. In this framework, a system is a controlled Markov chain whose transition probabilities depend on the actions of the agents. The agents are also described in a probabilistic way. The objective is to drive the system so that the joint state and agents actions are close to a set of given target probability distributions. The Kullback-Leibler divergence is used as a performance measure. The resulting algorithm uses dynamic programming interleaved with an iterative process that computes the behavior of each agent

Clustering of Gaussian Random Vector Fields in Multiple Trajectory Modelling

This paper concerns the estimation of multiple dynamical models from a set of observed trajectories. It proposes vector valued gaussian random fields, representing dynamical models and their vector fields, combined with a modified k- means clustering algorithm to assign observed trajectories to models. The assignment is done according to a likelihood function obtained from applying the random field associated to a cluster, to the data. The algorithm is shown to have several advantages when compared with others: 1) it does not depend on a grid, region of interest, grid resolution or interpolation method; 2) the estimated vector fields has an associated uncertainty which is given by the algorithm and taken into account. The paper presents results obtained on synthetic trajectories that illustrate the performance of the proposed algorithm

Nonlinear control of HIV-1 infection with a singular perturbation model

Using a singular perturbation approximation, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed with respect to the model parameter to the infection rate, showing that the controlled system remains stable in the presence of significant changes of this parameter with respect to the nominal value

Gaussian random field-based log odds occupancy mapping

This paper focuses on mapping problem with known robot pose in static environments and proposes a Gaussian random field-based log odds occupancy mapping (GRF-LOOM). In this method, occupancy probability is regarded as an unknown parameter and the dependence between parameters are considered. Given measurements and the dependence, the parameters of not only observed space but also unobserved space can be predicted. The occupancy probabilities in log odds form are regarded as a GRF. This mapping task can be solved by the well-known prediction equation in Gaussian processes, which involves an inverse problem. Instead of the prediction equation, a new recursive algorithm is also proposed to avoid the inverse problem. Finally, the proposed method is evaluated in simulations

Recursive bayesian identification of nonlinear autonomous systems

This paper concerns the recursive identification of nonlinear discrete-time systems for which the original equations of motion are not known. Since the true model structure is not available, we replace it with a generic nonlinear model. This generic model discretizes the state space into a finite grid and associates a set of velocity vectors to the nodes of the grid. The velocity vectors are then interpolated to define a vector field on the complete state space. The proposed method follows a Bayesian framework where the identified velocity vectors are selected by the maximum a posteriori (MAP) criterion. The resulting algorithms allow a recursive update of the velocity vectors as new data is obtained. Simulation examples using the recursive algorithm are presented

Alignment of velocity fields for video surveillance

Velocity fields play an important role in surveillance since they describe typical motion behaviors of video objects (e.g., pedestrians) in the scene. This paper presents an algorithm for the alignment of velocity fields acquired by different cameras, at different time intervals, from different viewpoints. Velocity fields are aligned using a warping function which maps corresponding points and vectors in both fields. The warping parameters are estimated by minimizing a non-linear least squares energy. Experimental tests show that the proposed model is able to compensate significant misalignments, including translation, rotation and scaling

Offline Bayesian Identification of Jump Markov Nonlinear Systems

This paper presents a framework for the offline identification of nonlinear switched systems with unknown model structure. Given a set of sampled trajectories, and under the assumption that they were generated by switching among a number of models, we estimate a set of vector fields and a stochastic switching mechanism that best describes the observed data. The switching mechanism is described by a position dependent hidden Markov model that provides the probabilities of the next active model given the current active model and the state vector. The vector fields and the stochastic matrix is obtained by interpolating a set of nodes distributed over a relevant region in the state space. The work follows a Bayesian formulation where the EM-algorithm is used for optimization

Online learning occupancy grid maps for mobile robots

Robot mapping is the basic work for robot navigation and path planning. Static map is also important to deal with dynamic environment. Occupancy grid maps are used to represent the environment. This paper focuses on the dependence between grid cells. We assume that if one point of the map is free, then the neighbors are likely to be free. This knowledge is encoded in a Markov random field (MRF) that is used as our prior belief about the world. Data from range sensors will then update our knowledge. By maximizing the posterior distribution of MRF model, a linear filter is generated. It can be used to filter the noise in observations or static maps. This linear filter can be implemented online. It is also additive if the sensor model is in the log odds form

Interactive Air Traffic Control automation in oceanic airspace

Air traffic controllers workload limits impose upper bounds to the amount of traffic manageable in a given air sector for a given time frame. Air Traf- fic Control (ATC) automation methods open the possibility of reducing this workload by shifting to the machine the tasks of (1) detecting poten- tial conflicts, and of (2) proposing to the controller ATC instructions that prevent such conflicts. We propose a decision support system based on a combinatorial optimization approach using a branch-and-bound method. Given a known traffic situation, we proceed by simulating the trajecto- ries of traffic, taking into account possible instructions to separate traffic. In this study we considered only flight level change instructions, given at report fixes. The cost function employed includes both a measure of vertical deviation from the filed flight plan (FPL) and the total amount of ATC instructions. The multi-criteria problem is solved interactively, as the operator directs the algorithm towards the solution, indicating its preferences at intermediate points in the simulation. As a case study, we analyse the problem of oceanic airspace, where conventional ATC is used due to the lack of radar coverage