Understanding the dynamics of urban environments is crucial for path planning and safe navigation. However, the dynamics might be extremely complex making learning the environment an unfathomable task. Within the methods available for learning dynamic environments, dynamic Gaussian process occupancy maps (DGPOM) are very attractive because they can produce spatially-continuous occupancy maps taking into account neighborhood information, and provide probabilistic estimates, naturally inferring the uncertainty of predictions. Despite these properties, they are extremely slow, especially in dynamic mapping where the parameters of the map have to be updated as new data arrive from range sensors such as LiDARs. In this work, we leverage recent advancements in stochastic variational inference (SVI) to quickly learn dynamic areas in an online fashion. Further, we propose an information-driven technique to “intelligently” select inducing points required for SVI without relying on any object trackers which essentially improves computational time as well as robustness. These long-term occupancy maps entertain all attractive properties of DGPOM while the learning process is significantly faster, yet accurate. Our experiments with both simulation and real robot data on road intersections show a significant improvement in speed while maintaining a comparable or better accuracy.

Understanding and predicting how influenza propagates is vital to reduce its impact. In this paper we develop a nonparametric model based on Gaussian process (GP) regression to capture the complex spatial and temporal dependencies present in the data. A stochastic variational inference approach was adopted to address scalability. Rather than modeling the problem as a time-series as in many studies, we capture the space-time dependencies by combining different kernels. A kernel averaging technique which converts spatially-diffused point processes to an area process is proposed to model geographical distribution. Additionally, to accurately model the variable behavior of the time-series, the GP kernel is further modified to account for non-stationarity and seasonality. Experimental results on two datasets of state-wide US weekly flu-counts consisting of 19,698 and 89,474 data points, ranging over several years, illustrate the robustness of the model as a tool for further epidemiological investigations.

We consider the problem of building continuous occupancy representations in dynamic environments for robotics applications. The problem has hardly been discussed previously due to the complexity of patterns in urban environments, which have both spatial and temporal dependencies. We address the problem as learning a kernel classifier on an efficient feature space. The key novelty of our approach is the incorporation of variations in the time domain into the spatial domain. We propose a method to propagate motion uncertainty into the kernel using a hierarchical model. The main benefit of this approach is that it can directly predict the occupancy state of the map in the future from past observations, being a valuable tool for robot trajectory planning under uncertainty. Our approach preserves the main computational benefits of static Hilbert maps — using stochastic gradient descent for fast optimization of model parameters and incremental updates as new data are captured. Experiments conducted in road intersections of an urban environment demonstrated that spatio-temporal Hilbert maps can accurately model changes in the map while outperforming other techniques on various aspects.

We present a novel estimation algorithm for filtering and regression with a number of advantages over existing methods. The algorithm has wide application in robotics as no assumptions are made about the underlying distributions, it can represent non-Gaussian multi-modal posteriors, and learn arbitrary non-linear models from noisy data. Our method is a generalisation of the Kernel Bayes' Rule that produces multi-modal posterior estimates represented as Gaussian mixtures. The algorithm learns non-linear state transition and observation models from data and represents all distributions internally as elements in a reproducing kernel Hilbert space. Inference occurs in the Hilbert space and can be performed recursively. When an estimate of the posterior distribution is required, we apply a quadratic programming pre-image method to determine the Gaussian mixture components of the posterior representation. We demonstrate our algorithm with two filtering experiments and one regression experiment; a multi-modal tracking simulation, a real tracking problem involving a miniature slot-car with an attached inertial measurement unit, and a regression problem of estimating the velocity field of a set of pedestrian paths for robot path-planning. Our algorithm compares favourably with the Gaussian process in the regression case, and a particle filter with learned process and observation models (the “GP-BayesFilter” particle filter).

We address the problem of building a continuous occupancy representation of the environment with ranging sensors. Observations from such sensors provide two types of information: a line segment or a beam indicating no returns along them (free-space); a point or return at the end of the segment representing an occupied surface. To model these two types of observations in a principled statistical manner, we propose a novel methodology based on integral kernels. We show that integral kernels can be directly incorporated into a Gaussian process classification (GPC) framework to provide a continuous non-parametric Bayesian estimation of occupancy. Directly handling line segment and point observations avoids the need to discretise segments into points, reducing the computational cost of GPC inference and learning. We present experiments on 2D and 3D datasets demonstrating the benefits of the approach.

Observing human motion patterns is informative for social robots that share the environment with people. This paper presents a methodology to allow a robot to navigate in a complex environment by observing pedestrian positional traces. A continuous probabilistic function is determined using Gaussian process learning and used to infer the direction a robot should take in different parts of the environment. The approach learns and filters noise in the data producing a smooth underlying function that yields more natural movements. Our method combines prior conventional planning strategies with most probable trajectories followed by people in a principled statistical manner, and adapts itself online as more observations become available. The use of learning methods are automatic and require minimal tuning as compared to potential fields or spline function regression. This approach is demonstrated testing in cluttered office and open forum environments using laser and vision sensing modalities. It yields paths that are similar to the expected human behaviour without any a priori knowledge of the environment or explicit programming.

This paper describes a method of incorporating sensor and localisation uncertainty into contextual occupancy maps to provide for robust mapping. This paper builds on a recently proposed application of the Gaussian process (GP) to occupancy mapping. An extension of GPs is employed which incorporates uncertain inputs into the covariance function. In turn, this allows statistically consistent, multi-resolution maps to be constructed which exploit the spatial inference properties of GPs while correctly accounting for sensor and localisation errors. Experiments are described, with both synthetic and real data, which show the benefits of complete uncertainty modeling and how contextual occupancy maps may be constructed by fusing data from different sensors on different robots in a common probabilistic representation.

In this paper we introduce a new statistical modeling technique for building occupancy maps. The problem of mapping is addressed as a classification task where the robot's environment is classified into regions of occupancy and unoccupancy. Our model provides both a continuous representation of the robot's surroundings and an associated predictive variance. This is obtained by employing a Gaussian process as a non-parametric Bayesian learning technique to exploit the fact that real-world environments inherently possess structure. This structure introduces a correlation between points on the map which is not accounted for by many common mapping techniques such as occupancy grids. Using a trained neural network covariance function to model the highly non-stationary datasets, it is possible to generate accurate representations of large environments at resolutions which suit the desired applications while also providing inferences into occluded regions, between beams, and beyond the range of the sensor, even with relatively few sensor readings. We demonstrate the benefits of our approach in a simulated data set with known ground-truth, and in an outdoor urban environment covering an area of 120,000 m2.