Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the sampling-based approach is the prevalent method. The main drawback of such techniques is that the reasoning about the expected cost of a plan is limited to the search heuristic used by each method. We introduce a novel planning method based on trajectory optimisation to plan safe and efficient paths in continuous occupancy maps. We extend the expressiveness of the state-of-the-art functional gradient optimisation methods by devising a stochastic gradient update rule to optimise a path represented as a Gaussian process. This approach avoids the need to commit to a specific resolution of the path representation, whether spatial or parametric. We utilise a continuous occupancy map representation in order to define our optimisation objective, which enables fast computation of occupancy gradients. We show that this approach is essential in order to ensure convergence to the optimal path, and present results and comparisons to other planning methods in both simulation and with real laser data. The experiments demonstrate the benefits of using this technique when planning for safe and efficient paths in continuous occupancy maps.
Traditional occupancy grid maps discretise the map into a fixed grid in order to estimate the occupancy posterior @cite_7 . In order to make computations tractable each cell is considered as an independent random variable. The computational gains are substantial since the posterior calculation can be done separately for each cell. The drawback is the loss of spatial relationship between neighbouring cells. To alleviate this problem, a non-parametric approach based on Gaussian Processes (GPs) was proposed in @cite_14 . The (GPOM) produces probabilistic occupancy posteriors based on sensor observations. Using a parameterised covariance function, GPOM captures spatial relationships, which enables continuous inference. The computational complexity is its main limitation, as it scales cubically with the number of observations.
@cite_14 @cite_7
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We introduce a new statistical modelling 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 free space. This is obtained by employing a modified Gaussian process as a non-parametric Bayesian learning technique to exploit the fact that real-world environments inherently possess structure. This structure introduces dependencies between points on the map which are not accounted for by many common mapping techniques such as occupancy grids. Our approach is an 'anytime' algorithm that is capable of generating accurate representations of large environments at arbitrary resolutions to suit many applications. It also provides inferences with associated variances into occluded regions and between sensor beams, even with relatively few observations. Crucially, the technique can handle noisy data, potentially from multiple sources, and fuse it into a robust common probabilistic representation of the robot's surroundings. We demonstrate the benefits of our approach on simulated datasets with known ground truth and in outdoor urban environments. An approach to robot perception and world modeling that uses a probabilistic tesselated representation of spatial information called the occupancy grid is reviewed. The occupancy grid is a multidimensional random field that maintains stochastic estimates of the occupancy state of the cells in a spatial lattice. To construct a sensor-derived map of the robot's world, the cell state estimates are obtained by interpreting the incoming range readings using probabilistic sensor models. Bayesian estimation procedures allow the incremental updating of the occupancy grid, using readings taken from several sensors over multiple points of view. The use of occupancy grids from mapping and for navigation is examined. Operations on occupancy grids and extensions of the occupancy grid framework are briefly considered. >