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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Occupancy grids have been a popular mapping technique in mobile robotics for nearly 30 years. Occupancy grids offer a discrete representation of the world and seek to determine the occupancy probability of each cell. Traditional occupancy grid mapping methods make two assumptions for computational efficiency and it has been shown that the full posterior is computationally intractable for real-world mapping applications without these assumptions. The two assumptions result in tuning parameters that control the information gained from each distance measurement. In this paper, several tuning parameters found in the literature are optimized against the full posterior in 1D. In addition, this paper presents a new parameterization of the update function that outperforms existing methods in terms of capturing residual uncertainty. Capturing the residual uncertainty better estimates the position of obstacles and prevents under- and over-confidence in both the occupied and unoccupied cells. The paper concludes by showing that the new update function better captures the residual uncertainty in each cell when compared to an offline mapping method for realistic 2D simulations. We present a novel algorithm to produce descriptive online 3D occupancy maps using Gaussian processes (GPs). GP regression and classification have met with recent success in their application to robot mapping, as GPs are capable of expressing rich correlation among map cells and sensor data. However, the cubic computational complexity has limited its application to large-scale mapping and online use. In this paper we address this issue first by proposing test-data octrees, octrees within blocks of the map that prune away nodes of the same state, condensing the number of test data used in a regression, in addition to allowing fast data retrieval. We also propose a nested Bayesian committee machine which, after new sensor data is partitioned among several GP regressions, fuses the result and updates the map with greatly reduced complexity. Finally, by adjusting the range of influence of the training data and tuning a variance threshold implemented in our method's binary classification step, we are able to control the richness of inference achieved by GPs - and its tradeoff with classification accuracy. The performance of the proposed approach is evaluated with both simulated and real data, demonstrating that the method may serve both as an improved-accuracy classifier, and as a predictive tool to support autonomous navigation. Occupancy grid filtering is important for navigation and localization in dynamic environments. The techniques that have been proposed in the past research, such as the Bayesian occupancy filter and the sequential Monte Carlo Bayesian occupancy filter, involve the independent consideration of all grid cells and, thus, are inaccurate and computationally expensive. To solve this problem, we propose a fast occupancy grid filtering method that uses a grid state map. We apply a superpixel-based clustering concept called a grid cell cluster (GCC) to 3D particles measured using light detection and ranging and dense depth maps extracted from a stereo vision sensor. The GCC locates a connection among similar data items according to certain criteria. In our proposed method, a GCC consisting of several grid cells has one dynamic state. Thus, we can reduce the computational cost and the number of computational errors by using the same prediction matrices is generated from the grid cells belonging to an object. Our method was evaluated on the KITTI benchmark data set. The results showed that the proposed method was faster (by approximately 38.9 ) than Mekahanachas method and approximately 12 more accurate (on the intersection-over-union metric) than prevalent techniques. In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field model that maintains probabilistic estimates of the occupancy state of each cell in a spatial lattice. Bayesian estimation mechanisms employing stochastic sensor models allow incremental updating of the Occupancy Grid using multi-view, multi-sensor data, composition of multiple maps, decision-making, and incorporation of robot and sensor position uncertainty. We present the underlying stochastic formulation of the Occupancy Grid framework, and discuss its application to a variety of robotic tusks. These include range-based mapping, multi-sensor integration, path-planning and obstacle avoidance, handling of robot position uncertainty, incorporation of pre-compiled maps, recovery of geometric representations, and other related problems. The experimental results show that the Occupancy Grid approach generates dense world models, is robust under sensor uncertainty and errors, and allows explicit handling of uncertainty. It supports the development of robust and agile sensor interpretation methods, incremental discovery procedures, and composition of information from multiple sources. Furthermore, the results illustrate that robotic tasks can be addressed through operations performed di- rectly on the Occupancy Grid, and that these operations have strong parallels to operations performed in the image processing domain.