arXiv subjects

Jonathan D. Gammell

Publications and source records attributed to Jonathan D. Gammell.

25 records · Page 2Linked to original sources

arXiv2020

Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as respectively used by informed graph-based searches and anytime sampling-based planners. Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient but leaves their performance dependent on the chosen approximation. If its resolution is too low then they may not find a (suitable) solution but if it is too high then they may take a prohibitively long time to do so. Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously and but may be prohibitively inefficient at containing a solution. This paper unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.

cs.RO↗

arXiv2019

The Oxford Multimotion Dataset: Multiple SE(3) Motions with Ground Truth

Datasets advance research by posing challenging new problems and providing standardized methods of algorithm comparison. High-quality datasets exist for many important problems in robotics and computer vision, including egomotion estimation and motion/scene segmentation, but not for techniques that estimate every motion in a scene. Metric evaluation of these multimotion estimation techniques requires datasets consisting of multiple, complex motions that also contain ground truth for every moving body. The Oxford Multimotion Dataset provides a number of multimotion estimation problems of varying complexity. It includes both complex problems that challenge existing algorithms as well as a number of simpler problems to support development. These include observations from both static and dynamic sensors, a varying number of moving bodies, and a variety of different 3D motions. It also provides a number of experiments designed to isolate specific challenges of the multimotion problem, including rotation about the optical axis and occlusion. In total, the Oxford Multimotion Dataset contains over 110 minutes of multimotion data consisting of stereo and RGB-D camera images, IMU data, and Vicon ground-truth trajectories. The dataset culminates in a complex toy car segment representative of many challenging real-world scenarios. This paper describes each experiment with a focus on its relevance to the multimotion estimation problem.

cs.RO↗

arXiv2018

Multimotion Visual Odometry (MVO): Simultaneous Estimation of Camera and Third-Party Motions

Estimating motion from images is a well-studied problem in computer vision and robotics. Previous work has developed techniques to estimate the motion of a moving camera in a largely static environment (e.g., visual odometry) and to segment or track motions in a dynamic scene using known camera motions (e.g., multiple object tracking). It is more challenging to estimate the unknown motion of the camera and the dynamic scene simultaneously. Most previous work requires a priori object models (e.g., tracking-by-detection), motion constraints (e.g., planar motion), or fails to estimate the full SE(3) motions of the scene (e.g., scene flow). While these approaches work well in specific application domains, they are not generalizable to unconstrained motions. This paper extends the traditional visual odometry (VO) pipeline to estimate the full SE(3) motion of both a stereo/RGB-D camera and the dynamic scene. This multimotion visual odometry (MVO) pipeline requires no a priori knowledge of the environment or the dynamic objects. Its performance is evaluated on a real-world dynamic dataset with ground truth for all motions from a motion capture system.

cs.RO↗

arXiv2018

Surface Edge Explorer (SEE): Planning Next Best Views Directly from 3D Observations

Surveying 3D scenes is a common task in robotics. Systems can do so autonomously by iteratively obtaining measurements. This process of planning observations to improve the model of a scene is called Next Best View (NBV) planning. NBV planning approaches often use either volumetric (e.g., voxel grids) or surface (e.g., triangulated meshes) representations. Volumetric approaches generalise well between scenes as they do not depend on surface geometry but do not scale to high-resolution models of large scenes. Surface representations can obtain high-resolution models at any scale but often require tuning of unintuitive parameters or multiple survey stages. This paper presents a scene-model-free NBV planning approach with a density representation. The Surface Edge Explorer (SEE) uses the density of current measurements to detect and explore observed surface boundaries. This approach is shown experimentally to provide better surface coverage in lower computation time than the evaluated state-of-the-art volumetric approaches while moving equivalent distances.

cs.RO↗

arXiv2015

Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in $\mathbb{R}^2$ and $\mathbb{R}^8$ and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.

cs.RO↗

arXiv2014

Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

cs.RO↗

arXiv2014

On Recursive Random Prolate Hyperspheroids

This technical note analyzes the properties of a random sequence of prolate hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is defined by a sample drawn randomly from the previous volume such that the sample lies on the new surface (Fig. 1). Section 1 defines the prolate hyperspheroid coordinate system and the resulting differential volume, Section 2 calculates the expected value of the new transverse diameter given a uniform distribution over the existing prolate hyperspheroid, and Section 3 calculates the convergence rate of this sequence. For clarity, the differential volume and some of the identities used in the integration are verified in Appendix A through a calculation of the volume of a general prolate hyperspheroid.

math.ST↗