Scaling Robot Motion Planning to Multi-core Processors and the Cloud

Imagine a world in which robots safely interoperate with humans, gracefully and efficiently accomplishing everyday tasks. The robot's motions for these tasks, constrained by the design of the robot and task at hand, must avoid collisions with obstacles. Unfortunately, planning a constrained obstacle-free motion for a robot is computationally complex---often resulting in slow computation of inefficient motions. The methods in this dissertation speed up this motion plan computation with new algorithms and data structures that leverage readily available parallel processing, whether that processing power is on the robot or in the cloud, enabling robots to operate safer, more gracefully, and with improved efficiency. The contributions of this dissertation that enable faster motion planning are novel parallel lock-free algorithms, fast and concurrent nearest neighbor searching data structures, cache-aware operation, and split robot-cloud computation. Parallel lock-free algorithms avoid contention over shared data structures, resulting in empirical speedup proportional to the number of CPU cores working on the problem. Fast nearest neighbor data structures speed up searching in SO(3) and SE(3) metric spaces, which are needed for rigid body motion planning. Concurrent nearest neighbor data structures improve searching performance on metric spaces common to robot motion planning problems, while providing asymptotic wait-free concurrent operation. Cache-aware operation avoids long memory access times, allowing the algorithm to exhibit superlinear speedup. Split robot-cloud computation enables robots with low-power CPUs to react to changing environments by having the robot compute reactive paths in real-time from a set of motion plan options generated in a computationally intensive cloud-based algorithm. We demonstrate the scalability and effectiveness of our contributions in solving motion planning problems both in simulation and on physical robots of varying design and complexity. Problems include finding a solution to a complex motion planning problem, pre-computing motion plans that converge towards the optimal, and reactive interaction with dynamic environments. Robots include 2D holonomic robots, 3D rigid-body robots, a self-driving 1/10 scale car, articulated robot arms with and without mobile bases, and a small humanoid robot.Doctor of Philosoph

Causal Consistent Databases

Many consistency criteria have been considered in databases and the causal consistency is one of them. The causal consistency model has gained much attention in recent years because it provides ordering of relative operations. The causal consistency requires that all writes, which are potentially causally related, must be seen in the same order by all processes. The causal consistency is a weaker criteria than the sequential consistency, because there exists an execution, which is causally consistent but not sequentially consistent, however all executions satisfying the sequential consistency are also causally consistent. Furthermore, the causal consistency supports non-blocking operations; i.e. processes may complete read or write operations without waiting for global computation. Therefore, the causal consistency overcomes the primary limit of stronger criteria: communication latency. Additionally, several application semantics are precisely captured by the causal consistency, e.g. collaborative tools. In this paper, we review the state-of-the-art of causal consistent databases, discuss the features, functionalities and applications of the causal consistency model, and systematically compare it with other consistency models. We also discuss the implementation of causal consistency databases and identify limitations of the causal consistency model

Coordinated Robot Navigation via Hierarchical Clustering

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of $n$ perfectly sensed and actuated Euclidean spheres in a $d$-dimensional ambient space (for arbitrary $n$ and $d$). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in $n$ and algebraic in $d$ and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.Comment: 29 pages, 13 figures, 8 tables, extended version of a paper in preparation for submission to a journa

WAQS : a web-based approximate query system

The Web is often viewed as a gigantic database holding vast stores of information and provides ubiquitous accessibility to end-users. Since its inception, the Internet has experienced explosive growth both in the number of users and the amount of content available on it. However, searching for information on the Web has become increasingly difficult. Although query languages have long been part of database management systems, the standard query language being the Structural Query Language is not suitable for the Web content retrieval. In this dissertation, a new technique for document retrieval on the Web is presented. This technique is designed to allow a detailed retrieval and hence reduce the amount of matches returned by typical search engines. The main objective of this technique is to allow the query to be based on not just keywords but also the location of the keywords within the logical structure of a document. In addition, the technique also provides approximate search capabilities based on the notion of Distance and Variable Length Don\u27t Cares. The proposed techniques have been implemented in a system, called Web-Based Approximate Query System, which contains an SQL-like query language called Web-Based Approximate Query Language. Web-Based Approximate Query Language has also been integrated with EnviroDaemon, an environmental domain specific search engine. It provides EnviroDaemon with more detailed searching capabilities than just keyword-based search. Implementation details, technical results and future work are presented in this dissertation

Mutual information-based gradient-ascent control for distributed robotics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 167-179).This thesis presents the derivation, analysis, and implementation of a novel class of decentralized mutual information-based gradient-ascent controllers that continuously move robots equipped with sensors to better observe their environment. We begin with the fundamental problem of deploying a single ground robot equipped with a range sensor and tasked to build an occupancy grid map. The desired explorative behaviors of the robot for occupancy grid mapping highlight the correlation between the information content and the spatial realization of the robot's range measurements. We prove that any occupancy grid controller tasked to maximize a mutual information reward function is eventually attracted to unexplored space, i.e., areas of highest uncertainty. We show that mutual information encodes geometric relationships that are fundamental to robot control and yields geometrically relevant reward surfaces on which robots can navigate. Taking inspiration from geometric-based approaches to distributed robot coordination, we show that many multi-robot inference tasks can be cast in terms of an optimization problem. This optimization problem defines the task of minimizing the conditional entropy associated with the robots' inferred beliefs of the environment, which is equivalent to maximizing the mutual information between the environment state and the robots' next joint observation. Given simple robot dynamics and few probabilistic assumptions, none of which involve Gaussianity, we derive a gradientascent solution approach to these optimization problems that is convergent between sensor observations and locally optimal. More formally, we invoke LaSalle's Invariance Principle to prove that, given enough time between consecutive joint observations, robots following the gradient of mutual information will converge to goal positions that locally maximize the expected information gain resulting from the next observation. We show that the algorithmic implementation of the generalized gradient-ascent controller is not readily distributed among multiple robots, and thus sample-based methods are introduced to distributively approximate the likelihoods of the robots' joint observations. Not only are the involved non-parametric representations compatible with any type of Bayesian filter, but the computational complexities of the resulting decentralized controllers are independent with respect to the number of robots. Concerning the distributed approximations, we give two example consensus-based algorithms that run on an undirected network graph. The first consensus-based algorithm approximates discrete measurement probabilities, while the second approximates continuous likelihood distributions. We show that these anytime approximations provably converge to the correct values on a static and connected network graph without knowledge of the number of robots in the network or the corresponding graph's topology. Lastly, we incorporate the resulting consensus-based algorithms into both a hardware system and a simulation environment to allow for decentralized controller evaluation under non-ideal network settings. For the hardware experiments, the task is to infer the state of a bounded, planar environment by deploying five quadrotor flying robots with simulated sensors in both indoor and outdoor settings. For the numerical simulations, Monte Carlo-based analyses are performed for 100 robots, where each robot is simulated on an independent computer node within a computer cluster system. Simulations are also performed for 1000 robots using a single workstation computer equipped with a multicore GPU-enabled graphics card. The results from both the hardware experiments and numerical simulations validate our theoretical and computational claims throughout the thesis.by Brian John Julian.Ph.D

Parallel and Flow-Based High Quality Hypergraph Partitioning

Balanced hypergraph partitioning is a classic NP-hard optimization problem that is a fundamental tool in such diverse disciplines as VLSI circuit design, route planning, sharding distributed databases, optimizing communication volume in parallel computing, and accelerating the simulation of quantum circuits. Given a hypergraph and an integer $k$, the task is to divide the vertices into $k$ disjoint blocks with bounded size, while minimizing an objective function on the hyperedges that span multiple blocks. In this dissertation we consider the most commonly used objective, the connectivity metric, where we aim to minimize the number of different blocks connected by each hyperedge. The most successful heuristic for balanced partitioning is the multilevel approach, which consists of three phases. In the coarsening phase, vertex clusters are contracted to obtain a sequence of structurally similar but successively smaller hypergraphs. Once sufficiently small, an initial partition is computed. Lastly, the contractions are successively undone in reverse order, and an iterative improvement algorithm is employed to refine the projected partition on each level. An important aspect in designing practical heuristics for optimization problems is the trade-off between solution quality and running time. The appropriate trade-off depends on the specific application, the size of the data sets, and the computational resources available to solve the problem. Existing algorithms are either slow, sequential and offer high solution quality, or are simple, fast, easy to parallelize, and offer low quality. While this trade-off cannot be avoided entirely, our goal is to close the gaps as much as possible. We achieve this by improving the state of the art in all non-trivial areas of the trade-off landscape with only a few techniques, but employed in two different ways. Furthermore, most research on parallelization has focused on distributed memory, which neglects the greater flexibility of shared-memory algorithms and the wide availability of commodity multi-core machines. In this thesis, we therefore design and revisit fundamental techniques for each phase of the multilevel approach, and develop highly efficient shared-memory parallel implementations thereof. We consider two iterative improvement algorithms, one based on the Fiduccia-Mattheyses (FM) heuristic, and one based on label propagation. For these, we propose a variety of techniques to improve the accuracy of gains when moving vertices in parallel, as well as low-level algorithmic improvements. For coarsening, we present a parallel variant of greedy agglomerative clustering with a novel method to resolve cluster join conflicts on-the-fly. Combined with a preprocessing phase for coarsening based on community detection, a portfolio of from-scratch partitioning algorithms, as well as recursive partitioning with work-stealing, we obtain our first parallel multilevel framework. It is the fastest partitioner known, and achieves medium-high quality, beating all parallel partitioners, and is close to the highest quality sequential partitioner. Our second contribution is a parallelization of an n-level approach, where only one vertex is contracted and uncontracted on each level. This extreme approach aims at high solution quality via very fine-grained, localized refinement, but seems inherently sequential. We devise an asynchronous n-level coarsening scheme based on a hierarchical decomposition of the contractions, as well as a batch-synchronous uncoarsening, and later fully asynchronous uncoarsening. In addition, we adapt our refinement algorithms, and also use the preprocessing and portfolio. This scheme is highly scalable, and achieves the same quality as the highest quality sequential partitioner (which is based on the same components), but is of course slower than our first framework due to fine-grained uncoarsening. The last ingredient for high quality is an iterative improvement algorithm based on maximum flows. In the sequential setting, we first improve an existing idea by solving incremental maximum flow problems, which leads to smaller cuts and is faster due to engineering efforts. Subsequently, we parallelize the maximum flow algorithm and schedule refinements in parallel. Beyond the strive for highest quality, we present a deterministically parallel partitioning framework. We develop deterministic versions of the preprocessing, coarsening, and label propagation refinement. Experimentally, we demonstrate that the penalties for determinism in terms of partition quality and running time are very small. All of our claims are validated through extensive experiments, comparing our algorithms with state-of-the-art solvers on large and diverse benchmark sets. To foster further research, we make our contributions available in our open-source framework Mt-KaHyPar. While it seems inevitable, that with ever increasing problem sizes, we must transition to distributed memory algorithms, the study of shared-memory techniques is not in vain. With the multilevel approach, even the inherently slow techniques have a role to play in fast systems, as they can be employed to boost quality on coarse levels at little expense. Similarly, techniques for shared-memory parallelism are important, both as soon as a coarse graph fits into memory, and as local building blocks in the distributed algorithm

Algorithms for Triangles, Cones & Peaks

Three different geometric objects are at the center of this dissertation: triangles, cones and peaks. In computational geometry, triangles are the most basic shape for planar subdivisions. Particularly, Delaunay triangulations are a widely used for manifold applications in engineering, geographic information systems, telecommunication networks, etc. We present two novel parallel algorithms to construct the Delaunay triangulation of a given point set. Yao graphs are geometric spanners that connect each point of a given set to its nearest neighbor in each of $k$ cones drawn around it. They are used to aid the construction of Euclidean minimum spanning trees or in wireless networks for topology control and routing. We present the first implementation of an optimal $\mathcal{O}(n \log n)$-time sweepline algorithm to construct Yao graphs. One metric to quantify the importance of a mountain peak is its isolation. Isolation measures the distance between a peak and the closest point of higher elevation. Computing this metric from high-resolution digital elevation models (DEMs) requires efficient algorithms. We present a novel sweep-plane algorithm that can calculate the isolation of all peaks on Earth in mere minutes