On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are entire low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a six-dimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.Comment: 20 page

Multilevel Motion Planning: A Fiber Bundle Formulation

Motion planning problems involving high-dimensional state spaces can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles, which allows us to concisely describe and derive novel algorithms in terms of bundle restrictions and bundle sections. Fiber bundles essentially describe lower-dimensional projections of the state space using local product spaces. Given such a structure and a corresponding admissible constraint function, we can develop highly efficient and optimal search-based motion planning methods for high-dimensional state spaces. Our contributions are the following: We first introduce the terminology of fiber bundles, in particular the notion of restrictions and sections. Second, we use the notion of restrictions and sections to develop novel multilevel motion planning algorithms, which we call QRRT* and QMP*. We show these algorithms to be probabilistically complete and almost-surely asymptotically optimal. Third, we develop a novel recursive path section method based on an L1 interpolation over path restrictions, which we use to quickly find feasible path sections. And fourth, we evaluate all novel algorithms against all available OMPL algorithms on benchmarks of eight challenging environments ranging from 21 to 100 degrees of freedom, including multiple robots and nonholonomic constraints. Our findings support the efficiency of our novel algorithms and the benefit of exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR

Sampling-Based Motion Planning: A Comparative Review

Sampling-based motion planning is one of the fundamental paradigms to generate robot motions, and a cornerstone of robotics research. This comparative review provides an up-to-date guideline and reference manual for the use of sampling-based motion planning algorithms. This includes a history of motion planning, an overview about the most successful planners, and a discussion on their properties. It is also shown how planners can handle special cases and how extensions of motion planning can be accommodated. To put sampling-based motion planning into a larger context, a discussion of alternative motion generation frameworks is presented which highlights their respective differences to sampling-based motion planning. Finally, a set of sampling-based motion planners are compared on 24 challenging planning problems. This evaluation gives insights into which planners perform well in which situations and where future research would be required. This comparative review thereby provides not only a useful reference manual for researchers in the field, but also a guideline for practitioners to make informed algorithmic decisions.Comment: 25 pages, 7 figures, Accepted for Volume 7 (2024) of the Annual Review of Control, Robotics, and Autonomous System

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

Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.Comment: Kiril Solovey and Oren Salzman contributed equally to this pape

Learning of Generalized Manipulation Strategies in Service Robotics

This thesis makes a contribution to autonomous robotic manipulation. The core is a novel constraint-based representation of manipulation tasks suitable for flexible online motion planning. Interactive learning from natural human demonstrations is combined with parallelized optimization to enable efficient learning of complex manipulation tasks with limited training data. Prior planning results are encoded automatically into the model to reduce planning time and solve the correspondence problem

On Providing Efficient Real-Time Solutions to Motion Planning Problems of High Complexity

The holy grail of robotics is producing robotic systems capable of efficiently executing all the tasks that are hard, or even impossible, for humans. Humans, undoubtedly, from both a hardware and software perspective, are extremely complex systems capable of executing many complicated tasks. Thus, the complexity of many state-of-the-art robotic systems is also expected to progressively increase, with the goal to match or even surpass human abilities. Recent developments have emphasized mostly hardware, providing highly complex robots with exceptional capabilities. On the other hand, they have illustrated that one important bottleneck of realizing such systems as a common reality is real-time motion planning. This thesis aims to assist the development of complex robotic systems from a computational perspective. The primary focus is developing novel methodologies to address real-time motion planning that enables the robots to accomplish their goals safely and provide the building blocks for developing robust advanced robot behavior in the future. The proposed methods utilize and enhance state-of-the-art approaches to overcome three different types of complexity: 1. Motion planning for high-dimensional systems. RRT+, a new family of general sampling-based planners, was introduced to accelerate solving the motion planning problem for robotic systems with many degrees of freedom by iteratively searching in lowerdimensional subspaces of increasing dimension. RRT+ variants computed solutions orders of magnitude faster compared to state-of-the-art planners. Experiments in simulation of kinematic chains up to 50 degrees of freedom, and the Baxter humanoid robot validate the effectiveness of the proposed technique. 2. Underwater navigation for robots in cluttered environments. AquaNav, a real-time navigation pipeline for robots moving efficiently in challenging, unknown, and unstructured environments, was developed for Aqua2, a hexapod swimming robot with complex, yet to be fully discovered, dynamics. AquaNav was tested offline in known maps, and online in unknown maps utilizing vision-based SLAM. Rigorous testing in simulation, inpool, and open-water trials show the robustness of the method on providing efficient and safe performance, enabling the robot to navigate by avoiding static and dynamic obstacles in open-water settings with turbidity and surge. 3. Active perception of areas of interest during underwater operation. AquaVis, an extension of AquaNav, is a real-time navigation technique enabling robots, with arbitrary multi-sensor configurations, to safely reach their target, while at the same time observing multiple areas of interest from a desired proximity. Extensive simulations show safe behavior, and strong potential for improving underwater state estimation, monitoring, tracking, inspection, and mapping of objects of interest in the underwater domain, such as coral reefs, shipwrecks, marine life, and human infrastructure

Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency