Sparse roadmaps are important to compactly represent state spaces, to determine problems to be infeasible and to terminate in finite time. However, sparse roadmaps do not scale well to high-dimensional planning problems. In prior work, we showed improved planning performance on high-dimensional planning problems by using multilevel abstractions to simplify state spaces. In this work, we generalize sparse roadmaps to multilevel abstractions by developing a novel algorithm, the sparse multilevel roadmap planner (SMLR). To this end, we represent multilevel abstractions using the language of fiber bundles, and generalize sparse roadmap planners by using the concept of restriction sampling with visibility regions. We argue SMLR to be probabilistically complete and asymptotically near-optimal by inheritance from sparse roadmap planners. In evaluations, we outperform sparse roadmap planners on challenging planning problems, in particular problems which are high-dimensional, contain narrow passages or are infeasible. We thereby demonstrate sparse multilevel roadmaps as an efficient tool for feasible and infeasible high-dimensional planning problems.
Stanford University（斯坦福大学）；Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）
We propose an algorithmic framework for efficient anytime motion planning on large dense geometric roadmaps, in domains where collision checks and therefore edge evaluations are computationally expensive. A large dense roadmap (graph) can typically ensure the existence of high quality solutions for most motion-planning problems, but the size of the roadmap, particularly in high-dimensional spaces, makes existing search-based planning algorithms computationally expensive. We deal with the challenges of expensive search and collision checking in two ways. First, we frame the problem of anytime m…
Zhejiang University（浙江大学）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）；DJI（大疆创新）
Free-space-oriented roadmaps typically generate a series of convex geometric primitives, which constitute the safe region for motion planning. However, a static environment is assumed for this kind of roadmap. This assumption makes it unable to deal with dynamic obstacles and limits its applications. In this paper, we present a dynamic free-space roadmap, which provides feasible spaces and a navigation graph for safe quadrotor motion planning. Our roadmap is constructed by continuously seeding and extracting free regions in the environment. In order to adapt our map to environments with dynami…
We propose the Selective Densification method for fast motion planning through configuration space. We create a sequence of roadmaps by iteratively adding configurations. We organize these roadmaps into layers and add edges between identical configurations between layers. We find a path using best-first search, guided by our proposed estimate of remaining planning time. This estimate prefers to expand nodes closer to the goal and nodes on sparser layers. We present proofs of the path quality and maximum depth of nodes expanded using our proposed graph and heuristic. We also present experiments…
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 scenari…
Multi-robot motion planning problems often have many local minima. It is essential to visualize those local minima such that we can better understand, debug and interact with multi-robot systems. Towards this goal, we present the multi-robot motion explorer, an algorithm which extends previous results on multilevel Morse theory by introducing a component-based framework, where we reduce multi-robot configuration spaces by reducing each robots component space using fiber bundles. Our algorithm exploits this component structure to search for and visualize local minima. A user of the algorithm ca…
Indian Institute of Technology, Kharagpur（印度理工学院克勒格布尔分校）；University of Washington（华盛顿大学）
We consider the problem of leveraging prior experience to generate roadmaps in sampling-based motion planning. A desirable roadmap is one that is sparse, allowing for fast search, with nodes spread out at key locations such that a low-cost feasible path exists. An increasingly popular approach is to learn a distribution of nodes that would produce such a roadmap. State-of-the-art is to train a conditional variational auto-encoder (CVAE) on the prior dataset with the shortest paths as target input. While this is quite effective on many problems, we show it can fail in the face of complex obstac…
We present Roadmap Sparsification by Edge Contraction (RSEC), a simple and effective algorithm for reducing the size of a motion-planning roadmap. The algorithm exhibits minimal effect on the quality of paths that can be extracted from the new roadmap. The primitive operation used by RSEC is edge contraction - the contraction of a roadmap edge to a single vertex and the connection of the new vertex to the neighboring vertices of the contracted edge. For certain scenarios, we compress more than 98% of the edges and vertices at the cost of degradation of average shortest path length by at most 2…
We present an evaluation of several representative sampling-based and optimization-based motion planners, and then introduce an integrated motion planning system which incorporates recent advances in trajectory optimization into a sparse roadmap framework. Through experiments in 4 common application scenarios with 5000 test cases each, we show that optimization-based or sampling-based planners alone are not effective for realistic problems where fast planning times are required. To the best of our knowledge, this is the first work that presents such a systematic and comprehensive evaluation of…
We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches $\mathcal{G}$, running in $O(V\textrm{log}V + E) \approx O(n^2)$ time, becomes unacceptably expensive. We are therefore interested in anytime search to obtain successively shorter feasible paths and converge to the shortest path in $\mathcal{G}$. Our key insight is to provide existing path-planning algorithms with a sequence of increasingly dense subgraphs …
Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院人类工程与机器人研究所）；Robotics and Autonomous Systems, Institute of Applied Research, Karlsruhe University of Applied Sciences（卡尔斯鲁厄应用技术大学应用研究所机器人与自主系统部）
Real-time motion planning is a vital function of robotic systems. Different from existing roadmap algorithms which first determine the free space and then determine the collision-free path, researchers recently proposed several convex relaxation based smoothing algorithms which first select an initial path to link the starting configuration and the goal configuration and then reshape this path to meet other requirements (e.g., collision-free conditions) by using convex relaxation. However, convex relaxation based smoothing algorithms often fail to give a satisfactory path, since the initial pa…
University of Colorado（科罗拉多大学）；Google [x]；Rice University（莱斯大学）
We present an experienced-based planning framework called Thunder that learns to reduce computation time required to solve high-dimensional planning problems in varying environments. The approach is especially suited for large configuration spaces that include many invariant constraints, such as those found with whole body humanoid motion planning. Experiences are generated using probabilistic sampling and stored in a sparse roadmap spanner (SPARS), which provides asymptotically near-optimal coverage of the configuration space, making storing, retrieving, and repairing past experiences very ef…
In this paper, we extend the recent body of work on planning under uncertainty to include the fact that sensors may not provide any measurement owing to misdetection. This is caused either by adverse environmental conditions that prevent the sensors from making measurements or by the fundamental limitations of the sensors. Examples include RF-based ranging devices that intermittently do not receive the signal from beacons because of obstacles; the misdetection of features by a camera system in detrimental lighting conditions; a LIDAR sensor that is pointed at a glass-based material such as a w…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Technical University of Berlin（柏林工业大学）
Sampling-based planning methods often become inefficient due to narrow passages. Narrow passages induce a higher runtime, because the chance to sample them becomes vanishingly small. In recent work, we showed that narrow passages can be approached by relaxing the problem using admissible lower-dimensional projections of the state space. Those relaxations often increase the volume of narrow passages under projection. Solving the relaxed problem is often efficient and produces an admissible heuristic we can exploit. However, given a base path, i.e. a solution to a relaxed problem, there are curr…
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Carnegie Mellon University（卡内基梅隆大学）
Inspection planning, the task of planning motions that allow a robot to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans that inspect the points of interest grows exponentially with the number of inspected points. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of inspected points asymptotically converge to those of an optimal inspection plan. IRIS increm…
Sampling-based motion planning techniques have emerged as an efficient algorithmic paradigm for solving complex motion planning problems. These approaches use a set of probing samples to construct an implicit graph representation of the robot's state space, allowing arbitrarily accurate representations as the number of samples increases to infinity. In practice, however, solution trajectories only rely on a few critical states, often defined by structure in the state space (e.g., doorways). In this work we propose a general method to identify these critical states via graph-theoretic technique…
Tokyo Institute of Technology（东京工业大学）；OMRON SINIC X（欧姆龙先尼克斯）
Multi-agent path planning (MAPP) in continuous spaces is a challenging problem with significant practical importance. One promising approach is to first construct graphs approximating the spaces, called roadmaps, and then apply multi-agent pathfinding (MAPF) algorithms to derive a set of conflict-free paths. While conventional studies have utilized roadmap construction methods developed for single-agent planning, it remains largely unexplored how we can construct roadmaps that work effectively for multiple agents. To this end, we propose a novel concept of roadmaps called cooperative timed roa…
Australian National University（澳大利亚国立大学）；CSIRO（澳大利亚联邦科学与工业研究组织）
Planning under partial obervability is essential for autonomous robots. A principled way to address such planning problems is the Partially Observable Markov Decision Process (POMDP). Although solving POMDPs is computationally intractable, substantial advancements have been achieved in developing approximate POMDP solvers in the past two decades. However, computing robust solutions for systems with complex dynamics remain challenging. Most on-line solvers rely on a large number of forward-simulations and standard Monte-Carlo methods to compute the expected outcomes of actions the robot can per…
Sampling based probabilistic roadmap planners (PRM) have been successful in motion planning of robots with higher degrees of freedom, but may fail to capture the connectivity of the configuration space in scenarios with a critical narrow passage. In this paper, we show a novel technique based on Levy Flights to generate key samples in the narrow regions of configuration space, which, when combined with a PRM, improves the completeness of the planner. The technique substantially improves sample quality at the expense of a minimal additional computation, when compared with pure random walk based…
We study the problem of motion-planning for free-flying multi-link robots and develop a sampling-based algorithm that is specifically tailored for the task. Our work is based on the simple observation that the set of configurations for which the robot is self-collision free is independent of the obstacles or of the exact placement of the robot. This allows to eliminate the need to perform costly self-collision checks online when solving motion-planning problems, assuming some offline preprocessing. In particular, given a specific robot type our algorithm precomputes a tiling roadmap, which eff…
A motion planning algorithm computes the motion of a robot by computing a path through its configuration space. To improve the runtime of motion planning algorithms, we propose to nest robots in each other, creating a nested quotient-space decomposition of the configuration space. Based on this decomposition we define a new roadmap-based motion planning algorithm called the Quotient-space roadMap Planner (QMP). The algorithm starts growing a graph on the lowest dimensional quotient space, switches to the next quotient space once a valid path has been found, and keeps updating the graphs on eac…
Montefiore Institute（蒙特菲奥雷研究所）；University of Liège（列日大学）
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be followed around a given set of obstacles. Our solution consists in an original refinement algorithm for constrained Delaunay triangulations, aimed at generating a roadmap graph suited for planning paths with arbitrary clearance. In other words, a minimum distance to the obstacles can be specified, and the graph does not have to be recomputed if this distance…
We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown…
Motion planning has been studied for nearly four decades now. Complete, combinatorial motion planning approaches are theoretically well-rooted with completeness guarantees but they are hard to implement. Sampling-based and heuristic methods are easy to implement and quite simple to customize but they lack completeness guarantees. Can the best of both worlds be ever achieved, particularly for mission critical applications such as robotic surgery, space explorations, and handling hazardous material? In this paper, we answer affirmatively to that question. We present a new methodology, NUROA, to …
Sampling based planners have been successful in robot motion planning, with many degrees of freedom, but still remain ineffective in the presence of narrow passages within the configuration space. There exist several heuristics, which generate samples in the critical regions and improve the efficiency of probabilistic roadmap planners. In this paper, we present an evaluation of success probability of one such heuristic method, called obstacle based probabilistic roadmap planners or OBPRM, using geometric probability theory. The result indicates that the probability of success of generating fre…
A landmark based heuristic is investigated for reducing query phase run-time of the probabilistic roadmap (\PRM) motion planning method. The heuristic is generated by storing minimum spanning trees from a small number of vertices within the \PRM graph and using these trees to approximate the cost of a shortest path between any two vertices of the graph. The intermediate step of preprocessing the graph increases the time and memory requirements of the classical motion planning technique in exchange for speeding up individual queries making the method advantageous in multi-query applications. Th…
We study the effectiveness of metrics for Multi-Robot Motion-Planning (MRMP) when using RRT-style sampling-based planners. These metrics play the crucial role of determining the nearest neighbors of configurations and in that they regulate the connectivity of the underlying roadmaps produced by the planners and other properties like the quality of solution paths. After screening over a dozen different metrics we focus on the five most promising ones- two more traditional metrics, and three novel ones which we propose here, adapted from the domain of shape-matching. In addition to the novel mul…
Serialized Red-Green-Gray: Quicker Heuristic Validation of Edges in Dynamic Roadmap Graphs
Siebel School of Computing and Data Science, University of Illinois（伊利诺伊大学西贝尔计算与数据科学学院）；Department of Computer Science, Instituto Tecnológico Autónomo de México (ITAM)（墨西哥自治技术学院计算机科学系）
University of Washington（华盛顿大学）；Carnegie Mellon University（卡内基梅隆大学）
Motion-planning problems, such as manipulation in cluttered environments, often require a collision-free shortest path to be computed quickly given a roadmap graph. Typically, the computational cost of evaluating whether an edge of the roadmap graph is collision-free dominates the running time of search algorithms. Algorithms such as Lazy Weighted A* (LWA*) and LazySP have been proposed to reduce the number of edge evaluations by employing a lazy lookahead (one-step lookahead and infinite-step lookahead, respectively). However, this comes at the expense of additional graph operations: the larg…
Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that they solve challenges efficiently by giving up formal guarantees and instead attain asymptotic properties in terms of completeness and optimality. Recent work has argued based on Monte Carlo experiments that these approaches also exhibit desirable probabilistic properties in terms of completeness and optimality after finite computation. The current paper formal…
Texas A&M University（德克萨斯农工大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Instituto Tecnológico Autónomo de México (ITAM)（墨西哥自治技术研究所）
We present a hierarchical skeleton-guided motion planning algorithm to guide mobile robots. A good skeleton maps the connectivity of the subspace of c-space containing significant degrees of freedom and is able to guide the planner to find the desired solutions fast. However, sometimes the skeleton does not closely represent the free c-space, which often misleads current skeleton-guided planners. The hierarchical skeleton-guided planning strategy gradually relaxes its reliance on the workspace skeleton as C space is sampled, thereby incrementally returning a sub-optimal path, a feature that is…
Georgia Institute of Technology（佐治亚理工学院）；California Institute of Technology（加州理工学院）
A new belief space planning algorithm, called covariance steering Belief RoadMap (CS-BRM), is introduced, which is a multi-query algorithm for motion planning of dynamical systems under simultaneous motion and observation uncertainties. CS-BRM extends the probabilistic roadmap (PRM) approach to belief spaces and is based on the recently developed theory of covariance steering (CS) that enables guaranteed satisfaction of terminal belief constraints in finite-time. The nodes in the CS-BRM are sampled in belief space and represent distributions of the system states. A covariance steering controll…
This paper introduces Probabilistic Chekov (p-Chekov), a chance-constrained motion planning system that can be applied to high degree-of-freedom (DOF) robots under motion uncertainty and imperfect state information. Given process and observation noise models, it can find feasible trajectories which satisfy a user-specified bound over the probability of collision. Leveraging our previous work in deterministic motion planning which integrated trajectory optimization into a sparse roadmap framework, p-Chekov shows superiority in its planning speed for high-dimensional tasks. P-Chekov incorporates…
Univ. of Michigan（密歇根大学）；Rutgers Univ.（罗格斯大学）；Tel Aviv Univ.（特拉维夫大学）
Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle, by exploring the composite space of all robots. Sampling-based planners do so by building a roadmap or a tree data structure in the corresponding configuration space and can achieve asymptotic optimality. The hardness of motion planning, however, renders the explicit construction of such structures in the composite space of multiple robots impractical. This…
