We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli (2011) and subsequent work. Particularly, we prove the existence of a critical connection radius proportional to ${Θ(n^{-1/d})}$ for $n$ samples and ${d}$ dimensions: Below this value the planner is guaranteed to fail (similarly shown by the aforementioned work, ibid.). More importantly, for larger radius values the planner is asymptotically (near-)optimal. Furthermore, our analysis yields an explicit lower bound of ${1-O( n^{-1})}$ on the probability of success. A practical implication of our work is that asymptotic (near-)optimality is achieved when each sample is connected to only ${Θ(1)}$ neighbors. This is in stark contrast to previous work which requires ${Θ(\log n)}$ connections, that are induced by a radius of order ${\left(\frac{\log n}{n}\right)^{1/d}}$. Our analysis is not restricted to PRM and applies to a variety of PRM-based planners, including RRG, FMT* and BTT. Continuum percolation plays an important role in our proofs. Lastly, we develop similar theory for all the aforementioned planners when constructed with deterministic samples, which are then sparsified in a randomized fashion. We believe that this new model, and its analysis, is interesting in its own right.
Institute for Robotics and Intelligent Machines（机器人与智能机器研究所）；Georgia Institute of Technology（佐治亚理工学院）
Sampling-based algorithms solve the path planning problem by generating random samples in the search-space and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased towards exploration to acquire information about the search-space. In contrast, this work proposes an optimization-based procedure that generates new samples to improve the cost-to-come value of vertices in a neighborhood. The application of proposed algorithm adds an exploitative-bias to sampling and results in a faster convergence to the optimal solution com…
Sampling-based motion planning under task constraints is challenging because the null-measure constraint manifold in the configuration space makes rejection sampling extremely inefficient, if not impossible. This paper presents a learning-based sampling strategy for constrained motion planning problems. We investigate the use of two well-known deep generative models, the Conditional Variational Autoencoder (CVAE) and the Conditional Generative Adversarial Net (CGAN), to generate constraint-satisfying sample configurations. Instead of precomputed graphs, we use generative models conditioned on …
Zhejiang University（浙江大学）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）；The University of Hong Kong（香港大学）
For real-time multirotor kinodynamic motion planning, the efficiency of sampling-based methods is usually hindered by difficult-to-sample homotopy classes like narrow passages. In this paper, we address this issue by a hybrid scheme. We firstly propose a fast regional optimizer exploiting the information of local environments and then integrate it into a global sampling process to ensure faster convergence. The incorporation of local optimization on different sampling-based methods shows significantly improved success rates and less planning time in various types of challenging environments. W…
GAIDE: Graph-based Attention Masking for Spatial- and Embodiment-aware Motion Planning
J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA（J. Mike Walker ’66 机械工程系，德克萨斯A&M大学，College Station, TX 77843, USA）；Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843 USA（Zachry 市政与环境工程系，德克萨斯A&M大学，College Station, TX 77843 USA）
The University of Sydney（悉尼大学）；University of Utah（犹他大学）；NVIDIA（英伟达）
We propose Parallelised Diffeomorphic Sampling-based Motion Planning (PDMP). PDMP is a novel parallelised framework that uses bijective and differentiable mappings, or diffeomorphisms, to transform sampling distributions of sampling-based motion planners, in a manner akin to normalising flows. Unlike normalising flow models which use invertible neural network structures to represent these diffeomorphisms, we develop them from gradient information of desired costs, and encode desirable behaviour, such as obstacle avoidance. These transformed sampling distributions can then be used for sampling-…
Improving Efficiency of Sampling-based Motion Planning via Message-Passing Monte Carlo
CSAIL, MIT（MIT计算机科学与人工智能实验室）；ELLIS Institute（埃里克·林斯研究所）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Tübingen AI Center（图宾根人工智能中心）；Case Western Reserve University（凯斯西储大学）
Among the most prevalent motion planning techniques, sampling and trajectory optimization have emerged successful due to their ability to handle tight constraints and high-dimensional systems, respectively. However, limitations in sampling in higher dimensions and local minima issues in optimization have hindered their ability to excel beyond static scenes in offline settings. Here we consider highly dynamic environments with long horizons that necessitate a fast online solution. We present a unified approach that leverages the complementary strengths of sampling and optimization, and interlea…
Sampling-based motion planning is a popular approach in robotics for finding paths in continuous configuration spaces. Checking collision with obstacles is the major computational bottleneck in this process. We propose new learning-based methods for reducing collision checking to accelerate motion planning by training graph neural networks (GNNs) that perform path exploration and path smoothing. Given random geometric graphs (RGGs) generated from batch sampling, the path exploration component iteratively predicts collision-free edges to prioritize their exploration. The path smoothing componen…
FZI Research Center for Information Technology（FZI信息技术研究中心）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
Decision making under uncertainty can be framed as a partially observable Markov decision process (POMDP). Finding exact solutions of POMDPs is generally computationally intractable, but the solution can be approximated by sampling-based approaches. These sampling-based POMDP solvers rely on multi-armed bandit (MAB) heuristics, which assume the outcomes of different actions to be uncorrelated. In some applications, like motion planning in continuous spaces, similar actions yield similar outcomes. In this paper, we utilize variants of MAB heuristics that make Lipschitz continuity assumptions on…
Multicopters with collision-resilient designs can operate with trajectories involving collisions. This paper presents a sampling-based method that can exploit collisions for better motion planning. The method is built upon the basis of the RRT* algorithm and takes advantages of fast motion primitive generation and collision checking for multicopters. It generates collision states by detecting potential intersections between motion primitives and obstacles, and connects these states with other sampled states to form collision-inclusive trajectories. We show that allowing collision helps improve…
Generalizing Informed Sampling for Asymptotically Optimal Sampling-based Kinodynamic Planning via Markov Chain Monte Carlo
Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Paul G. Allen School of Computer Science & Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学院）
Optimal Sampling-Based Motion Planning under Differential Constraints: the Driftless Case
Institute for Computational & Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Department of Statistics, Stanford University（斯坦福大学统计系）；Department of Aeronautics and Astronautics, Stanford University（斯坦福大学航空航天系）
Asymptotically Optimal Lazy Lifelong Sampling-based Algorithm for Efficient Motion Planning in Dynamic Environments
Department of Mechanical Engineering, City University of Hongkong（机械工程系，香港城市大学）；Department of Electronic and Electrical Engineering, Southern University of Science and Technology（电子与电气工程系，南方科技大学）；Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology（电子与计算机工程系，香港科技大学）
Relevant Region Sampling Strategy with Adaptive Heuristic for Asymptotically Optimal Path Planning
The Chinese University of Hong Kong（香港中文大学）；Southern University of Science and Technology（南方科技大学）；Shenzhen Research Institute of the Chinese University of Hong Kong（香港中文大学深圳研究院）
Robot motion planning involves computing a sequence of valid robot configurations that take the robot from its initial state to a goal state. Solving a motion planning problem optimally using analytical methods is proven to be PSPACE-Hard. Sampling-based approaches have tried to approximate the optimal solution efficiently. Generally, sampling-based planners use uniform samplers to cover the entire state space. In this paper, we propose a deep-learning-based framework that identifies robot configurations in the environment that are important to solve the given motion planning problem. These st…
University of Stuttgart（斯图加特大学）；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）
Contact-based motion planning for manipulation, object exploration or balancing often requires finding sequences of fixed and sliding contacts and planning the transition from one contact in the environment to another. However, most existing algorithms concentrate on the control and learning aspect of sliding contacts, but do not embed the problem into a principled framework to provide guarantees on completeness or optimality. To address this problem, we propose a method to extend constraint-based planning using contact transitions for sliding contacts. Such transitions are elementary operatio…
Asymptotically optimal sampling-based planners require an intelligent exploration strategy to accelerate convergence. After an initial solution is found, a necessary condition for improvement is to generate new samples in the so-called "Informed Set". However, Informed Sampling can be ineffective in focusing search if the chosen heuristic fails to provide a good estimate of the solution cost. This work proposes an algorithm to sample the "Relevant Region" instead, which is a subset of the Informed Set. The Relevant Region utilizes cost-to-come information from the planner's tree structure, red…
Indian Institute of Technology Kharagpur（印度理工学院哈拉格普尔分校）
Sampling based methods are widely used for robotic motion planning. Traditionally, these samples are drawn from probabilistic ( or deterministic ) distributions to cover the state space uniformly. Despite being probabilistically complete, they fail to find a feasible path in a reasonable amount of time in constrained environments where it is essential to go through narrow passages (bottleneck regions). Current state of the art techniques train a learning model (learner) to predict samples selectively on these bottleneck regions. However, these algorithms depend completely on samples generated …
The Chinese University of Hong Kong（香港中文大学）；Southern University of Science and Technology（南方科技大学）；Shenzhen Research Institute of The Chinese University of Hong Kong（香港中文大学深圳研究院）
Sampling-based path planning algorithms usually implement uniform sampling methods to search the state space. However, uniform sampling may lead to unnecessary exploration in many scenarios, such as the environment with a few dead ends. Our previous work proposes to use the promising region to guide the sampling process to address the issue. However, the predicted promising regions are often disconnected, which means they cannot connect the start and goal state, resulting in a lack of probabilistic completeness. This work focuses on enhancing the connectivity of predicted promising regions. Ou…
Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also optimize a cost function, such as path length. Formal path-quality guarantees for continuously valued search spaces are an active area of research interest. Recent results have proven that some sampling-based planning methods probabilistically converge toward the optimal solution as computational effort approaches infinity. This survey summarizes the assump…
This work investigates the use of Neural implicit representations, specifically Neural Radiance Fields (NeRF), for geometrical queries and motion planning. We show that by adding the capacity to infer occupancy in a radius to a pre-trained NeRF, we are effectively learning an approximation to a Euclidean Signed Distance Field (ESDF). Using backward differentiation of the augmented network, we obtain an obstacle gradient that is integrated into an obstacle avoidance policy based on the Riemannian Motion Policies (RMP) framework. Thus, our findings allow for very fast sampling-free obstacle avoi…
Combining Sampling- and Gradient-based Planning for Contact-rich Manipulation
Politecnico di Milano（米兰理工大学）；Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA)（达勒·莫勒人工智能研究所）；Scuola Universitaria Professionale della Svizzera Italiana (SUPSI)（瑞士意大利语区应用科学大学）；Università della Svizzera Italiana (USI)（瑞士意大利语区大学）；Fraunhofer IPK（弗劳恩霍夫制造工程和自动化研究所）
This paper presents a hybrid robot motion planner that generates long-horizon motion plans for robot navigation in environments with obstacles. We propose a hybrid planner, RRT* with segmented trajectory optimization (RRT*-sOpt), which combines the merits of sampling-based planning, optimization-based planning, and trajectory splitting to quickly plan for a collision-free and dynamically-feasible motion plan. When generating a plan, the RRT* layer quickly samples a semi-optimal path and sets it as an initial reference path. Then, the sOpt layer splits the reference path and performs optimizati…
Sampling-based motion planners such as RRT* and BIT*, when applied to kinodynamic motion planning, rely on steering functions to generate time-optimal solutions connecting sampled states. Implementing exact steering functions requires either analytical solutions to the time-optimal control problem, or nonlinear programming (NLP) solvers to solve the boundary value problem given the system's kinodynamic equations. Unfortunately, analytical solutions are unavailable for many real-world domains, and NLP solvers are prohibitively computationally expensive, hence fast and optimal kinodynamic motion…
Informative path planning is an important and challenging problem in robotics that remains to be solved in a manner that allows for wide-spread implementation and real-world practical adoption. Among various reasons for this, one is the lack of approaches that allow for informative path planning in high-dimensional spaces and non-trivial sensor constraints. In this work we present a sampling-based approach that allows us to tackle the challenges of large and high-dimensional search spaces. This is done by performing informed sampling in the high-dimensional continuous space and incorporating p…
Planning for legged-wheeled machines is typically done using trajectory optimization because of many degrees of freedom, thus rendering legged-wheeled planners prone to falling prey to bad local minima. We present a combined sampling and optimization-based planning approach that can cope with challenging terrain. The sampling-based stage computes whole-body configurations and contact schedule, which speeds up the optimization convergence. The optimization-based stage ensures that all the system constraints, such as non-holonomic rolling constraints, are satisfied. The evaluations show the impo…
