Kostas E. Bekris

Shiyang Lu, Haonan Chang, Eric Pu Jing et al.

This work presents OVIR-3D, a straightforward yet effective method for open-vocabulary 3D object instance retrieval without using any 3D data for training. Given a language query, the proposed method is able to return a ranked set of 3D object instance segments based on the feature similarity of the instance and the text query. This is achieved by a multi-view fusion of text-aligned 2D region proposals into 3D space, where the 2D region proposal network could leverage 2D datasets, which are more accessible and typically larger than 3D datasets. The proposed fusion process is efficient as it can be performed in real-time for most indoor 3D scenes and does not require additional training in 3D space. Experiments on public datasets and a real robot show the effectiveness of the method and its potential for applications in robot navigation and manipulation.

Haonan Chang, Kowndinya Boyalakuntla, Shiyang Lu et al.

We present an Open-Vocabulary 3D Scene Graph (OVSG), a formal framework for grounding a variety of entities, such as object instances, agents, and regions, with free-form text-based queries. Unlike conventional semantic-based object localization approaches, our system facilitates context-aware entity localization, allowing for queries such as ``pick up a cup on a kitchen table" or ``navigate to a sofa on which someone is sitting". In contrast to existing research on 3D scene graphs, OVSG supports free-form text input and open-vocabulary querying. Through a series of comparative experiments using the ScanNet dataset and a self-collected dataset, we demonstrate that our proposed approach significantly surpasses the performance of previous semantic-based localization techniques. Moreover, we highlight the practical application of OVSG in real-world robot navigation and manipulation experiments.

Troy McMahon, Aravind Sivaramakrishnan, Edgar Granados et al.

Sampling-based methods are widely adopted solutions for robot motion planning. The methods are straightforward to implement, effective in practice for many robotic systems. It is often possible to prove that they have desirable properties, such as probabilistic completeness and asymptotic optimality. Nevertheless, they still face challenges as the complexity of the underlying planning problem increases, especially under tight computation time constraints, which impact the quality of returned solutions or given inaccurate models. This has motivated machine learning to improve the computational efficiency and applicability of Sampling-Based Motion Planners (SBMPs). This survey reviews such integrative efforts and aims to provide a classification of the alternative directions that have been explored in the literature. It first discusses how learning has been used to enhance key components of SBMPs, such as node sampling, collision detection, distance or nearest neighbor computation, local planning, and termination conditions. Then, it highlights planners that use learning to adaptively select between different implementations of such primitives in response to the underlying problem's features. It also covers emerging methods, which build complete machine learning pipelines that reflect the traditional structure of SBMPs. It also discusses how machine learning has been used to provide data-driven models of robots, which can then be used by a SBMP. Finally, it provides a comparative discussion of the advantages and disadvantages of the approaches covered, and insights on possible future directions of research. An online version of this survey can be found at: https://prx-kinodynamic.github.io/

Rui Wang, Kai Gao, Jingjin Yu et al.

Object rearrangement is important for many applications but remains challenging, especially in confined spaces, such as shelves, where objects cannot be accessed from above and they block reachability to each other. Such constraints require many motion planning and collision checking calls, which are computationally expensive. In addition, the arrangement space grows exponentially with the number of objects. To address these issues, this work introduces a lazy evaluation framework with a local monotone solver and a global planner. Monotone instances are those that can be solved by moving each object at most once. A key insight is that reachability constraints at the grasps for objects' starts and goals can quickly reveal dependencies between objects without having to execute expensive motion planning queries. Given that, the local solver builds lazily a search tree that respects these reachability constraints without verifying that the arm paths are collision free. It only collision checks when a promising solution is found. If a monotone solution is not found, the non-monotone planner loads the lazy search tree and explores ways to move objects to intermediate locations from where monotone solutions to the goal can be found. Results show that the proposed framework can solve difficult instances in confined spaces with up to 16 objects, which state-of-the-art methods fail to solve. It also solves problems faster than alternatives, when the alternatives find a solution. It also achieves high-quality solutions, i.e., only 1.8 additional actions on average are needed for non-monotone instances.

Junchi Liang, Bowen Wen, Kostas Bekris et al.

This work aims to learn how to perform complex robot manipulation tasks that are composed of several, consecutively executed low-level sub-tasks, given as input a few visual demonstrations of the tasks performed by a person. The sub-tasks consist of moving the robot's end-effector until it reaches a sub-goal region in the task space, performing an action, and triggering the next sub-task when a pre-condition is met. Most prior work in this domain has been concerned with learning only low-level tasks, such as hitting a ball or reaching an object and grasping it. This paper describes a new neural network-based framework for learning simultaneously low-level policies as well as high-level policies, such as deciding which object to pick next or where to place it relative to other objects in the scene. A key feature of the proposed approach is that the policies are learned directly from raw videos of task demonstrations, without any manual annotation or post-processing of the data. Empirical results on object manipulation tasks with a robotic arm show that the proposed network can efficiently learn from real visual demonstrations to perform the tasks, and outperforms popular imitation learning algorithms.

Kristin J. Dana, Clinton Andrews, Kostas Bekris et al.

Emerging applications of robotics, and concerns about their impact, require the research community to put human-centric objectives front-and-center. To meet this challenge, we advocate an interdisciplinary approach, socially cognizant robotics, which synthesizes technical and social science methods. We argue that this approach follows from the need to empower stakeholder participation (from synchronous human feedback to asynchronous societal assessment) in shaping AI-driven robot behavior at all levels, and leads to a range of novel research perspectives and problems both for improving robots' interactions with individuals and impacts on society. Drawing on these arguments, we develop best practices for socially cognizant robot design that balance traditional technology-based metrics (e.g. efficiency, precision and accuracy) with critically important, albeit challenging to measure, human and society-based metrics.

Shuai Li, Azarakhsh Keipour, Kevin Jamieson et al.

Automating warehouse operations can reduce logistics overhead costs, ultimately driving down the final price for consumers, increasing the speed of delivery, and enhancing the resiliency to market fluctuations. This extended abstract showcases a large-scale package manipulation from unstructured piles in Amazon Robotics' Robot Induction (Robin) fleet, which is used for picking and singulating up to 6 million packages per day and so far has manipulated over 2 billion packages. It describes the various heuristic methods developed over time and their successor, which utilizes a pick success predictor trained on real production data. To the best of the authors' knowledge, this work is the first large-scale deployment of learned pick quality estimation methods in a real production system.

Edgar Granados, Patrick Meng, Charles Tang et al.

Tensegrity robots offer compliance and adaptability, but their nonlinear, and underconstrained dynamics make state estimation challenging. Reliable continuous-time estimation of all rigid links is crucial for closed-loop control, system identification, and machine learning; however, conventional methods often fall short. This paper proposes a two-stage approach for robust state or trajectory estimation (i.e., filtering or smoothing) of a cable-driven tensegrity robot. For online state estimation, this work introduces a factor-graph-based method, which fuses measurements from an RGB-D camera with on-board cable length sensors. To the best of the authors' knowledge, this is the first application of factor graphs in this domain. Factor graphs are a natural choice, as they exploit the robot's structural properties and provide effective sensor fusion solutions capable of handling nonlinearities in practice. Both the Mahalanobis distance-based clustering algorithm, used to handle noise, and the Chebyshev polynomial method, used to estimate the most probable velocities and intermediate states, are shown to perform well on simulated and real-world data, compared to an ICP-based algorithm. Results show that the approach provides high fidelity, continuous-time state and trajectory estimates for complex tensegrity robot motions.

Shiyang Lu, Yunfu Deng, Abdeslam Boularias et al.

This work proposes a self-supervised learning system for segmenting rigid objects in RGB images. The proposed pipeline is trained on unlabeled RGB-D videos of static objects, which can be captured with a camera carried by a mobile robot. A key feature of the self-supervised training process is a graph-matching algorithm that operates on the over-segmentation output of the point cloud that is reconstructed from each video. The graph matching, along with point cloud registration, is able to find reoccurring object patterns across videos and combine them into 3D object pseudo labels, even under occlusions or different viewing angles. Projected 2D object masks from 3D pseudo labels are used to train a pixel-wise feature extractor through contrastive learning. During online inference, a clustering method uses the learned features to cluster foreground pixels into object segments. Experiments highlight the method's effectiveness on both real and synthetic video datasets, which include cluttered scenes of tabletop objects. The proposed method outperforms existing unsupervised methods for object segmentation by a large margin.

Shiyang Lu, William R. Johnson, Kun Wang et al.

Tensegrity robots, which are composed of compressive elements (rods) and flexible tensile elements (e.g., cables), have a variety of advantages, including flexibility, low weight, and resistance to mechanical impact. Nevertheless, the hybrid soft-rigid nature of these robots also complicates the ability to localize and track their state. This work aims to address what has been recognized as a grand challenge in this domain, i.e., the state estimation of tensegrity robots through a markerless, vision-based method, as well as novel, onboard sensors that can measure the length of the robot's cables. In particular, an iterative optimization process is proposed to track the 6-DoF pose of each rigid element of a tensegrity robot from an RGB-D video as well as endcap distance measurements from the cable sensors. To ensure that the pose estimates of rigid elements are physically feasible, i.e., they are not resulting in collisions between rods or with the environment, physical constraints are introduced during the optimization. Real-world experiments are performed with a 3-bar tensegrity robot, which performs locomotion gaits. Given ground truth data from a motion capture system, the proposed method achieves less than 1~cm translation error and 3 degrees rotation error, which significantly outperforms alternatives. At the same time, the approach can provide accurate pose estimation throughout the robot's motion, while motion capture often fails due to occlusions.

Kai Gao, Darren Lau, Baichuan Huang et al.

In this paper, we examine the problem of rearranging many objects on a tabletop in a cluttered setting using overhand grasps. Efficient solutions for the problem, which capture a common task that we solve on a daily basis, are essential in enabling truly intelligent robotic manipulation. In a given instance, objects may need to be placed at temporary positions ("buffers") to complete the rearrangement, but allocating these buffer locations can be highly challenging in a cluttered environment. To tackle the challenge, a two-step baseline planner is first developed, which generates a primitive plan based on inherent combinatorial constraints induced by start and goal poses of the objects and then selects buffer locations assisted by the primitive plan. We then employ the "lazy" planner in a tree search framework which is further sped up by adapting a novel preprocessing routine. Simulation experiments show our methods can quickly generate high-quality solutions and are more robust in solving large-scale instances than existing state-of-the-art approaches. source:github.com/arc-l/TRLB

Rui Wang, Yinglong Miao, Kostas E. Bekris

Prehensile object rearrangement in cluttered and confined spaces has broad applications but is also challenging. For instance, rearranging products in a grocery shelf means that the robot cannot directly access all objects and has limited free space. This is harder than tabletop rearrangement where objects are easily accessible with top-down grasps, which simplifies robot-object interactions. This work focuses on problems where such interactions are critical for completing tasks. It proposes a new efficient and complete solver under general constraints for monotone instances, which can be solved by moving each object at most once. The monotone solver reasons about robot-object constraints and uses them to effectively prune the search space. The new monotone solver is integrated with a global planner to solve non-monotone instances with high-quality solutions fast. Furthermore, this work contributes an effective pre-processing tool to significantly speed up online motion planning queries for rearrangement in confined spaces. Experiments further demonstrate that the proposed monotone solver, equipped with the pre-processing tool, results in 57.3% faster computation and 3 times higher success rate than state-of-the-art methods. Similarly, the resulting global planner is computationally more efficient and has a higher success rate, while producing high-quality solutions for non-monotone instances (i.e., only 1.3 additional actions are needed on average). Videos of demonstrating solutions on a real robotic system and codes can be found at https://github.com/Rui1223/uniform_object_rearrangement.

Bowen Wen, Kostas Bekris

Tracking the 6D pose of objects in video sequences is important for robot manipulation. Most prior efforts, however, often assume that the target object's CAD model, at least at a category-level, is available for offline training or during online template matching. This work proposes BundleTrack, a general framework for 6D pose tracking of novel objects, which does not depend upon 3D models, either at the instance or category-level. It leverages the complementary attributes of recent advances in deep learning for segmentation and robust feature extraction, as well as memory-augmented pose graph optimization for spatiotemporal consistency. This enables long-term, low-drift tracking under various challenging scenarios, including significant occlusions and object motions. Comprehensive experiments given two public benchmarks demonstrate that the proposed approach significantly outperforms state-of-art, category-level 6D tracking or dynamic SLAM methods. When compared against state-of-art methods that rely on an object instance CAD model, comparable performance is achieved, despite the proposed method's reduced information requirements. An efficient implementation in CUDA provides a real-time performance of 10Hz for the entire framework. Code is available at: https://github.com/wenbowen123/BundleTrack

Bowen Wen, Chaitanya Mitash, Kostas Bekris

Tracking the 6D pose of objects in video sequences is important for robot manipulation. This work presents se(3)-TrackNet, a data-driven optimization approach for long term, 6D pose tracking. It aims to identify the optimal relative pose given the current RGB-D observation and a synthetic image conditioned on the previous best estimate and the object's model. The key contribution in this context is a novel neural network architecture, which appropriately disentangles the feature encoding to help reduce domain shift, and an effective 3D orientation representation via Lie Algebra. Consequently, even when the network is trained solely with synthetic data can work effectively over real images. Comprehensive experiments over multiple benchmarks show se(3)-TrackNet achieves consistently robust estimates and outperforms alternatives, even though they have been trained with real images. The approach runs in real time at 90.9Hz. Code, data and supplementary video for this project are available at https://github.com/wenbowen123/iros20-6d-pose-tracking

Bowen Wen, Chaitanya Mitash, Sruthi Soorian et al.

Many manipulation tasks, such as placement or within-hand manipulation, require the object's pose relative to a robot hand. The task is difficult when the hand significantly occludes the object. It is especially hard for adaptive hands, for which it is not easy to detect the finger's configuration. In addition, RGB-only approaches face issues with texture-less objects or when the hand and the object look similar. This paper presents a depth-based framework, which aims for robust pose estimation and short response times. The approach detects the adaptive hand's state via efficient parallel search given the highest overlap between the hand's model and the point cloud. The hand's point cloud is pruned and robust global registration is performed to generate object pose hypotheses, which are clustered. False hypotheses are pruned via physical reasoning. The remaining poses' quality is evaluated given agreement with observed data. Extensive evaluation on synthetic and real data demonstrates the accuracy and computational efficiency of the framework when applied on challenging, highly-occluded scenarios for different object types. An ablation study identifies how the framework's components help in performance. This work also provides a dataset for in-hand 6D object pose estimation. Code and dataset are available at: https://github.com/wenbowen123/icra20-hand-object-pose

Rahul Shome, Wei N. Tang, Changkyu Song et al.

Many order fulfillment applications in logistics, such as packing, involve picking objects from unstructured piles before tightly arranging them in bins or shipping containers. Desirable robotic solutions in this space need to be low-cost, robust, easily deployable and simple to control. The current work proposes a complete pipeline for solving packing tasks for cuboid objects, given access only to RGB-D data and a single robot arm with a vacuum-based end-effector, which is also used as a pushing or dragging finger. The pipeline integrates perception for detecting the objects and planning so as to properly pick and place objects. The key challenges correspond to sensing noise and failures in execution, which appear at multiple steps of the process. To achieve robustness, three uncertainty-reducing manipulation primitives are proposed, which take advantage of the end-effector's and the workspace's compliance, to successfully and tightly pack multiple cuboid objects. The overall solution is demonstrated to be robust to execution and perception errors. The impact of each manipulation primitive is evaluated in extensive real-world experiments by considering different versions of the pipeline. Furthermore, an open-source simulation framework is provided for modeling such packing operations. Ablation studies are performed within this simulation environment to evaluate features of the proposed primitives.

Kostas E. Bekris, Joe Doerr, Patrick Meng et al.

This paper reviews the large spectrum of methods for generating robot motion proposed over the 50 years of robotics research culminating in recent developments. It crosses the boundaries of methodologies, typically not surveyed together, from those that operate over explicit models to those that learn implicit ones. The paper discusses the current state-of-the-art as well as properties of varying methodologies, highlighting opportunities for integration.

Che Wang, Jeroen van Baar, Chaitanya Mitash et al.

This work demonstrates how autonomously learning aspects of robotic operation from sparsely-labeled, real-world data of deployed, engineered solutions at industrial scale can provide with solutions that achieve improved performance. Specifically, it focuses on multi-suction robot picking and performs a comprehensive study on the application of multi-modal visual encoders for predicting the success of candidate robotic picks. Picking diverse items from unstructured piles is an important and challenging task for robot manipulation in real-world settings, such as warehouses. Methods for picking from clutter must work for an open set of items while simultaneously meeting latency constraints to achieve high throughput. The demonstrated approach utilizes multiple input modalities, such as RGB, depth and semantic segmentation, to estimate the quality of candidate multi-suction picks. The strategy is trained from real-world item picking data, with a combination of multimodal pretrain and finetune. The manuscript provides comprehensive experimental evaluation performed over a large item-picking dataset, an item-picking dataset targeted to include partial occlusions, and a package-picking dataset, which focuses on containers, such as boxes and envelopes, instead of unpackaged items. The evaluation measures performance for different item configurations, pick scenes, and object types. Ablations help to understand the effects of in-domain pretraining, the impact of different modalities and the importance of finetuning. These ablations reveal both the importance of training over multiple modalities but also the ability of models to learn during pretraining the relationship between modalities so that during finetuning and inference, only a subset of them can be used as input.

Shuai Li, Azarakhsh Keipour, Sicong Zhao et al.

Warehouse automation plays a pivotal role in enhancing operational efficiency, minimizing costs, and improving resilience to workforce variability. While prior research has demonstrated the potential of machine learning (ML) models to increase picking success rates in large-scale robotic fleets by prioritizing high-probability picks and packages, these efforts primarily focused on predicting success probabilities for picks sampled using heuristic methods. Limited attention has been given, however, to leveraging data-driven approaches to directly optimize sampled picks for better performance at scale. In this study, we propose an ML-based framework that predicts transform adjustments as well as improving the selection of suction cups for multi-suction end effectors for sampled picks to enhance their success probabilities. The framework was integrated and evaluated in test workcells that resemble the operations of Amazon Robotics' Robot Induction (Robin) fleet, which is used for package manipulation. Evaluated on over 2 million picks, the proposed method achieves a 20\% reduction in pick failure rates compared to a heuristic-based pick sampling baseline, demonstrating its effectiveness in large-scale warehouse automation scenarios.

Shuai Li, Azarakhsh Keipour, Kevin Jamieson et al.

Automating warehouse operations can reduce logistics overhead costs, ultimately driving down the final price for consumers, increasing the speed of delivery, and enhancing the resiliency to workforce fluctuations. The past few years have seen increased interest in automating such repeated tasks but mostly in controlled settings. Tasks such as picking objects from unstructured, cluttered piles have only recently become robust enough for large-scale deployment with minimal human intervention. This paper demonstrates a large-scale package manipulation from unstructured piles in Amazon Robotics' Robot Induction (Robin) fleet, which utilizes a pick success predictor trained on real production data. Specifically, the system was trained on over 394K picks. It is used for singulating up to 5 million packages per day and has manipulated over 200 million packages during this paper's evaluation period. The developed learned pick quality measure ranks various pick alternatives in real-time and prioritizes the most promising ones for execution. The pick success predictor aims to estimate from prior experience the success probability of a desired pick by the deployed industrial robotic arms in cluttered scenes containing deformable and rigid objects with partially known properties. It is a shallow machine learning model, which allows us to evaluate which features are most important for the prediction. An online pick ranker leverages the learned success predictor to prioritize the most promising picks for the robotic arm, which are then assessed for collision avoidance. This learned ranking process is demonstrated to overcome the limitations and outperform the performance of manually engineered and heuristic alternatives. To the best of the authors' knowledge, this paper presents the first large-scale deployment of learned pick quality estimation methods in a real production system.

Kun Wang, William R. Johnson, Shiyang Lu et al.

Tensegrity robots, composed of rigid rods and flexible cables, exhibit high strength-to-weight ratios and significant deformations, which enable them to navigate unstructured terrains and survive harsh impacts. They are hard to control, however, due to high dimensionality, complex dynamics, and a coupled architecture. Physics-based simulation is a promising avenue for developing locomotion policies that can be transferred to real robots. Nevertheless, modeling tensegrity robots is a complex task due to a substantial sim2real gap. To address this issue, this paper describes a Real2Sim2Real (R2S2R) strategy for tensegrity robots. This strategy is based on a differentiable physics engine that can be trained given limited data from a real robot. These data include offline measurements of physical properties, such as mass and geometry for various robot components, and the observation of a trajectory using a random control policy. With the data from the real robot, the engine can be iteratively refined and used to discover locomotion policies that are directly transferable to the real robot. Beyond the R2S2R pipeline, key contributions of this work include computing non-zero gradients at contact points, a loss function for matching tensegrity locomotion gaits, and a trajectory segmentation technique that avoids conflicts in gradient evaluation during training. Multiple iterations of the R2S2R process are demonstrated and evaluated on a real 3-bar tensegrity robot.

Kun Wang, Mridul Aanjaneya, Kostas Bekris

Tensegrity robots, composed of rigid rods and flexible cables, are difficult to accurately model and control given the presence of complex dynamics and high number of DoFs. Differentiable physics engines have been recently proposed as a data-driven approach for model identification of such complex robotic systems. These engines are often executed at a high-frequency to achieve accurate simulation. Ground truth trajectories for training differentiable engines, however, are not typically available at such high frequencies due to limitations of real-world sensors. The present work focuses on this frequency mismatch, which impacts the modeling accuracy. We proposed a recurrent structure for a differentiable physics engine of tensegrity robots, which can be trained effectively even with low-frequency trajectories. To train this new recurrent engine in a robust way, this work introduces relative to prior work: (i) a new implicit integration scheme, (ii) a progressive training pipeline, and (iii) a differentiable collision checker. A model of NASA's icosahedron SUPERballBot on MuJoCo is used as the ground truth system to collect training data. Simulated experiments show that once the recurrent differentiable engine has been trained given the low-frequency trajectories from MuJoCo, it is able to match the behavior of MuJoCo's system. The criterion for success is whether a locomotion strategy learned using the differentiable engine can be transferred back to the ground-truth system and result in a similar motion. Notably, the amount of ground truth data needed to train the differentiable engine, such that the policy is transferable to the ground truth system, is 1% of the data needed to train the policy directly on the ground-truth system.

Ewerton R. Vieira, Edgar Granados, Aravind Sivaramakrishnan et al.

Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing more effective hybrid controllers. This paper proposes a topological framework to analyze the global dynamics of robot controllers, even data-driven ones, in an effective and explainable way. It builds a combinatorial representation representing the underlying system's state space and non-linear dynamics, which is summarized in a directed acyclic graph, the Morse graph. The approach only probes the dynamics locally by forward propagating short trajectories over a state-space discretization, which needs to be a Lipschitz-continuous function. The framework is evaluated given either numerical or data-driven controllers for classical robotic benchmarks. It is compared against established analytical and recent machine learning alternatives for estimating the RoAs of such controllers. It is shown to outperform them in accuracy and efficiency. It also provides deeper insights as it describes the global dynamics up to the discretization's resolution. This allows to use the Morse graph to identify how to synthesize controllers to form improved hybrid solutions or how to identify the physical limitations of a robotic system.

Ewerton R. Vieira, Daniel Nakhimovich, Kai Gao et al.

This work explores the use of topological tools for achieving effective non-prehensile manipulation in cluttered, constrained workspaces. In particular, it proposes the use of persistent homology as a guiding principle in identifying the appropriate non-prehensile actions, such as pushing, to clean a cluttered space with a robotic arm so as to allow the retrieval of a target object. Persistent homology enables the automatic identification of connected components of blocking objects in the space without the need for manual input or tuning of parameters. The proposed algorithm uses this information to push groups of cylindrical objects together and aims to minimize the number of pushing actions needed to reach to the target. Simulated experiments in a physics engine using a model of the Baxter robot show that the proposed topology-driven solution is achieving significantly higher success rate in solving such constrained problems relatively to state-of-the-art alternatives from the literature. It manages to keep the number of pushing actions low, is computationally efficient and the resulting decisions and motion appear natural for effectively solving such tasks.

Bowen Wen, Wenzhao Lian, Kostas Bekris et al.

Promising results have been achieved recently in category-level manipulation that generalizes across object instances. Nevertheless, it often requires expensive real-world data collection and manual specification of semantic keypoints for each object category and task. Additionally, coarse keypoint predictions and ignoring intermediate action sequences hinder adoption in complex manipulation tasks beyond pick-and-place. This work proposes a novel, category-level manipulation framework that leverages an object-centric, category-level representation and model-free 6 DoF motion tracking. The canonical object representation is learned solely in simulation and then used to parse a category-level, task trajectory from a single demonstration video. The demonstration is reprojected to a target trajectory tailored to a novel object via the canonical representation. During execution, the manipulation horizon is decomposed into longrange, collision-free motion and last-inch manipulation. For the latter part, a category-level behavior cloning (CatBC) method leverages motion tracking to perform closed-loop control. CatBC follows the target trajectory, projected from the demonstration and anchored to a dynamically selected category-level coordinate frame. The frame is automatically selected along the manipulation horizon by a local attention mechanism. This framework allows to teach different manipulation strategies by solely providing a single demonstration, without complicated manual programming. Extensive experiments demonstrate its efficacy in a range of challenging industrial tasks in highprecision assembly, which involve learning complex, long-horizon policies. The process exhibits robustness against uncertainty due to dynamics as well as generalization across object instances and scene configurations. The supplementary video is available at https://www.youtube.com/watch?v=WAr8ZY3mYyw

Andrew S. Morgan, Kaiyu Hang, Bowen Wen et al.

Constraining contacts to remain fixed on an object during manipulation limits the potential workspace size, as motion is subject to the hand's kinematic topology. Finger gaiting is one way to alleviate such restraints. It allows contacts to be freely broken and remade so as to operate on different manipulation manifolds. This capability, however, has traditionally been difficult or impossible to practically realize. A finger gaiting system must simultaneously plan for and control forces on the object while maintaining stability during contact switching. This work alleviates the traditional requirement by taking advantage of system compliance, allowing the hand to more easily switch contacts while maintaining a stable grasp. Our method achieves complete SO(3) finger gaiting control of grasped objects against gravity by developing a manipulation planner that operates via orthogonal safe modes of a compliant, underactuated hand absent of tactile sensors or joint encoders. During manipulation, a low-latency 6D pose object tracker provides feedback via vision, allowing the planner to update its plan online so as to adaptively recover from trajectory deviations. The efficacy of this method is showcased by manipulating both convex and non-convex objects on a real robot. Its robustness is evaluated via perturbation rejection and long trajectory goals. To the best of the authors' knowledge, this is the first work that has autonomously achieved full SO(3) control of objects within-hand via finger gaiting and without a support surface, elucidating a valuable step towards realizing true robot in-hand manipulation capabilities.

Seth Karten, Aravind Sivaramakrishnan, Edgar Granados et al.

This paper aims to improve the path quality and computational efficiency of kinodynamic planners used for vehicular systems. It proposes a learning framework for identifying promising controls during the expansion process of sampling-based motion planners for systems with dynamics. Offline, the learning process is trained to return the highest-quality control that reaches a local goal state (i.e., a waypoint) in the absence of obstacles from an input difference vector between its current state and a local goal state. The data generation scheme provides bounds on the target dispersion and uses state space pruning to ensure high-quality controls. By focusing on the system's dynamics, this process is data efficient and takes place once for a dynamical system, so that it can be used for different environments with modular expansion functions. This work integrates the proposed learning process with a) an exploratory expansion function that generates waypoints with biased coverage over the reachable space, and b) proposes an exploitative expansion function for mobile robots, which generates waypoints using medial axis information. This paper evaluates the learning process and the corresponding planners for a first and second-order differential drive systems. The results show that the proposed integration of learning and planning can produce better quality paths than kinodynamic planning with random controls in fewer iterations and computation time.

Aravind Sivaramakrishnan, Edgar Granados, Seth Karten et al.

This paper aims to improve the path quality and computational efficiency of sampling-based kinodynamic planners for vehicular navigation. It proposes a learning framework for identifying promising controls during the expansion process of sampling-based planners. Given a dynamics model, a reinforcement learning process is trained offline to return a low-cost control that reaches a local goal state (i.e., a waypoint) in the absence of obstacles. By focusing on the system's dynamics and not knowing the environment, this process is data-efficient and takes place once for a robotic system. In this way, it can be reused in different environments. The planner generates online local goal states for the learned controller in an informed manner to bias towards the goal and consecutively in an exploratory, random manner. For the informed expansion, local goal states are generated either via (a) medial axis information in environments with obstacles, or (b) wavefront information for setups with traversability costs. The learning process and the resulting planning framework are evaluated for a first and second-order differential drive system, as well as a physically simulated Segway robot. The results show that the proposed integration of learning and planning can produce higher quality paths than sampling-based kinodynamic planning with random controls in fewer iterations and computation time.

Shiyang Lu, Rui Wang, Yinglong Miao et al.

This work proposes a robotic pipeline for picking and constrained placement of objects without geometric shape priors. Compared to recent efforts developed for similar tasks, where every object was assumed to be novel, the proposed system recognizes previously manipulated objects and performs online model reconstruction and reuse. Over a lifelong manipulation process, the system keeps learning features of objects it has interacted with and updates their reconstructed models. Whenever an instance of a previously manipulated object reappears, the system aims to first recognize it and then register its previously reconstructed model given the current observation. This step greatly reduces object shape uncertainty allowing the system to even reason for parts of objects, which are currently not observable. This also results in better manipulation efficiency as it reduces the need for active perception of the target object during manipulation. To get a reusable reconstructed model, the proposed pipeline adopts: i) TSDF for object representation, and ii) a variant of the standard particle filter algorithm for pose estimation and tracking of the partial object model. Furthermore, an effective way to construct and maintain a dataset of manipulated objects is presented. A sequence of real-world manipulation experiments is performed. They show how future manipulation tasks become more effective and efficient by reusing reconstructed models of previously manipulated objects, which were generated during their prior manipulation, instead of treating objects as novel every time.

Bowen Wen, Wenzhao Lian, Kostas Bekris et al.

Task-relevant grasping is critical for industrial assembly, where downstream manipulation tasks constrain the set of valid grasps. Learning how to perform this task, however, is challenging, since task-relevant grasp labels are hard to define and annotate. There is also yet no consensus on proper representations for modeling or off-the-shelf tools for performing task-relevant grasps. This work proposes a framework to learn task-relevant grasping for industrial objects without the need of time-consuming real-world data collection or manual annotation. To achieve this, the entire framework is trained solely in simulation, including supervised training with synthetic label generation and self-supervised, hand-object interaction. In the context of this framework, this paper proposes a novel, object-centric canonical representation at the category level, which allows establishing dense correspondence across object instances and transferring task-relevant grasps to novel instances. Extensive experiments on task-relevant grasping of densely-cluttered industrial objects are conducted in both simulation and real-world setups, demonstrating the effectiveness of the proposed framework. Code and data are available at https://sites.google.com/view/catgrasp.

Andrew S. Morgan, Bowen Wen, Junchi Liang et al.

Highly constrained manipulation tasks continue to be challenging for autonomous robots as they require high levels of precision, typically less than 1mm, which is often incompatible with what can be achieved by traditional perception systems. This paper demonstrates that the combination of state-of-the-art object tracking with passively adaptive mechanical hardware can be leveraged to complete precision manipulation tasks with tight, industrially-relevant tolerances (0.25mm). The proposed control method closes the loop through vision by tracking the relative 6D pose of objects in the relevant workspace. It adjusts the control reference of both the compliant manipulator and the hand to complete object insertion tasks via within-hand manipulation. Contrary to previous efforts for insertion, our method does not require expensive force sensors, precision manipulators, or time-consuming, online learning, which is data hungry. Instead, this effort leverages mechanical compliance and utilizes an object agnostic manipulation model of the hand learned offline, off-the-shelf motion planning, and an RGBD-based object tracker trained solely with synthetic data. These features allow the proposed system to easily generalize and transfer to new tasks and environments. This paper describes in detail the system components and showcases its efficacy with extensive experiments involving tight tolerance peg-in-hole insertion tasks of various geometries as well as open-world constrained placement tasks.

Rui Wang, Kai Gao, Daniel Nakhimovich et al.

Object rearrangement is a widely-applicable and challenging task for robots. Geometric constraints must be carefully examined to avoid collisions and combinatorial issues arise as the number of objects increases. This work studies the algorithmic structure of rearranging uniform objects, where robot-object collisions do not occur but object-object collisions have to be avoided. The objective is minimizing the number of object transfers under the assumption that the robot can manipulate one object at a time. An efficiently computable decomposition of the configuration space is used to create a "region graph", which classifies all continuous paths of equivalent collision possibilities. Based on this compact but rich representation, a complete dynamic programming primitive DFSDP performs a recursive depth first search to solve monotone problems quickly, i.e., those instances that do not require objects to be moved first to an intermediate buffer. DFSDP is extended to solve single-buffer, non-monotone instances, given a choice of an object and a buffer. This work utilizes these primitives as local planners in an informed search framework for more general, non-monotone instances. The search utilizes partial solutions from the primitives to identify the most promising choice of objects and buffers. Experiments demonstrate that the proposed solution returns near-optimal paths with higher success rate, even for challenging non-monotone instances, than other leading alternatives.

Sebastian Höfer, Kostas Bekris, Ankur Handa et al.

This report presents the debates, posters, and discussions of the Sim2Real workshop held in conjunction with the 2020 edition of the "Robotics: Science and System" conference. Twelve leaders of the field took competing debate positions on the definition, viability, and importance of transferring skills from simulation to the real world in the context of robotics problems. The debaters also joined a large panel discussion, answering audience questions and outlining the future of Sim2Real in robotics. Furthermore, we invited extended abstracts to this workshop which are summarized in this report. Based on the workshop, this report concludes with directions for practitioners exploiting this technology and for researchers further exploring open problems in this area.

Kun Wang, Mridul Aanjaneya, Kostas Bekris

Learning policies in simulation is promising for reducing human effort when training robot controllers. This is especially true for soft robots that are more adaptive and safe but also more difficult to accurately model and control. The sim2real gap is the main barrier to successfully transfer policies from simulation to a real robot. System identification can be applied to reduce this gap but traditional identification methods require a lot of manual tuning. Data-driven alternatives can tune dynamical models directly from data but are often data hungry, which also incorporates human effort in collecting data. This work proposes a data-driven, end-to-end differentiable simulator focused on the exciting but challenging domain of tensegrity robots. To the best of the authors' knowledge, this is the first differentiable physics engine for tensegrity robots that supports cable, contact, and actuation modeling. The aim is to develop a reasonably simplified, data-driven simulation, which can learn approximate dynamics with limited ground truth data. The dynamics must be accurate enough to generate policies that can be transferred back to the ground-truth system. As a first step in this direction, the current work demonstrates sim2sim transfer, where the unknown physical model of MuJoCo acts as a ground truth system. Two different tensegrity robots are used for evaluation and learning of locomotion policies, a 6-bar and a 3-bar tensegrity. The results indicate that only 0.25\% of ground truth data are needed to train a policy that works on the ground truth system when the differentiable engine is used for training against training the policy directly on the ground truth system.

Kun Wang, Mridul Aanjaneya, Kostas Bekris

We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system \emph{and} its parameters, we modularize the design of our engine using a discrete form of the governing equations of motion, similar to a traditional physics engine. We further reduce the dimension from 3D to 1D for each module, which allows efficient learning of system parameters using linear regression. The regression parameters correspond to physical quantities, such as spring stiffness or the mass of the rod, making the pipeline explainable. The approach significantly reduces the amount of training data required, and also avoids iterative identification of data sampling and model training. We compare the performance of the proposed engine with previous solutions, and demonstrate its efficacy on tensegrity systems, such as NASA's icosahedron.

Rui Wang, Chaitanya Mitash, Shiyang Lu et al.

Picking an item in the presence of other objects can be challenging as it involves occlusions and partial views. Given object models, one approach is to perform object pose estimation and use the most likely candidate pose per object to pick the target without collisions. This approach, however, ignores the uncertainty of the perception process both regarding the target's and the surrounding objects' poses. This work proposes first a perception process for 6D pose estimation, which returns a discrete distribution of object poses in a scene. Then, an open-loop planning pipeline is proposed to return safe and effective solutions for moving a robotic arm to pick, which (a) minimizes the probability of collision with the obstructing objects; and (b) maximizes the probability of reaching the target item. The planning framework models the challenge as a stochastic variant of the Minimum Constraint Removal (MCR) problem. The effectiveness of the methodology is verified given both simulated and real data in different scenarios. The experiments demonstrate the importance of considering the uncertainty of the perception process in terms of safe execution. The results also show that the methodology is more effective than conservative MCR approaches, which avoid all possible object poses regardless of the reported uncertainty.

Bowen Wen, Chaitanya Mitash, Baozhang Ren et al.

Tracking the 6D pose of objects in video sequences is important for robot manipulation. This task, however, introduces multiple challenges: (i) robot manipulation involves significant occlusions; (ii) data and annotations are troublesome and difficult to collect for 6D poses, which complicates machine learning solutions, and (iii) incremental error drift often accumulates in long term tracking to necessitate re-initialization of the object's pose. This work proposes a data-driven optimization approach for long-term, 6D pose tracking. It aims to identify the optimal relative pose given the current RGB-D observation and a synthetic image conditioned on the previous best estimate and the object's model. The key contribution in this context is a novel neural network architecture, which appropriately disentangles the feature encoding to help reduce domain shift, and an effective 3D orientation representation via Lie Algebra. Consequently, even when the network is trained only with synthetic data can work effectively over real images. Comprehensive experiments over benchmarks - existing ones as well as a new dataset with significant occlusions related to object manipulation - show that the proposed approach achieves consistently robust estimates and outperforms alternatives, even though they have been trained with real images. The approach is also the most computationally efficient among the alternatives and achieves a tracking frequency of 90.9Hz.

Chaitanya Mitash, Rahul Shome, Bowen Wen et al.

Recent progress in robotic manipulation has dealt with the case of previously unknown objects in the context of relatively simple tasks, such as bin-picking. Existing methods for more constrained problems, however, such as deliberate placement in a tight region, depend more critically on shape information to achieve safe execution. This work deals with pick-and-constrained placement of objects without access to geometric models. The objective is to pick an object and place it safely inside a desired goal region without any collisions, while minimizing the time and the sensing operations required to complete the task. An algorithmic framework is proposed for this purpose, which performs manipulation planning simultaneously over a conservative and an optimistic estimate of the object's volume. The conservative estimate ensures that the manipulation is safe while the optimistic estimate guides the sensor-based manipulation process when no solution can be found for the conservative estimate. To maintain these estimates and dynamically update them during manipulation, objects are represented by a simple volumetric representation, which stores sets of occupied and unseen voxels. The effectiveness of the proposed approach is demonstrated by developing a robotic system that picks a previously unseen object from a table-top and places it in a constrained space. The system comprises of a dual-arm manipulator with heterogeneous end-effectors and leverages hand-offs as a re-grasping strategy. Real-world experiments show that straightforward pick-sense-and-place alternatives frequently fail to solve pick-and-constrained placement problems. The proposed pipeline, however, achieves more than 95% success rate and faster execution times as evaluated over multiple physical experiments.

Rahul Shome, Kostas E. Bekris

Solving task planning problems involving multiple objects and multiple robotic arms poses scalability challenges. Such problems involve not only coordinating multiple high-DoF arms, but also searching through possible sequences of actions including object placements, and handoffs. The current work identifies a useful connection between multi-arm rearrangement and recent results in multi-body path planning on graphs with vertex capacity constraints. Solving a synchronized multi-arm rearrangement at a high-level involves reasoning over a modal graph, where nodes correspond to stable object placements and object transfer states by the arms. Edges of this graph correspond to pick, placement and handoff operations. The objects can be viewed as pebbles moving over this graph, which has capacity constraints. For instance, each arm can carry a single object but placement locations can accumulate many objects. Efficient integer linear programming-based solvers have been proposed for the corresponding pebble problem. The current work proposes a heuristic to guide the task planning process for synchronized multi-arm rearrangement. Results indicate good scalability to multiple arms and objects, and an algorithm that can find high-quality solutions fast and exhibiting desirable anytime behavior.

Kun Wang, Mridul Aanjaneya, Kostas Bekris

We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system and its parameters, we modularize the design of our engine using a discrete form of the governing equations of motion, similar to a traditional physics engine. We further reduce the dimension from 3D to 1D for each module, which allows efficient learning of system parameters using linear regression. As a side benefit, the regression parameters correspond to physical quantities, such as spring stiffness or the mass of the rod, making the pipeline explainable. The approach significantly reduces the amount of training data required, and also avoids iterative identification of data sampling and model training. We compare the performance of the proposed engine with previous solutions, and demonstrate its efficacy on tensegrity systems, such as NASA's icosahedron.

Malihe Alikhani, Baber Khalid, Rahul Shome et al.

Collaborative robotics requires effective communication between a robot and a human partner. This work proposes a set of interpretive principles for how a robotic arm can use pointing actions to communicate task information to people by extending existing models from the related literature. These principles are evaluated through studies where English-speaking human subjects view animations of simulated robots instructing pick-and-place tasks. The evaluation distinguishes two classes of pointing actions that arise in pick-and-place tasks: referential pointing (identifying objects) and locating pointing (identifying locations). The study indicates that human subjects show greater flexibility in interpreting the intent of referential pointing compared to locating pointing, which needs to be more deliberate. The results also demonstrate the effects of variation in the environment and task context on the interpretation of pointing. Our corpus, experiments and design principles advance models of context, common sense reasoning and communication in embodied communication.

Kostas E. Bekris, Rahul Shome

An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This comprehensive article covers the theoretical characteristics of asymptotic optimality of motion planning algorithms, and traces its origins, analysis models, practical performance, extensions, and applications.

Chaitanya Mitash, Bowen Wen, Kostas Bekris et al.

This paper introduces key machine learning operations that allow the realization of robust, joint 6D pose estimation of multiple instances of objects either densely packed or in unstructured piles from RGB-D data. The first objective is to learn semantic and instance-boundary detectors without manual labeling. An adversarial training framework in conjunction with physics-based simulation is used to achieve detectors that behave similarly in synthetic and real data. Given the stochastic output of such detectors, candidates for object poses are sampled. The second objective is to automatically learn a single score for each pose candidate that represents its quality in terms of explaining the entire scene via a gradient boosted tree. The proposed method uses features derived from surface and boundary alignment between the observed scene and the object model placed at hypothesized poses. Scene-level, multi-instance pose estimation is then achieved by an integer linear programming process that selects hypotheses that maximize the sum of the learned individual scores, while respecting constraints, such as avoiding collisions. To evaluate this method, a dataset of densely packed objects with challenging setups for state-of-the-art approaches is collected. Experiments on this dataset and a public one show that the method significantly outperforms alternatives in terms of 6D pose accuracy while trained only with synthetic datasets.

Michal Kleinbort, Edgar Granados, Kiril Solovey et al.

We present a novel analysis of AO-RRT: a tree-based planner for motion planning with kinodynamic constraints, originally described by Hauser and Zhou (AO-X, 2016). AO-RRT explores the state-cost space and has been shown to efficiently obtain high-quality solutions in practice without relying on the availability of a computationally-intensive two-point boundary-value solver. Our main contribution is an optimality proof for the single-tree version of the algorithm---a variant that was not analyzed before. Our proof only requires a mild and easily-verifiable set of assumptions on the problem and system: Lipschitz-continuity of the cost function and the dynamics. In particular, we prove that for any system satisfying these assumptions, any trajectory having a piecewise-constant control function and positive clearance from the obstacles can be approximated arbitrarily well by a trajectory found by AO-RRT. We also discuss practical aspects of AO-RRT and present experimental comparisons of variants of the algorithm.

Aravind Sivaramakrishnan, Zakary Littlefield, Kostas E. Bekris

Planning for systems with dynamics is challenging as often there is no local planner available and the only primitive to explore the state space is forward propagation of controls. In this context, tree sampling-based planners have been developed, some of which achieve asymptotic optimality by propagating random controls during each iteration. While desirable for the analysis, random controls result in slow convergence to high quality trajectories in practice. This short position statement first argues that if a kinodynamic planner has access to local maneuvers that appropriately balance an exploitation-exploration trade-off, the planner's per iteration performance is significantly improved. Generating such maneuvers during planning can be achieved by curating a large sample of random controls. This is, however, computationally very expensive. If such maneuvers can be generated fast, the planner's performance will also improve as a function of computation time. Towards objective, this short position statement argues for the integration of modern machine learning frameworks with state-of-the-art, informed and asymptotically optimal kinodynamic planners. The proposed approach involves using using neural networks to infer local maneuvers for a robotic system with dynamics, which properly balance the above exploitation-exploration trade-off. In particular, a neural network architecture is proposed, which is trained to reflect the choices of an online curation process, given local obstacle and heuristic information. The planner uses these maneuvers to efficiently explore the underlying state space, while still maintaining desirable properties. Preliminary indications in simulated environments and systems are promising but also point to certain challenges that motivate further research in this direction.

Rahul Shome, Kostas E. Bekris

Automation applications are pushing the deployment of many high DoF manipulators in warehouse and manufacturing environments. This has motivated many efforts on optimizing manipulation tasks involving a single arm. Coordinating multiple arms for manipulation, however, introduces additional computational challenges arising from the increased DoFs, as well as the combinatorial increase in the available operations that many manipulators can perform, including handoffs between arms. The focus here is on the case of pick-and-place tasks, which require a sequence of handoffs to be executed, so as to achieve computational efficiency, asymptotic optimality and practical anytime performance. The paper leverages recent advances in multi-robot motion planning for high DoF systems to propose a novel multi-modal extension of the dRRT* algorithm. The key insight is that, instead of naively solving a sequence of motion planning problems, it is computationally advantageous to directly explore the composite space of the integrated multi-arm task and motion planning problem, given input sets of possible pick and handoff configurations. Asymptotic optimality guarantees are possible by sampling additional picks and handoffs over time. The evaluation shows that the approach finds initial solutions fast and improves their quality over time. It also succeeds in finding solutions to harder problem instances relative to alternatives and can scale effectively as the number of robots increases.

Rahul Shome, Daniel Nakhimovich, Kostas E. Bekris

Integrated task and motion planning problems describe a multi-modal state space, which is often abstracted as a set of smooth manifolds that are connected via sets of transitions states. One approach to solving such problems is to sample reachable states in each of the manifolds, while simultaneously sampling transition states. Prior work has shown that in order to achieve asymptotically optimal (AO) solutions for such piecewise-smooth task planning problems, it is sufficient to double the connection radius required for AO sampling-based motion planning. This was shown under the assumption that the transition sets themselves are smooth. The current work builds upon this result and demonstrates that it is sufficient to use the same connection radius as for standard AO motion planning. Furthermore, the current work studies the case that the transition sets are non-smooth boundary points of the valid state space, which is frequently the case in practice, such as when a gripper grasps an object. This paper generalizes the notion of clearance that is typically assumed in motion and task planning to include such individual, potentially non-smooth transition states. It is shown that asymptotic optimality is retained under this generalized regime.

Rahul Shome, Kiril Solovey, Jingjin Yu et al.

Rearranging objects on a planar surface arises in a variety of robotic applications, such as product packaging. Using two arms can improve efficiency but introduces new computational challenges. This paper studies the structure of dual-arm rearrangement for synchronous, monotone tabletop setups and develops an optimal mixed integer model. It then describes an efficient and scalable algorithm, which first minimizes the cost of object transfers and then of moves between objects. This is motivated by the fact that, asymptotically, object transfers dominate the cost of solutions. Moreover, a lazy strategy minimizes the number of motion planning calls and results in significant speedups. Theoretical arguments support the benefits of using two arms and indicate that synchronous execution, in which the two arms perform together either transfers or moves, introduces only a small overhead. Experiments support these points and show that the scalable method can quickly compute solutions close to the optimal for the considered setup.

David Surovik, Kun Wang, Kostas E. Bekris

The dynamical properties of tensegrity robots give them appealing ruggedness and adaptability, but present major challenges with respect to locomotion control. Due to high-dimensionality and complex contact responses, data-driven approaches are apt for producing viable feedback policies. Guided Policy Search (GPS), a sample-efficient and model-free hybrid framework for optimization and reinforcement learning, has recently been used to produce periodic locomotion for a spherical 6-bar tensegrity robot on flat or slightly varied surfaces. This work provides an extension to non-periodic locomotion and achieves rough terrain traversal, which requires more broadly varied, adaptive, and non-periodic rover behavior. The contribution alters the control optimization step of GPS, which locally fits and exploits surrogate models of the dynamics, and employs the existing supervised learning step. The proposed solution incorporates new processes to ensure effective local modeling despite the disorganized nature of sample data in rough terrain locomotion. Demonstrations in simulation reveal that the resulting controller sustains the highly adaptive behavior necessary to reliably traverse rough terrain.

Michal Kleinbort, Kiril Solovey, Zakary Littlefield et al.

The Rapidly-exploring Random Tree (RRT) algorithm has been one of the most prevalent and popular motion-planning techniques for two decades now. Surprisingly, in spite of its centrality, there has been an active debate under which conditions RRT is probabilistically complete. We provide two new proofs of probabilistic completeness (PC) of RRT with a reduced set of assumptions. The first one for the purely geometric setting, where we only require that the solution path has a certain clearance from the obstacles. For the kinodynamic case with forward propagation of random controls and duration, we only consider in addition mild Lipschitz-continuity conditions. These proofs fill a gap in the study of RRT itself. They also lay sound foundations for a variety of more recent and alternative sampling-based methods, whose PC property relies on that of RRT. Our original publication contains an error in the analysis of the case of the kinodynamic RRT. Here, we rectify the problem by modifying the proof of Theorem 2, which, in particular, necessitated a revision of Lemma 3. Briefly, the original (and erroneous) proof of Theorem 2 used a sequence of equal-size balls. The correction uses a sequence of balls of increasing radii. We emphasize that the correction is in Lemma 3 and the proof of Theorem 2 only. The main results remain unchanged.