Leveraging Two Robotic Arms for Tight Assembly Performance Gains

We provide a novel end-to-end framework for the execution of an assembly operation by two robotic arms, given the digital CAD models of the parts and their desired relative placement in their assembled state. We analyze and demonstrate the advantages of using two robotic arms simultaneously in tight assembly operations, compared to single-arm systems. Our method is implemented in both simulation and using physical robots. It provides theoretical guarantees on execution time and trajectory accuracy, supported by empirical evidence. In particular, we show that coordinated movement of two arms reduces average execution time by more than 50% compared to using a single arm only, produces higher-quality trajectories, and accelerates the search for valid robot placements. Furthermore, we establish bounds on the required dimensions of the robotic cell. Our open source software together with real-life video demonstrations are available in our project page.

Manifold-Guided Motion Planning for Tight Assemblies

Motion planning for rigid-body assembly poses a fundamental challenge in robotics due to tight geometric constraints. In such scenarios, feasible motions often require passing through (near-)zero clearance configurations in which the parts are tightly constrained by contact. In this work, we introduce Critical-Manifold Guided RRT (CMG-RRT), a sampling-based planner designed specifically for tight assembly problems. Our key observation is that in tight assemblies, valid solution paths lie on or near a critical manifold: the subset of configuration space consisting of poses with at least one contact point between parts. CMG-RRT guides exploration by adaptively biasing sampling toward neighborhoods of the critical manifold using a hierarchical subdivision of the configuration space. We prove that CMG-RRT is probabilistically complete under standard clearance assumptions. Empirical evaluation on challenging rotational assembly benchmarks demonstrates a 100% success rate across all tested instances, including, to the best of our knowledge, the first fully automatic solution of the Elk disentanglement puzzle. Our open source software is available through our project page: https://www.cgl.cs.tau.ac.il/projects/tight-assembly-planning.

Lifelong Localization in Dynamic Indoor Environments Combining Odometry with Sparse Distance Sampling

Localization is a key task in robot navigation, and many techniques exist for it. In many plausible scenarios, a robot might face unforeseen, dynamic obstacles, rendering any pre-determined map inaccurate for localization. In this work, we propose a robust lifelong localization framework in dynamic planar indoor environments, using the robot's odometry and sparse distance sampling. We demonstrate how distance samples can be used to provide a robust prior on the robot's location. This technique can solve the kidnapped robot problem in real time, up to symmetries. Based on insights from real-world recorded data, we also account for dynamic obstacles. We then fuse this prior, over time, with the odometry to converge to the robot's location. A central property of our method is that it provably converges to the robot's ground truth pose even in large indoor environments when the environment is static. We further show that this guarantee also holds in dynamic environments, as long as the nature of those changes has been correctly learned. We demonstrate the effectiveness of our approach in different real-world indoor environments. In particular, we achieve a localization comparable to SLAM with merely a few (sixteen) distance samples, as opposed to the full LiDAR range. Sufficing with only sparse distance sampling is advantageous in terms of sensor cost, privacy, storage space, and transmission bandwidth.

Algorithms for Nonlinear Mixed-Integer Location Estimation

For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares problem. Existing algorithms linearize the problem, orthogonally project it to eliminate real variables, and then solve the integer least-square problem. There is now considerable interest in developing similar localization techniques for terrestrial and indoor settings. We show that algorithms that linearize first fail in these settings and we propose several algorithms for computing the estimates. Some of our algorithms are elimination algorithms that start by eliminating the non-linear terms in the constraints; others construct a geometric arrangement that allows us to efficiently enumerate integer solutions (in polynomial time). We focus on simplified localization problems in which the measurements are range (distance) measurements and carrier phase range measurements, with no nuisance parameters. The simplified problem allows us to focus on the core question of untangling the nonlinearity and the integer nature of some parameters. We show using simulations that the new algorithms are effective at close ranges at which the linearize-first approach fails.

Point Cloud Based Scene Segmentation: A Survey

Autonomous driving is a safety-critical application, and it is therefore a top priority that the accompanying assistance systems are able to provide precise information about the surrounding environment of the vehicle. Tasks such as 3D Object Detection deliver an insufficiently detailed understanding of the surrounding scene because they only predict a bounding box for foreground objects. In contrast, 3D Semantic Segmentation provides richer and denser information about the environment by assigning a label to each individual point, which is of paramount importance for autonomous driving tasks, such as navigation or lane changes. To inspire future research, in this review paper, we provide a comprehensive overview of the current state-of-the-art methods in the field of Point Cloud Semantic Segmentation for autonomous driving. We categorize the approaches into projection-based, 3D-based and hybrid methods. Moreover, we discuss the most important and commonly used datasets for this task and also emphasize the importance of synthetic data to support research when real-world data is limited. We further present the results of the different methods and compare them with respect to their segmentation accuracy and efficiency.

A Note on the Time Complexity of Using Subdivision Methods for the Approximation of Fibers

Subdivision methods such as quadtrees, octrees, and higher-dimensional orthrees are standard practice in different domains of computer science. We can use these methods to represent given geometries, such as curves, meshes, or surfaces. This representation is achieved by splitting some bounding voxel recursively while further splitting only sub-voxels that intersect with the given geometry. It is fairly known that subdivision methods are more efficient than traversing a fine-grained voxel grid. In this short note, we propose another outlook on analyzing the construction time complexity of orthrees to represent implicitly defined geometries that are fibers (preimages) of some function. This complexity is indeed asymptotically better than traversing dense voxel grids, under certain conditions, which we specify in the note. In fact, the complexity is output sensitive, and is closely related to the Hausdorff measure and Hausdorff dimension of the resulting geometry.

Ten Problems in Geobotics

Robots sense, move and act in the physical world. It is therefore natural that algorithmic problems in robotics and automation have a geometric component, often central to the problem. Below we review ten challenging problems at the intersection of robotics and computational geometry -- let's call this intersection Geobotics. What is common to most of these problems is that the prevalent algorithmic techniques used in robotics do not seem suitable for solving them, or at least do not suggest quality guarantees for the solution. Solving some of them, even partially, can shed light on less well-understood aspects of computation in robotics.

Localization in Dynamic Planar Environments Using Few Distance Measurements

We present a method for determining the unknown location of a sensor placed in a known 2D environment in the presence of unknown dynamic obstacles, using only few distance measurements. We present guarantees on the quality of the localization, which are robust under mild assumptions on the density of the unknown/dynamic obstacles in the known environment. We demonstrate the effectiveness of our method in simulated experiments for different environments and varying dynamic-obstacle density. Our open source software is available at https://github.com/TAU-CGL/vb-fdml2-public.

Near-Optimal Min-Sum Motion Planning for Two Square Robots in a Polygonal Environment

Let $\mathcal{W} \subset \mathbb{R}^2$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A,B$ be two robots, each modeled as an axis-aligned unit square, that can translate inside $\mathcal{W}$. Given source and target placements $s_A,t_A,s_B,t_B \in \mathcal{W}$ of $A$ and $B$, respectively, the goal is to compute a \emph{collision-free motion plan} $\mathbf{\pi}^*$, i.e., a motion plan that continuously moves $A$ from $s_A$ to $t_A$ and $B$ from $s_B$ to $t_B$ so that $A$ and $B$ remain inside $\mathcal{W}$ and do not collide with each other during the motion. Furthermore, if such a plan exists, then we wish to return a plan that minimizes the sum of the lengths of the paths traversed by the robots, $\left|\mathbf{\pi}^*\right|$. Given $\mathcal{W}, s_A,t_A,s_B,t_B$ and a parameter $\varepsilon > 0$, we present an $n^2\varepsilon^{-O(1)} \log n$-time $(1+\varepsilon)$-approximation algorithm for this problem. We are not aware of any polynomial time algorithm for this problem, nor do we know whether the problem is NP-Hard. Our result is the first polynomial-time $(1+\varepsilon)$-approximation algorithm for an optimal motion planning problem involving two robots moving in a polygonal environment.

Coordination of Multiple Robots along Given Paths with Bounded Junction Complexity

We study a fundamental NP-hard motion coordination problem for multi-robot/multi-agent systems: We are given a graph $G$ and set of agents, where each agent has a given directed path in $G$. Each agent is initially located on the first vertex of its path. At each time step an agent can move to the next vertex on its path, provided that the vertex is not occupied by another agent. The goal is to find a sequence of such moves along the given paths so that each reaches its target, or to report that no such sequence exists. The problem models guidepath-based transport systems, which is a pertinent abstraction for traffic in a variety of contemporary applications, ranging from train networks or Automated Guided Vehicles (AGVs) in factories, through computer game animations, to qubit transport in quantum computing. It also arises as a sub-problem in the more general multi-robot motion-planning problem. We provide a fine-grained tractability analysis of the problem by considering new assumptions and identifying minimal values of key parameters for which the problem remains NP-hard. Our analysis identifies a critical parameter called vertex multiplicity (VM), defined as the maximum number of paths passing through the same vertex. We show that a prevalent variant of the problem, which is equivalent to Sequential Resource Allocation (concerning deadlock prevention for concurrent processes), is NP-hard even when VM is 3. On the positive side, for VM $\le$ 2 we give an efficient algorithm that iteratively resolves cycles of blocking relations among agents. We also present a variant that is NP-hard when the VM is 2 even when $G$ is a 2D grid and each path lies in a single grid row or column. By studying highly distilled yet NP-hard variants, we deepen the understanding of what makes the problem intractable and thereby guide the search for efficient solutions under practical assumptions.