When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or downweighting attention depending on the relationship between the query and keys in the graph. In this paper, we propose to parameterise topological masks as a learnable function of a weighted adjacency matrix -- a novel, flexible approach which incorporates a strong structural inductive bias. By approximating this mask with graph random features (for which we prove the first known concentration bounds), we show how this can be made fully compatible with linear attention, preserving $\mathcal{O}(N)$ time and space complexity with respect to the number of input tokens. The fastest previous alternative was $\mathcal{O}(N \log N)$ and only suitable for specific graphs. Our efficient masking algorithms provide strong performance gains for image and point cloud data, including with $>30$k nodes.

We introduce $\textbf{STRING}$: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides $\textbf{exact}$ translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods. Videos of STRING-based robotics controllers can be found here: https://sites.google.com/view/string-robotics.

This video presents the recent upgrades of the mobile humanoid Agile Justin, bringing it closer to an ideal platform for research in autonomous manipulation. Significant upgrades have been made in the fields of mechatronics, 3D sensors, tactile skin, massive GPGPU based computing power, and software communication framework. In addition, first algorithms and two experimental scenarios are presented that take advantage of these new capabilities.

For such common tasks as motion planning or object recognition robots need to perceive their environment and create a dense 3D map of it. A recent breakthrough in this area was the KinectFusion algorithm [16], which relies on step by step matching a depth image to the map via ICP to recover the sensor pose and updating the map based on that pose. In so far it ignores techniques developed in the graph-SLAM area such as fusion with odometry, modeling of uncertainty and distributing an observed inconsistency over the map. This paper presents a method to integrate a dense geometric truncated signed distance function (TSDF) representation as KinectFusion uses with a sparse parametric representation as common in graph SLAM. The key idea is to have local TSDF sub-maps attached to reference nodes in the SLAM graph and derive graph-SLAM links via ICP by matching a map to a depth image. By moving these reference nodes according to the graph-SLAM estimate, the overall map can be deformed without touching individual sub-maps so that re-building of sub-maps is only needed in case of significant deformation within a sub-map. Also, further information can be added to the graph as common in graph SLAM. Examples are odometry or the fact that the ground is roughly but not exactly planar. Additionally, the paper proposes a modification of the KinectFusion algorithm to improve handling of long range data by taking the range dependent uncertainty into account.

The Kinect sensor and KinectFusion algorithm have revolutionized environment modeling. We bring these advances to optimization-based motion planning by computing the obstacle and self-collision avoidance objective functions and their gradients directly from the KinectFusion model on the GPU without ever transferring any model to the CPU. Based on this, we implement a proof-of-concept motion planner which we validate in an experiment with a 19-DOF humanoid robot using real data from a tabletop work space. The summed-up time from taking the first look at the scene until the planned path avoiding an obstacle on the table is executed is only three seconds.

Without a precise and up-to-date model of its environment a humanoid robot cannot move safely or act usefully. Ideally, the robot should create a dense 3D environment model in real-time, all the time, and respect obstacle information from it in every move it makes as well as obtain the information it needs for fine manipulation with its fingers from the same map. We propose to use a multi-scale truncated signed distance function (TSDF) map consisting of concentric, nested cubes with exponentially decreasing resolution for this purpose. We show how to extend the KinectFusion real-time SLAM algorithm to the multi-scale case as well as how to compute a multi-scale Euclidean distance transform (EDT) thereby establishing the link to optimization-based planning. We overcome the inability of KinectFusion's localization to handle scenes without enough constraining geometry by switching to mapping-with-known-poses based on forward kinematics. The latter is always available and we know when it is precise. The resulting map has the desired properties: It is computed in real-time (7.5 ms per depth frame for a (8 m)3multi-scale TSDF volume), covers the entire laboratory, does not depend on scene properties (geometry, texture, etc.) and is precise enough to facilitate grasp planning for fine manipulation tasks - all in a single map.

This paper shows that the field of visual SLAM has matured enough to build a visual SLAM system from open source components. The system consists of feature detection, data association, and sparse bundle adjustment. For all three modules we evaluate different libraries w.r.t. ground truth.

Non-linear optimization on constraint graphs has recently been applied very successfully in a variety of SLAM backends. We combine this technique with a principled way of handling non-Euclidean spaces, 3D orientations in particular, based on manifolds to build a generic and very flexible framework, the Manifold Toolkit for Matlab (MTKM). We show that MTKM makes it particularly easy to solve non-trivial multi-sensor calibration problems while remaining generic enough to handle a very different class of problems, namely SLAM, as well: After an introductory example on single camera calibration we apply MTKM to calibration of stereo vision and IMU w.r.t. the kinematic chain of a service robot, RGB-D and accelerometer calibration of a Microsoft Kinect, stereo calibration on a Nao soccer robot, and several SLAM benchmark data sets illustrating MTKM's versatility. MTKM and all presented examples are available as open source from http://openslam.org/MTK.html.