We define a molecular caging complex as a pair of molecules in which one molecule (the "host" or "cage") possesses a cavity that can encapsulate the other molecule (the "guest") and prevent it from escaping. Molecular caging complexes can be useful in applications such as molecular shape sorting, drug delivery, and molecular immobilization in materials science, to name just a few. However, the design and computational discovery of new caging complexes is a challenging task, as it is hard to predict whether one molecule can encapsulate another because their shapes can be quite complex. In this paper, we propose a computational screening method that predicts whether a given pair of molecules form a caging complex. Our method is based on a caging verification algorithm that was designed by our group for applications in robotic manipulation. We tested our algorithm on three pairs of molecules that were previously described in a pioneering work on molecular caging complexes and found that our results are fully consistent with the previously reported ones. Furthermore, we performed a screening experiment on a data set consisting of 46 hosts and four guests and used our algorithm to predict which pairs are likely to form caging complexes. Our method is computationally efficient and can be integrated into a screening pipeline to complement experimental techniques.

In order for robots to share their workspace with people, they need to reason about human motion efficiently. In this work we leverage large datasets of paths in order to infer local models that are able to perform long-term predictions of human motion. Further, since our method is based on simple dynamics, it is conceptually simple to understand and allows one to interpret the predictions produced, as well as to extract a cost function that can be used for planning. The main difference between our method and similar systems, is that we employ a map of the space and translate the motion of groups of paths into vector fields on that map. We test our method on synthetic data and show its performance on the Edinburgh forum pedestrian long-term tracking dataset [1] where we were able to outperform a Gaussian Mixture Model tasked with extracting dynamics from the paths.

We present sequential windowed inverse reinforcement learning (SWIRL), a policy search algorithm that is a hybrid of exploration and demonstration paradigms for robot learning. We apply unsupervised learning to a small number of initial expert demonstrations to structure future autonomous exploration. SWIRL approximates a long time horizon task as a sequence of local reward functions and subtask transition conditions. Over this approximation, SWIRL applies Q-learning to compute a policy that maximizes rewards. Experiments suggest that SWIRL requires significantly fewer rollouts than pure reinforcement learning and fewer expert demonstrations than behavioral cloning to learn a policy. We evaluate SWIRL in two simulated control tasks, parallel parking and a two-link pendulum. On the parallel parking task, SWIRL achieves the maximum reward on the task with 85% fewer rollouts than Q-learning, and one-eight of demonstrations needed by behavioral cloning. We also consider physical experiments on surgical tensioning and cutting deformable sheets using a da Vinci surgical robot. On the deformable tensioning task, SWIRL achieves a 36% relative improvement in reward compared with a baseline of behavioral cloning with segmentation.

Voronoi cell decompositions provide a classical avenue to classification. Typical approaches however only utilize point-wise cell-membership information by means of nearest neighbor queries and do not utilize further geometric information about Voronoi cells since the computation of Voronoi diagrams is prohibitively expensive in high dimensions. We propose a Monte-Carlo integration based approach that instead computes a weighted integral over the boundaries of Voronoi cells, thus incorporating additional information about the Voronoi cell structure. We demonstrate the scalability of our approach in up to 3072 dimensional spaces and analyze convergence based on the number of Monte Carlo samples and choice of weight functions. Experiments comparing our approach to Nearest Neighbors, SVM and Random Forests indicate that while our approach performs similarly to Random Forests for large data sizes, the algorithm exhibits non-trivial data-dependent performance characteristics for smaller datasets and can be analyzed in terms of a geometric confidence measure, thus adding to the repertoire of geometric approaches to classification while having the benefit of not requiring any model changes or retraining as new training samples or classes are added.

We describe the Coefficient-Flow algorithm for calculating the bounding chain of an (n-1)-boundary on an n-manifold-like simplicial complex S. We prove its correctness and show that it has a computational time complexity of O(vertical bar S(n-1)vertical bar) (where S(n-1) is the set of (n-1)-faces of S). We estimate the big-O coefficient which depends on the dimension of S and the implementation. We present an implementation, experimentally evaluate the complexity of our algorithm, and compare its performance with that of solving the underlying linear system.

Path clustering has found many applications in recent years. Common approaches to this problem use aggregates of the distances between points to provide a measure of dissimilarity between paths which do not satisfy the triangle inequality. Furthermore, they do not take into account the topology of the space where the paths are embedded. To tackle this, we extend previous work in path clustering with relative homology, by employing minimum homology area as a measure of distance between homologous paths in a triangulated mesh. Further, we show that the resulting distance satisfies the triangle inequality, and how we can exploit the properties of homology to reduce the amount of pairwise distance calculations necessary to cluster a set of paths. We further compare the output of our algorithm with that of DTW on a toy dataset of paths, as well as on a dataset of real-world paths.

For applications such as manufacturing, caging grasps restrict object motion without requiring complete immobilization, providing a robust alternative to force-and form-closure grasps. Energy-bounded cages are a new class of caging grasps that relax the requirement of complete caging in the presence of external forces such as gravity or constant velocity pushing in the horizontal plane with Coulomb friction. We address the problem of synthesizing planar energy-bounded cages by identifying gripper and force-direction configurations that maximize the energy required for the object to escape. We present Energy-Bounded-Cage-Synthesis-2-D (EBCS-2-D), a sampling-based algorithm that uses persistent homology, a recently-developed multiscale approach for topological analysis, to efficiently compute candidate rigid configurations of obstacles that form energy-bounded cages of an object from an alpha-shape approximation to the configuration space. If a synthesized configuration has infinite escape energy then the object is completely caged. EBCS-2-D runs in O(s(3) + sn(2)) time, where s is the number of samples and n is the number of object and obstacle vertices, where typically n << s. We observe runtimes closer to O(s) for fixed n. We implement EBCS-2-D using the persistent homology algorithms toolbox and study performance on a set of seven planar objects and four gripper types. Experiments suggest that EBCS-2-D takes 2-3 min on a 6 core processor with 200 000 pose samples. We also confirm that an rapidly-exploring random tree* motion planner is unable to find escape paths with lower energy. Physical experiments on a five degree of freedom Zymark Zymate and ABB YuMi suggest that push grasps synthesized by EBCS-2-D are robust to perturbations. Data and code are available at http://berkeleyautomation.github.io/caging/.

We present a novel approach and database which combines the inexpensive generation of 3D object models via monocular or RGB-D camera images with 3D printing and a state of the art object tracking algorithm. Unlike recent efforts towards the creation of 3D object databases for robotics, our approach does not require expensive and controlled 3D scanning setups and aims to enable anyone with a camera to scan, print and track complex objects for manipulation research. The proposed approach results in detailed textured mesh models whose 3D printed replicas provide close approximations of the originals. A key motivation for utilizing 3D printed objects is the ability to precisely control and vary object properties such as the size, material properties and mass distribution in the 3D printing process to obtain reproducible conditions for robotic manipulation research. We present CapriDB – an extensible database resulting from this approach containing initially 40 textured and 3D printable mesh models together with tracking features to facilitate the adoption of the proposed approach.

The robustness of a parallel-jaw grasp can be estimated by Monte Carlo sampling of perturbations in pose and friction but this is not computationally efficient. As an alternative, we consider fast methods using large-scale supervised learning, where the input is a description of a local surface patch at each of two contact points. We train and test with disjoint subsets of a corpus of 1.66 million grasps where robustness is estimated by Monte Carlo sampling using Dex-Net 1.0. We use the BIDMach machine learning toolkit to compare the performance of two supervised learning methods: Random Forests and Deep Learning. We find that both of these methods learn to estimate grasp robustness fairly reliably in terms of Mean Absolute Error (MAE) and ROC Area Under Curve (AUC) on a held-out test set. Speedups over Monte Carlo sampling are approximately 7500x for Random Forests and 1500x for Deep Learning.

Estimation and forecasting of dynamic state are fundamental to the design of autonomous systems such as intelligent robots. State-of-the-art algorithms, such as the particle filter, face computational limitations when needing to maintain beliefs over a hypothesis space that is made large by the dynamic nature of the environment. We propose an algorithm that utilises a hierarchy of such filters, exploiting a filtration arising from the geometry of the underlying hypothesis space. In addition to computational savings, such a method can accommodate the availability of evidence at varying degrees of coarseness. We show, using synthetic trajectory datasets, that our method achieves a better normalised error in prediction and better time to convergence to a true class when compared against baselines that do not similarly exploit geometric structure.