Joint Search of Optimal Topology and Trajectory for Planar Linkages

We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex periodic motion, refined{which is an important component when building low-cost, modular robots, mechanical toys, and foldable structures in our daily lives (chairs, bikes, and shelves). The design of such structures require trial and error even for experienced engineers. Our research provides semi-automatic methods for exploring novel designs given high-level specifications and constraints.} We formulate this problem as a non-smooth numerical optimization with quadratic objective functions and non-convex quadratic constraints involving mixed-integer decision variables (MIQCQP). We propose and compare three approximate algorithms to solve this problem: mixed-integer conic-programming (MICP), mixed-integer nonlinear programming (MINLP), and simulated annealing (SA). We evaluated these algorithms searching for planar linkages involving $10-14$ rigid links. Our results show that the best performance can be achieved by combining MICP and MINLP, leading to a hybrid algorithm capable of finding the planar linkages within a couple of hours on a desktop machine, which significantly outperforms the SA baseline in terms of optimality. We highlight the effectiveness of our optimized planar linkages by using them as legs of a walking robot.

Multi-Robot Path Planning in Complex Environments via Graph Embedding

We propose an approach to solve multi-agent path planning (MPP) problems for complex environments. Our method first designs a special pebble graph with a set of feasibility constraints, under which MPP problems have feasibility guarantee. We further propose an algorithm to greedily improve the optimality of planned MPP solutions via parallel pebble motions. As a second step, we develop a mesh optimization algorithm to embed our pebble graph into arbitrarily complex environments. We show that the feasibility constraints of a pebble graph can be converted into differentiable geometric constraints, such that our mesh optimizer can satisfy these constraints via constrained numerical optimization. We have evaluated the effectiveness and efficiency of our method using a set of environments with complex geometries, on which our method achieves an average of 99.0% free-space coverage and 30.3% robot density within hours of computation on a desktop machine.

Planning of Power Grasps Using Infinite Program Under Complementary Constraints

We propose an optimization-based approach to plan power grasps. Central to our method is a reformulation of grasp planning as an infinite program under complementary constraints (IPCC), which allows contacts to happen between arbitrary pairs of points on the object and the robot gripper. We show that IPCC can be reduced to a conventional finite-dimensional nonlinear program (NLP) using a kernel-integral relaxation. Moreover, the values and Jacobian matrices of the kernel-integral can be evaluated efficiently using a modified Fast Multipole Method (FMM). We further guarantee that the planned grasps are collision-free using primal barrier penalties. We demonstrate the effectiveness, robustness, and efficiency of our grasp planner on a row of challenging 3D objects and high-DOF grippers, such as Barrett Hand and Shadow Hand, where our method achieves superior grasp qualities over competitors.

Boost-R: Gradient Boosted Trees for Recurrence Data

Recurrence data arise from multi-disciplinary domains spanning reliability, cyber security, healthcare, online retailing, etc. This paper investigates an additive-tree-based approach, known as Boost-R (Boosting for Recurrence Data), for recurrent event data with both static and dynamic features. Boost-R constructs an ensemble of gradient boosted additive trees to estimate the cumulative intensity function of the recurrent event process, where a new tree is added to the ensemble by minimizing the regularized L2 distance between the observed and predicted cumulative intensity. Unlike conventional regression trees, a time-dependent function is constructed by Boost-R on each tree leaf. The sum of these functions, from multiple trees, yields the ensemble estimator of the cumulative intensity. The divide-and-conquer nature of tree-based methods is appealing when hidden sub-populations exist within a heterogeneous population. The non-parametric nature of regression trees helps to avoid parametric assumptions on the complex interactions between event processes and features. Critical insights and advantages of Boost-R are investigated through comprehensive numerical examples. Datasets and computer code of Boost-R are made available on GitHub. To our best knowledge, Boost-R is the first gradient boosted additive-tree-based approach for modeling large-scale recurrent event data with both static and dynamic feature information.

An Adversarial Transfer Network for Knowledge Representation Learning

Knowledge representation learning has received a lot of attention in the past few years. The success of existing methods heavily relies on the quality of knowledge graphs. The entities with few triplets tend to be learned with less expressive power. Fortunately, there are many knowledge graphs constructed from various sources, the representations of which could contain much information. We propose an adversarial embedding transfer network ATransN, which transfers knowledge from one or more teacher knowledge graphs to a target one through an aligned entity set without explicit data leakage. Specifically, we add soft constraints on aligned entity pairs and neighbours to the existing knowledge representation learning methods. To handle the problem of possible distribution differences between teacher and target knowledge graphs, we introduce an adversarial adaption module. The discriminator of this module evaluates the degree of consistency between the embeddings of an aligned entity pair. The consistency score is then used as the weights of soft constraints. It is not necessary to acquire the relations and triplets in teacher knowledge graphs because we only utilize the entity representations. Knowledge graph completion results show that ATransN achieves better performance against baselines without transfer on three datasets, CN3l, WK3l, and DWY100k. The ablation study demonstrates that ATransN can bring steady and consistent improvement in different settings. The extension of combining other knowledge graph embedding algorithms and the extension with three teacher graphs display the promising generalization of the adversarial transfer network.

Enhance Information Propagation for Graph Neural Network by Heterogeneous Aggregations

Graph neural networks are emerging as continuation of deep learning success w.r.t. graph data. Tens of different graph neural network variants have been proposed, most following a neighborhood aggregation scheme, where the node features are updated via aggregating features of its neighboring nodes from layer to layer. Though related research surges, the power of GNNs are still not on-par-with their counterpart CNNs in computer vision and RNNs in natural language processing. We rethink this problem from the perspective of information propagation, and propose to enhance information propagation among GNN layers by combining heterogeneous aggregations. We argue that as richer information are propagated from shallow to deep layers, the discriminative capability of features formulated by GNN can benefit from it. As our first attempt in this direction, a new generic GNN layer formulation and upon this a new GNN variant referred as HAG-Net is proposed. We empirically validate the effectiveness of HAG-Net on a number of graph classification benchmarks, and elaborate all the design options and criterions along with.

New Formulation of Mixed-Integer Conic Programming for Globally Optimal Grasp Planning

We present a two-level branch-and-bound (BB) algorithm to compute the optimal gripper pose that maximizes a grasp metric in a restricted search space. Our method can take the grippers kinematics feasibility into consideration to ensure that a given gripper can reach the set of grasp points without collisions or predict infeasibility with finite-time termination when no pose exists for a given set of grasp points. Our main technical contribution is a novel mixed-integer conic programming (MICP) formulation for the inverse kinematics of the gripper that uses a small number of binary variables and tightened constraints, which can be efficiently solved via a low-level BB algorithm. Our experiments show that optimal gripper poses for various target objects can be computed taking 20-180 minutes of computation on a desktop machine and the computed grasp quality, in terms of the Q1 metric, is better than those generated using sampling-based planners.

Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one

Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an $(m,n,3,lambda_a,1)$-OOSPC with $lambda_a=2,3$ is established. The exact number of codewords of an optimal $(m,n,3,lambda_a,1)$-OOSPC is determined for any positive integers $m,nequiv2 ({rm mod } 4)$ and $lambda_ain{2,3}$.

High strangeness dibaryons in the extended quark delocalization, color screening model

Dibaryon candidates with strangeness S=-2,-3,-4,-5,-6 are studied in terms of the extended quark delocalization and color screening model. The results show that there are only a few promising low lying dibaryon states: The H and di-Omega may be marginally strong interaction stable but model uncertainties are too large to allow any definitive statement. The SIJ=-3,1/2,2 N-Omega state is 62 MeV lower than the N-Omega threshold and 24 MeV lower than the Lambda-Xi-pi threshold. It might appear as a narrow dibaryon resonance and be detectable in the RHIC detector through the reconstruction of the vertex mass of the Lambda-Xi two body decay. The effects of explicit K and eta meson exchange have been studied and found to be negligible in this model. The mechanisms of effective intermediate range attraction, sigma meson exchange and kinetic energy reduction due to quark delocalization are discussed.