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In recent years, neural implicit representations gained popularity in 3D reconstruction due to their expressiveness and flexibility. However, the implicit nature of neural implicit representations results in slow inference time and requires careful initialization. In this paper, we revisit the classic yet ubiquitous point cloud representation and introduce a differentiable point-to-mesh layer using a differentiable formulation of Poisson Surface Reconstruction (PSR) that allows for a GPU-accelerated fast solution of the indicator function given an oriented point cloud. The differentiable PSR layer allows us to efficiently and differentiably bridge the explicit 3D point representation with the 3D mesh via the implicit indicator field, enabling end-to-end optimization of surface reconstruction metrics such as Chamfer distance. This duality between points and meshes hence allows us to represent shapes as oriented point clouds, which are explicit, lightweight and expressive. Compared to neural implicit representations, our Shape-As-Points (SAP) model is more interpretable, lightweight, and accelerates inference time by one order of magnitude. Compared to other explicit representations such as points, patches, and meshes, SAP produces topology-agnostic, watertight manifold surfaces. We demonstrate the effectiveness of SAP on the task of surface reconstruction from unoriented point clouds and learning-based reconstruction.

Manipulating articulated objects requires multiple robot arms in general. It is challenging to enable multiple robot arms to collaboratively complete manipulation tasks on articulated objects. In this paper, we present $\textbf{V-MAO}$, a framework for learning multi-arm manipulation of articulated objects. Our framework includes a variational generative model that learns contact point distribution over object rigid parts for each robot arm. The training signal is obtained from interaction with the simulation environment which is enabled by planning and a novel formulation of object-centric control for articulated objects. We deploy our framework in a customized MuJoCo simulation environment and demonstrate that our framework achieves a high success rate on six different objects and two different robots. We also show that generative modeling can effectively learn the contact point distribution on articulated objects.

In this paper we present a new perspective on error analysis of Legendre approximations for differentiable functions. We start by introducing a sequence of Legendre-Gauss-Lobatto polynomials and prove their theoretical properties, such as an explicit and optimal upper bound. We then apply these properties to derive a new and explicit bound for the Legendre coefficients of differentiable functions and establish some explicit and optimal error bounds for Legendre projections in the $L^2$ and $L^{\infty}$ norms. Illustrative examples are provided to demonstrate the sharpness of our new results.

In design, fabrication, and control problems, we are often faced with the task of synthesis, in which we must generate an object or configuration that satisfies a set of constraints while maximizing one or more objective functions. The synthesis problem is typically characterized by a physical process in which many different realizations may achieve the goal. This many-to-one map presents challenges to the supervised learning of feed-forward synthesis, as the set of viable designs may have a complex structure. In addition, the non-differentiable nature of many physical simulations prevents efficient direct optimization. We address both of these problems with a two-stage neural network architecture that we may consider to be an autoencoder. We first learn the decoder: a differentiable surrogate that approximates the many-to-one physical realization process. We then learn the encoder, which maps from goal to design, while using the fixed decoder to evaluate the quality of the realization. We evaluate the approach on two case studies: extruder path planning in additive manufacturing and constrained soft robot inverse kinematics. We compare our approach to direct optimization of the design using the learned surrogate, and to supervised learning of the synthesis problem. We find that our approach produces higher quality solutions than supervised learning, while being competitive in quality with direct optimization, at a greatly reduced computational cost.

Deep reinforcement learning algorithms require large and diverse datasets in order to learn successful policies for perception-based mobile navigation. However, gathering such datasets with a single robot can be prohibitively expensive. Collecting data with multiple different robotic platforms with possibly different dynamics is a more scalable approach to large-scale data collection. But how can deep reinforcement learning algorithms leverage such heterogeneous datasets? In this work, we propose a deep reinforcement learning algorithm with hierarchically integrated models (HInt). At training time, HInt learns separate perception and dynamics models, and at test time, HInt integrates the two models in a hierarchical manner and plans actions with the integrated model. This method of planning with hierarchically integrated models allows the algorithm to train on datasets gathered by a variety of different platforms, while respecting the physical capabilities of the deployment robot at test time. Our mobile navigation experiments show that HInt outperforms conventional hierarchical policies and single-source approaches.

A seamless integration of robots into human environments requires robots to learn how to use existing human tools. Current approaches for learning tool manipulation skills mostly rely on expert demonstrations provided in the target robot environment, for example, by manually guiding the robot manipulator or by teleoperation. In this work, we introduce an automated approach that replaces an expert demonstration with a Youtube video for learning a tool manipulation strategy. The main contributions are twofold. First, we design an alignment procedure that aligns the simulated environment with the real-world scene observed in the video. This is formulated as an optimization problem that finds a spatial alignment of the tool trajectory to maximize the sparse goal reward given by the environment. Second, we describe an imitation learning approach that focuses on the trajectory of the tool rather than the motion of the human. For this we combine reinforcement learning with an optimization procedure to find a control policy and the placement of the robot based on the tool motion in the aligned environment. We demonstrate the proposed approach on spade, scythe and hammer tools in simulation, and show the effectiveness of the trained policy for the spade on a real Franka Emika Panda robot demonstration.

This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based optimization. We achieve this by extending the Combinatorial Equilibrium Modeling (CEM) framework in three important ways. Firstly, we introduce a new topological object, the auxiliary trail, to expand the range of structures that can be form-found with the framework. Secondly, we leverage automatic differentiation (AD) to obtain an exact value of the gradient of the sequential and iterative calculations of the CEM form-finding algorithm, instead of a numerical approximation. We finally encapsulate our research developments into an open-source design tool written in Python that is usable across different CAD platforms and operating systems. After studying four different structures -- a self-stressed planar tensegrity, a tree canopy, a curved suspension bridge, and a spiral staircase -- we show that our approach allows solving constrained form-finding problems on a diverse range of structures more efficiently than in previous work.

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) method to approximate them. This instability arises in the presence of eigenvalues that are close to each other. This makes integrating eigendecomposition into deep networks difficult and often results in poor convergence, particularly when dealing with large matrices. While this can be mitigated by partitioning the data into small arbitrary groups, doing so has no theoretical basis and makes it impossible to exploit the full power of eigendecomposition. In previous work, we mitigated this using SVD during the forward pass and PI to compute the gradients during the backward pass. However, the iterative deflation procedure required to compute multiple eigenvectors using PI tends to accumulate errors and yield inaccurate gradients. Here, we show that the Taylor expansion of the SVD gradient is theoretically equivalent to the gradient obtained using PI without relying in practice on an iterative process and thus yields more accurate gradients. We demonstrate the benefits of this increased accuracy for image classification and style transfer.

Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.