Software Downloads
MERL software freely available for noncommercial use.
MERL is making some software available to the research community. Simply click the 'Download Now' button below to gain access to the software.

CITO — ContactImplicit Trajectory Optimization
This package provides a generalized solution for planning dynamic contactinteraction trajectories. The software package leverages existing opensource code for [Contact Implicit Trajectory Optimization](https://github.com/aykutonol/cito) based on a variable smooth contact model and a successive convexification algorithm for the trajectory optimization. This software package adds a penalty loop that adjusts the penalty on the virtual forces automatically and a postprocess stage that improves solutions through a forward pass by exploiting the contact information implied by the utilization of the virtual forces.
Underactuated dynamics with frictional rigidbody contacts is modeled using [MuJoCo](http://mujoco.org/). The convex . . . 
OFENet — Online Feature Extractor Network
This Python code implements an online feature extractor network (OFENet) that uses neural nets to produce good representations to be used as inputs to deep RL algorithms. Even though the high dimensionality of input is usually supposed to make learning of RL agents more difficult, by using this network, we show that the RL agents in fact learn more efficiently with the highdimensional representation than with the lowerdimensional state observations. We believe that stronger feature propagation together with larger networks (and thus larger search space) allows RL agents to learn more complex functions of states and thus improves the sample efficiency. The code also contains several test problems. Through numerical experiments on these . . .

MotionNet
The ability to reliably perceive the environmental states, particularly the existence of objects and their motion behavior, is crucial for autonomous driving. In this work, we propose an efficient deep model, called MotionNet, to jointly perform perception and motion prediction from 3D point clouds. MotionNet takes a sequence of LiDAR sweeps as input and outputs a bird's eye view (BEV) map, which encodes the object category and motion information in each grid cell. The backbone of MotionNet is a novel spatiotemporal pyramid network, which extracts deep spatial and temporal features in a hierarchical fashion. To enforce the smoothness of predictions over both space and time, the training of MotionNet is further regularized with novel . . .

FMIEstimationDemo — Functional Mockup Interface Estimation Demo
This software demonstrates the use of the Functional Mockup Interface (FMI) to construct extended Kalman filters (EKF) and ensemble Kalman filters (EnKF) for state estimation in Modelica using the Dymola compiler.
One of the key advantages of Modelica is that it enables users to create largescale physical system models via the interconnection of simpler subsystem or component models, and thereby manage the complexity inherent in describing these large systems. While one candidate use for such models is in using data to estimate unmeasured variables of a complex system, the equation compilation process can make it difficult to work with the state vector directly when implementing state estimation methods. Functional mockup . . . 
FoldingNet++
This software is the pytorch implementation of FoldingNet++, which is a novel endtoend graphbased deep autoencoder to achieve compact representations of unorganized 3D point clouds in an unsupervised manner.
The encoder of the proposed networks adopts similar architectures as in PointNet, which is a wellacknowledged method for supervised learning of 3D point clouds, such as recognition and segmentation. The decoder of the proposed networks involves three novel modules: folding module, graphtopologyinference module, and graphfiltering module. The folding module folds a canonical 2D lattice to the underlying surface of a 3D point cloud, achieving coarse reconstruction; the graphtopologyinference module learns a graph . . . 
QNTRPO — QuasiNewton Trust Region Policy Optimization
We propose a trust region method for policy optimization that employs QuasiNewton approximation for the Hessian, called QuasiNewton Trust Region Policy Optimization (QNTRPO). Gradient descent has become the de facto algorithm for reinforcement learning tasks with continuous controls. The algorithms has achieved stateoftheart performance on wide variety of tasks and resulted in several improvements in performance of reinforcement learning algorithms across a wide range of systems. However, the algorithm suffers from a number of drawbacks including: lack of stepsize selection criterion, slow convergence, and dependence on problem scaling. We investigate the use of a dogleg method with a QuasiNewton approximation for the Hessian to . . .

RIDE — Robust Iterative Data Estimation
Recent studies have demonstrated that as classifiers, deep neural networks (e.g., CNNs) are quite vulnerable to adversarial attacks that only add quasiimperceptible perturbations to the input data but completely change the predictions of the classifiers. To defend classifiers against such adversarial attacks, here we focus on the whitebox adversarial defense where the attackers are granted full access to not only the classifiers but also defenders to produce as strong attack as possible. We argue that a successful whitebox defender should prevent the attacker from not only direct gradient calculation but also a gradient approximation. Therefore we propose viewing the defense from the perspective of a functional, a highorder function . . .

DSP — Discriminative Subspace Pooling
Human action recognition from video sequences is one of the fundamental problems in computer vision. In this research, we investigate and propose representation learning approaches towards solving this problem, which we call discriminative subspace pooling. Specifically, we combine recent deep learning approaches with techniques for generating adversarial perturbations into learning novel representations that can summarize long video sequences into compact descriptors – these descriptors capture essential properties of the input videos that are sufficient to achieve good recognition rates. We make two contributions. First, we propose a subspacebased discriminative classifier, similar to a nonlinear SVM, but having piecewiselinear . . .

GNI — Gradientbased NikaidoIsoda
Computing Nash equilibrium (NE) of multiplayer games has witnessed renewed interest due to recent advances in generative adversarial networks (GAN). However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradientbased NikaidoIsoda (GNI) function which serves as a merit function, vanishing only at the firstorder stationary points of each player’s optimization problem. Gradient descent is shown to converge sublinearly to a firstorder stationary point of the GNI function. For the particular case of bilinear minmax games and multiplayer quadratic games, the GNI function is convex. Hence, the application of gradient descent in this case yields linear convergence to an NE (when one exists).
. . . 
SSTL — SemiSupervised Transfer Learning
Successful stateoftheart machine learning techniques rely on the existence of large well sampled and labeled datasets. Today it is easy to obtain a finely sampled dataset because of the decreasing cost of connected lowenergy devices. However, it is often difficult to obtain a large number of labels. The reason for this is twofold. First, labels are often provided by people whose attention span is limited. Second, even if a person was able to label perpetually, this person would need to be shown data in a large variety of conditions. One approach to addressing these problems is to combine labeled data collected in different sessions through transfer learning. Still even this approach suffers from dataset limitations.
This . . . 
1bCRB — OneBit CRB
Massive multipleinput multipleoutput (MIMO) systems can significantly increase the spectral efficiency, mitigate propagation loss by exploiting large array gain, and reduce interuser interference with highresolution spatial beamforming. To reduce complexity and power consumption, several transceiver architectures have been proposed for mmWave massive MIMO systems: 1) an analog architecture, 2) a hybrid analog/digital architecture, and 3) a fully digital architecture with lowresolution ADCs.
To this end, we derive the CramerRao bound (CRB) on estimating angulardomain channel parameters including anglesofdeparture (AoDs), anglesofarrival (AoAs), and associated channel path gains. Our analysis provides a simple tool . . . 
FoldingNet
Recent deep networks that directly handle points in a point set, e.g., PointNet, have been stateoftheart for supervised learning tasks on point clouds such as classification and segmentation. In this work, a novel endtoend deep autoencoder is proposed to address unsupervised learning challenges on point clouds. On the encoder side, a graphbased enhancement is enforced to promote local structures on top of PointNet. Then, a novel foldingbased decoder deforms a canonical 2D grid onto the underlying 3D object surface of a point cloud, achieving low reconstruction errors even for objects with delicate structures. The proposed decoder only uses about 7% parameters of a decoder with fullyconnected neural networks, yet leads to a more . . .

Kernel Correlation Network
Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets. However, it does not take full advantage of a point's local neighborhood that contains finegrained structural information which turns out to be helpful towards better semantic learning. In this regard, we present two new operations to improve PointNet with a more efficient exploitation of local structures. The first one focuses on local 3D geometric structures. In analogy to a convolution kernel for images, we define a pointset kernel as a set of learnable 3D points that jointly respond to a set of . . .

FRPC — Fast Resampling on Point Clouds via Graphs
We propose a randomized resampling strategy to reduce the cost of storing, processing and visualizing a largescale point cloud, that selects a representative subset of points while preserving applicationdependent features. The strategy is based on graphs, which can represent underlying surfaces and lend themselves well to efficient computation. We use a general featureextraction operator to represent applicationdependent features and propose a general reconstruction error to evaluate the quality of resampling; by minimizing the error, we obtain a general form of optimal resampling distribution. The proposed resampling distribution is guaranteed to be shift, rotation and scaleinvariant in the 3D space.

PCQM — Point Cloud Quality Metric
It is challenging to measure the geometry distortion of point cloud introduced by point cloud compression. Conventionally, the errors between point clouds are measured in terms of pointtopoint or pointtosurface distances, that either ignores the surface structures or heavily tends to rely on specific surface reconstructions. To overcome these drawbacks, we propose using pointtoplane distances as a measure of geometric distortions on point cloud compression. The intrinsic resolution of the point clouds is proposed as a normalizer to convert the mean square errors to PSNR numbers. In addition, the perceived local planes are investigated at different scales of the point cloud. Finally, the proposed metric is independent of the size of . . .

ROSETA — Robust Online Subspace Estimation and Tracking Algorithm
This script implements a revised version of the robust online subspace estimation and tracking algorithm (ROSETA) that is capable of identifying and tracking a timevarying low dimensional subspace from incomplete measurements and in the presence of sparse outliers. The algorithm minimizes a robust l1 norm cost function between the observed measurements and their projection onto the estimated subspace. The projection coefficients and sparse outliers are computed using a LASSO solver and the subspace estimate is updated using a proximal point iteration with adaptive parameter selection.

CASENet — Deep CategoryAware Semantic Edge Detection
Boundary and edge cues are highly beneficial in improving a wide variety of vision tasks such as semantic segmentation, object recognition, stereo, and object proposal generation. Recently, the problem of edge detection has been revisited and significant progress has been made with deep learning. While classical edge detection is a challenging binary problem in itself, the categoryaware semantic edge detection by nature is an even more challenging multilabel problem. We model the problem such that each edge pixel can be associated with more than one class as they appear in contours or junctions belonging to two or more semantic classes. To this end, we propose a novel endtoend deep semantic edge learning architecture based on ResNet . . .

NDS — Nonnegative Dynamical System model
Nonnegative data arise in a variety of important signal processing domains, such as power spectra of signals, pixels in images, and count data. We introduce a novel nonnegative dynamical system model for sequences of such data. The model we propose is called nonnegative dynamical system (NDS), and bridges two active fields, dynamical systems and nonnegative matrix factorization (NMF). Its formulation follows that of linear dynamical systems, but the observation and the latent variables are assumed nonnegative, the linear transforms are assumed to involve nonnegative coefficients, and the additive random innovations both for the observation and the latent variables are replaced by multiplicative random innovations. The software . . .

JGU — Joint Geodesic Upsampling
We develop an algorithm utilizing geodesic distances to upsample a low resolution depth image using a registered high resolution color image. Specifically, it computes depth for each pixel in the high resolution image using geodesic paths to the pixels whose depths are known from the low resolution one. Though this is closely related to the allpairshortestpath problem which has O(n2 log n) complexity, we develop a novel approximation algorithm whose complexity grows linearly with the image size and achieve realtime performance. We compare our algorithm with the state of the art on the benchmark dataset and show that our approach provides more accurate depth upsampling with fewer artifacts. In addition, we show that the proposed . . .

EBAD — ExemplarBased Anomaly Detection
Anomaly detection in realvalued time series has important applications in many diverse areas. We have developed a general algorithm for detecting anomalies in realvalued time series that is computationally very efficient. Our algorithm is exemplarbased which means a set of exemplars are first learned from a normal time series (i.e. not containing any anomalies) which effectively summarizes all normal windows in the training time series. Anomalous windows of a testing time series can then be efficiently detected using the exemplarbased model.
The provided code implements our hierarchical exemplar learning algorithm, our exemplarbased anomaly detection algorithm, and a baseline bruteforce Euclidean distance anomaly . . . 
PEAC — Plane Extraction using Agglomerative Clustering
Realtime plane extraction in 3D point clouds is crucial to many robotics applications. We present a novel algorithm for reliably detecting multiple planes in real time in organized point clouds obtained from devices such as Kinect sensors. By uniformly dividing such a point cloud into nonoverlapping groups of points in the image space, we first construct a graph whose node and edge represent a group of points and their neighborhood respectively. We then perform an agglomerative hierarchical clustering on this graph to systematically merge nodes belonging to the same plane until the plane fitting mean squared error exceeds a threshold. Finally we refine the extracted planes using pixelwise region growing. Our experiments demonstrate that . . .

PQP — Parallel Quadratic Programming
An iterative multiplicative algorithm is proposed for the fast solution of quadratic programming (QP) problems that arise in the realtime implementation of Model Predictive Control (MPC). The proposed algorithm—Parallel Quadratic Programming (PQP)—is amenable to finegrained parallelization. Conditions on the convergence of the PQP algorithm are given and proved. Due to its extreme simplicity, even serial implementations offer considerable speed advantages. To demonstrate, PQP is applied to several simulation examples, including a standalone QP problem and two MPC examples. When implemented in MATLAB using singlethread computations, numerical simulations of PQP demonstrate a 5  10x speedup compared to the MATLAB activeset . . .