A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various conditions, which are encoded by class labels. Machine learning methods including Dirichlet process mixture model and maximum likelihood estimation are employed for uncertainty modeling. A DDSRO framework is further proposed based on the data-driven uncertainty model through a bi-level optimization structure. The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different data classes; adaptive robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. A decomposition-based algorithm is further developed to solve the resulting multi-level optimization problem efficiently. Case studies on process network design and planning are presented to demonstrate the applicability of the proposed framework and algorithm.

Impedance control and specifically stiffness control are widely applied for physical human-robot interaction. The series elastic actuator (SEA) provides inherent compliance, safety and further benefits. This paper aims to improve the stiffness control performance of a cable-driven SEA. Existing impedance controllers were designed within the full frequency domain, though human-robot interaction commonly falls in the low frequency range. We enhance the stiffness rendering performance under formulated constraints of passivity, actuator limitation, disturbance attenuation, noise rejection at their specific frequency ranges. Firstly, we reformulate this multiple frequency-band optimization problem into the $H_\infty$ synthesis framework. Then, the performance goals are quantitatively characterized by respective restricted frequency-domain specifications as norm bounds. Further, a structured controller is directly synthesized to satisfy all the competing performance requirements. Both simulation and experimental results showed that the produced controller enabled good interaction performance for each desired stiffness varying from 0 to 1 times of the physical spring constant. Compared with the passivity-based PID method, the proposed $H_\infty$ synthesis method achieved more accurate and robust stiffness control performance with guaranteed passivity.

The operational space of an autonomous vehicle (AV) can be diverse and vary significantly. This may lead to a scenario that was not postulated in the design phase. Due to this, formulating a rule based decision maker for selecting maneuvers may not be ideal. Similarly, it may not be effective to design an a-priori cost function and then solve the optimal control problem in real-time. In order to address these issues and to avoid peculiar behaviors when encountering unforeseen scenario, we propose a reinforcement learning (RL) based method, where the ego car, i.e., an autonomous vehicle, learns to make decisions by directly interacting with simulated traffic. The decision maker for AV is implemented as a deep neural network providing an action choice for a given system state. In a critical application such as driving, an RL agent without explicit notion of safety may not converge or it may need extremely large number of samples before finding a reliable policy. To best address the issue, this paper incorporates reinforcement learning with an additional short horizon safety check (SC). In a critical scenario, the safety check will also provide an alternate safe action to the agent provided if it exists. This leads to two novel contributions. First, it generalizes the states that could lead to undesirable "near-misses" or "collisions ". Second, inclusion of safety check can provide a safe and stable training environment. This significantly enhances learning efficiency without inhibiting meaningful exploration to ensure safe and optimal learned behavior. We demonstrate the performance of the developed algorithm in highway driving scenario where the trained AV encounters varying traffic density in a highway setting.

Unmanned Aerial Vehicle (UAV) path planning algorithms often assume a knowledge reward function or priority map, indicating the most important areas to visit. In this paper we propose a method to create priority maps for monitoring or intervention of dynamic spreading processes such as wildfires. The presented optimization framework utilizes the properties of positive systems, in particular the separable structure of value (cost-to-go) functions, to provide scalable algorithms for surveillance and intervention. We present results obtained for a 16 and 1000 node example and convey how the priority map responds to changes in the dynamics of the system. The larger example of 1000 nodes, representing a fictional landscape, shows how the method can integrate bushfire spreading dynamics, landscape and wind conditions. Finally, we give an example of combining the proposed method with a travelling salesman problem for UAV path planning for wildfire intervention.

Purpose: This paper presents an impedance control method with mixed $H_2/H_\infty$ synthesis and relaxed passivity for a cable-driven series elastic actuator to be applied for physical human-robot interaction. Design/methodology/approach: To shape the system's impedance to match a desired dynamic model, the impedance control problem was reformulated into an impedance matching structure. The desired competing performance requirements as well as constraints from the physical system can be characterized with weighting functions for respective signals. Considering the frequency properties of human movements, the passivity constraint for stable human-robot interaction, which is required on the entire frequency spectrum and may bring conservative solutions, has been relaxed in such a way that it only restrains the low frequency band. Thus, impedance control became a mixed $H_2/H_\infty$ synthesis problem, and a dynamic output feedback controller can be obtained. Findings: The proposed impedance control strategy has been tested for various desired impedance with both simulation and experiments on the cable-driven series elastic actuator platform. The actual interaction torque tracked well the desired torque within the desired norm bounds, and the control input was regulated below the motor velocity limit. The closed loop system can guarantee relaxed passivity at low frequency. Both simulation and experimental results have validated the feasibility and efficacy of the proposed method. Originality/value: This impedance control strategy with mixed $H_2/H_\infty$ synthesis and relaxed passivity provides a novel, effective and less conservative method for physical human-robot interaction control.

Exoskeletons which amplify the strength of their operators can enable heavy-duty manipulation of unknown objects. However, this type of behavior is difficult to accomplish; it requires the exoskeleton to sense and amplify the operator's interaction forces while remaining stable. But, the goals of amplification and robust stability when connected to the operator fundamentally conflict. As a solution, we introduce a design with a spring in series with the force sensitive cuff. This allows us to design an exoskeleton compliance behavior which is nominally passive, even with high amplification ratios. In practice, time delay and discrete time filters prevent our strategy from actually achieving passivity, but the designed compliance still makes the exoskeleton more robust to spring-like human behaviors. Our exoskeleton is actuated by a series elastic actuator (SEA), which introduces another spring into the system. We show that shaping the cuff compliance for the exoskeleton can be made into approximately the same problem as shaping the spring compliance of an SEA. We therefore introduce a feedback controller and gain tuning method which takes advantage of an existing compliance shaping technique for SEAs. We call our strategy the "double compliance shaping" method. With large amplification ratios, this controller tends to amplify nonlinear transmission friction effects, so we additionally propose a "transmission disturbance observer" to mitigate this drawback. Our methods are validated on a single-degree-of-freedom elbow exoskeleton.

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalman filter gain, given a single trajectory of output measurements over a finite horizon of length $N$. Based on a subspace identification algorithm and a finite number of $N$ output samples, we provide non-asymptotic high-probability upper bounds for the system parameter estimation errors. Our analysis uses recent results from random matrix theory, self-normalized martingales and SVD robustness, in order to show that with high probability the estimation errors decrease with a rate of $1/\sqrt{N}$. Our non-asymptotic bounds not only agree with classical asymptotic results, but are also valid even when the system is marginally stable.

Reinforcement Learning (RL) algorithms have found limited success beyond simulated applications, and one main reason is the absence of safety guarantees during the learning process. Real world systems would realistically fail or break before an optimal controller can be learned. To address this issue, we propose a controller architecture that combines (1) a model-free RL-based controller with (2) model-based controllers utilizing control barrier functions (CBFs) and (3) on-line learning of the unknown system dynamics, in order to ensure safety during learning. Our general framework leverages the success of RL algorithms to learn high-performance controllers, while the CBF-based controllers both guarantee safety and guide the learning process by constraining the set of explorable polices. We utilize Gaussian Processes (GPs) to model the system dynamics and its uncertainties. Our novel controller synthesis algorithm, RL-CBF, guarantees safety with high probability during the learning process, regardless of the RL algorithm used, and demonstrates greater policy exploration efficiency. We test our algorithm on (1) control of an inverted pendulum and (2) autonomous car-following with wireless vehicle-to-vehicle communication, and show that our algorithm attains much greater sample efficiency in learning than other state-of-the-art algorithms and maintains safety during the entire learning process.

Traffic flow forecasting has been regarded as a key problem of intelligent transport systems. In this work, we propose a hybrid multimodal deep learning method for short-term traffic flow forecasting, which can jointly and adaptively learn the spatial-temporal correlation features and long temporal interdependence of multi-modality traffic data by an attention auxiliary multimodal deep learning architecture. According to the highly nonlinear characteristics of multi-modality traffic data, the base module of our method consists of one-dimensional Convolutional Neural Networks (1D CNN) and Gated Recurrent Units (GRU) with the attention mechanism. The former is to capture the local trend features and the latter is to capture the long temporal dependencies. Then, we design a hybrid multimodal deep learning framework (HMDLF) for fusing share representation features of different modality traffic data by multiple CNN-GRU-Attention modules. The experimental results indicate that the proposed multimodal deep learning model is capable of dealing with complex nonlinear urban traffic flow forecasting with satisfying accuracy and effectiveness.

The area of building energy management has received a significant amount of interest in recent years. This area is concerned with combining advancements in sensor technologies, communications and advanced control algorithms to optimize energy utilization. Reinforcement learning is one of the most prominent machine learning algorithms used for control problems and has had many successful applications in the area of building energy management. This research gives a comprehensive review of the literature relating to the application of reinforcement learning to developing autonomous building energy management systems. The main direction for future research and challenges in reinforcement learning are also outlined.

One of the big attractions of low-dimensional models for gait design has been the ability to compute solutions rapidly, whereas one of their drawbacks has been the difficulty in mapping the solutions back to the target robot. This paper presents a set of tools for rapidly determining solutions for ``humanoids'' without removing or lumping degrees of freedom. The main tools are (1) C-FROST, an open-source C++ interface for FROST, a direct collocation optimization tool; and (2) multi-threading. The results will be illustrated on a 20-DoF floating-base model for a Cassie-series bipedal robot through numerical calculations and physical experiments.

Learning the dynamics of robots from data can help achieve more accurate tracking controllers, or aid their navigation algorithms. However, when the actual dynamics of the robots change due to external conditions, on-line adaptation of their models is required to maintain high fidelity performance. In this work, a framework for on-line learning of robot dynamics is developed to adapt to such changes. The proposed framework employs an incremental support vector regression method to learn the model sequentially from data streams. In combination with the incremental learning, strategies for including and forgetting data are developed to obtain better generalization over the whole state space. The framework is tested in simulation and real experimental scenarios demonstrating its adaptation capabilities to changes in the robot's dynamics.

Health management of complex dynamic systems has traditionally evolved separately from automated control, planning, and scheduling (generally referred to in the paper as decision making). A goal of Integrated System Health Management has been to enable coordination between system health management and decision making, although successful practical implementations have remained limited. This paper proposes that, rather than being treated as connected, yet distinct entities, system health management and decision making should be unified in their formulations. Enabled by advances in modeling and computing, we argue that the unified approach will increase a system's operational effectiveness and may also lead to a lower overall system complexity. We overview the prevalent system health management methodology and illustrate its limitations through numerical examples. We then describe the proposed unification approach and show how it accommodates the typical system health management concepts.

We present a new framework for motion planning that wraps around existing kinodynamic planners and guarantees recursive feasibility when operating in a priori unknown, static environments. Our approach makes strong guarantees about overall safety and collision avoidance by utilizing a robust controller derived from reachability analysis. We ensure that motion plans never exit the safe backward reachable set of the initial state, while safely exploring the space. This preserves the safety of the initial state, and guarantees that that we will eventually find the goal if it is possible to do so while exploring safely. We implement our framework in the Robot Operating System (ROS) software environment and demonstrate it in a real-time simulation.

Learning accurate dynamics models is necessary for optimal, compliant control of robotic systems. Current approaches to white-box modeling using analytic parameterizations, or black-box modeling using neural networks, can suffer from high bias or high variance. We address the need for a flexible, gray-box model of mechanical systems that can seamlessly incorporate prior knowledge where it is available, and train expressive function approximators where it is not. We propose to parameterize a mechanical system using neural networks to model its Lagrangian and the generalized forces that act on it. We test our method on a simulated, actuated double pendulum. We show that our method outperforms a naive, black-box model in terms of data-efficiency, as well as performance in model-based reinforcement learning. We also conduct a systematic study of our method's ability to incorporate available prior knowledge about the system to improve data efficiency.

We present ConFusion, an open-source package for online sensor fusion for robotic applications. ConFusion is a modular framework for fusing measurements from many heterogeneous sensors within a moving horizon estimator. ConFusion offers greater flexibility in sensor fusion problem design than filtering-based systems and the ability to scale the online estimate quality with the available computing power. We demonstrate its performance in comparison to an iterated extended Kalman filter in visual-inertial tracking, and show its versatility through whole-body sensor fusion on a mobile manipulator.

For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations of larger (kernel) model classes lead to algorithms, which naturally scale linearly in the amount of data points. For moderate-dimensional or high-dimensional regression tasks, these grid-based discretizations suffer from the curse of dimensionality. Here, sparse grid methods have proven to circumvent this problem to a large extent. In this context, space- and dimension-adaptive sparse grids, which can detect and exploit a given low effective dimensionality of nominally high-dimensional data, are particularly successful. They nevertheless rely on an axis-aligned structure of the solution and exhibit issues for data with predominantly skewed and rotated coordinates. In this paper we propose a preprocessing approach for these adaptive sparse grid algorithms that determines an optimized, problem-dependent coordinate system and, thus, reduces the effective dimensionality of a given data set in the ANOVA sense. We provide numerical examples on synthetic data as well as real-world data to show how an adaptive sparse grid least squares algorithm benefits from our preprocessing method.

Sampling efficiency in a highly constrained environment has long been a major challenge for sampling-based planners. In this work, we propose Rapidly-exploring Random disjointed-Trees* (RRdT*), an incremental optimal multi-query planner. RRdT* uses multiple disjointed-trees to exploit local-connectivity of spaces via Markov Chain random sampling, which utilises neighbourhood information derived from previous successful and failed samples. To balance local exploitation, RRdT* actively explore unseen global spaces when local-connectivity exploitation is unsuccessful. The active trade-off between local exploitation and global exploration is formulated as a multi-armed bandit problem. We argue that the active balancing of global exploration and local exploitation is the key to improving sample efficient in sampling-based motion planners. We provide rigorous proofs of completeness and optimal convergence for this novel approach. Furthermore, we demonstrate experimentally the effectiveness of RRdT*'s locally exploring trees in granting improved visibility for planning. Consequently, RRdT* outperforms existing state-of-the-art incremental planners, especially in highly constrained environments.

We consider the problem of extracting safe environments and controllers for reach-avoid objectives for systems with known state and control spaces, but unknown dynamics. In a given environment, a common approach is to synthesize a controller from an abstraction or a model of the system (potentially learned from data). However, in many situations, the relationship between the dynamics of the model and the \textit{actual system} is not known; and hence it is difficult to provide safety guarantees for the system. In such cases, the Standard Simulation Metric (SSM), defined as the worst-case norm distance between the model and the system output trajectories, can be used to modify a reach-avoid specification for the system into a more stringent specification for the abstraction. Nevertheless, the obtained distance, and hence the modified specification, can be quite conservative. This limits the set of environments for which a safe controller can be obtained. We propose SPEC, a specification-centric simulation metric, which overcomes these limitations by computing the distance using only the trajectories that violate the specification for the system. We show that modifying a reach-avoid specification with SPEC allows us to synthesize a safe controller for a larger set of environments compared to SSM. We also propose a probabilistic method to compute SPEC for a general class of systems. Case studies using simulators for quadrotors and autonomous cars illustrate the advantages of the proposed metric for determining safe environment sets and controllers.

Perfect tracking control for real-world Euler-Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows to maintain good tracking performance at low feedback gains. However, accurate models are often difficult to obtain. In this article, we address the problem of stable high-performance tracking control for unknown Euler-Lagrange systems. In particular, we employ Gaussian Process regression to obtain a data-driven model that is used for the feed-forward compensation of unknown dynamics of the system. The model fidelity is used to adapt the feedback gains allowing low feedback gains in state space regions of high model confidence. The proposed control law guarantees a globally bounded tracking error with a specific probability. Simulation studies demonstrate the superiority over state of the art tracking control approaches.

We study the control of a linear dynamical system with adversarial disturbances (as opposed to statistical noise). The objective we consider is one of regret: we desire an online control procedure that can do nearly as well as that of a procedure that has full knowledge of the disturbances in hindsight. Our main result is an efficient algorithm that provides nearly tight regret bounds for this problem. From a technical standpoint, this work generalizes upon previous work in two main aspects: our model allows for adversarial noise in the dynamics, and allows for general convex costs.

In this paper we consider the problem of how a reinforcement learning agent tasked with solving a set of related Markov decision processes can use knowledge acquired early in its lifetime to improve its ability to more rapidly solve novel, but related, tasks. One way of exploiting this experience is by identifying recurrent patterns in trajectories obtained from well-performing policies. We propose a three-step framework in which an agent 1) generates a set of candidate open-loop macros by compressing trajectories drawn from near-optimal policies; 2) evaluates the value of each macro; and 3) selects a maximally diverse subset of macros that spans the space of policies typically required for solving the set of related tasks. Our experiments show that extending the original primitive action-set of the agent with the identified macros allows it to more rapidly learn an optimal policy in unseen, but similar MDPs.

The problem of dispatching emergency responders to service traffic accidents, fire, distress calls and crimes plagues urban areas across the globe. While such problems have been extensively looked at, most approaches are offline. Such methodologies fail to capture the dynamically changing environments under which critical emergency response occurs, and therefore, fail to be implemented in practice. Any holistic approach towards creating a pipeline for effective emergency response must also look at other challenges that it subsumes - predicting when and where incidents happen and understanding the changing environmental dynamics. We describe a system that collectively deals with all these problems in an online manner, meaning that the models get updated with streaming data sources. We highlight why such an approach is crucial to the effectiveness of emergency response, and present an algorithmic framework that can compute promising actions for a given decision-theoretic model for responder dispatch. We argue that carefully crafted heuristic measures can balance the trade-off between computational time and the quality of solutions achieved and highlight why such an approach is more scalable and tractable than traditional approaches. We also present an online mechanism for incident prediction, as well as an approach based on recurrent neural networks for learning and predicting environmental features that affect responder dispatch. We compare our methodology with prior state-of-the-art and existing dispatch strategies in the field, which show that our approach results in a reduction in response time with a drastic reduction in computational time.

We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control constraints. Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving an integer program. Our method generalizes across system dynamics and learns a guaranteed subset of the constraint. We also provide theoretical analysis on what subset of the constraint can be learnable from safe demonstrations. We demonstrate our method on linear and nonlinear system dynamics, show that it can be modified to work with suboptimal demonstrations, and that it can also be used to learn constraints in a feature space.

High-dimensional data requires scalable algorithms. We propose and analyze three scalable and related algorithms for semi-supervised discriminant analysis (SDA). These methods are based on Krylov subspace methods which exploit the data sparsity and the shift-invariance of Krylov subspaces. In addition, the problem definition was improved by adding centralization to the semi-supervised setting. The proposed methods are evaluated on a industry-scale data set from a pharmaceutical company to predict compound activity on target proteins. The results show that SDA achieves good predictive performance and our methods only require a few seconds, significantly improving computation time on previous state of the art.

Early detection of incipient faults is of vital importance to reducing maintenance costs, saving energy, and enhancing occupant comfort in buildings. Popular supervised learning models such as deep neural networks are considered promising due to their ability to directly learn from labeled fault data; however, it is known that the performance of supervised learning approaches highly relies on the availability and quality of labeled training data. In Fault Detection and Diagnosis (FDD) applications, the lack of labeled incipient fault data has posed a major challenge to applying these supervised learning techniques to commercial buildings. To overcome this challenge, this paper proposes using Monte Carlo dropout (MC-dropout) to enhance the supervised learning pipeline, so that the resulting neural network is able to detect and diagnose unseen incipient fault examples. We also examine the proposed MC-dropout method on the RP-1043 dataset to demonstrate its effectiveness in indicating the most likely incipient fault types.

It is important to identify the change point of a system's health status, which usually signifies an incipient fault under development. The One-Class Support Vector Machine (OC-SVM) is a popular machine learning model for anomaly detection and hence could be used for identifying change points; however, it is sometimes difficult to obtain a good OC-SVM model that can be used on sensor measurement time series to identify the change points in system health status. In this paper, we propose a novel approach for calibrating OC-SVM models. The approach uses a heuristic search method to find a good set of input data and hyperparameters that yield a well-performing model. Our results on the C-MAPSS dataset demonstrate that OC-SVM can also achieve satisfactory accuracy in detecting change point in time series with fewer training data, compared to state-of-the-art deep learning approaches. In our case study, the OC-SVM calibrated by the proposed model is shown to be useful especially in scenarios with limited amount of training data.

We introduce a unique experimental testbed that consists of a fleet of 16 miniature Ackermann-steering vehicles. We are motivated by a lack of available low-cost platforms to support research and education in multi-car navigation and trajectory planning. This article elaborates the design of our miniature robotic car, the Cambridge Minicar, as well as the fleet's control architecture. Our experimental testbed allows us to implement state-of-the-art driver models as well as autonomous control strategies, and test their validity in a real, physical multi-lane setup. Through experiments on our miniature highway, we are able to tangibly demonstrate the benefits of cooperative driving on multi-lane road topographies. Our setup paves the way for indoor large-fleet experimental research.

In this paper, we consider the general problem of obstacle avoidance based on dynamical system. The modulation matrix is developed by introducing orthogonal coordinates, which makes the modulation matrix more reasonable. The new trajectory's direction can be represented by the linear combination of orthogonal coordinates. A orthogonal coordinates manipulating approach is proposed by introducing rotating matrix to solve the local minimal problem and provide more reasonable motions in 3-D or higher dimension space. The proposed method also provide a solution for patrolling around a convex shape. Experimental results on several designed dynamical systems demonstrate the effectiveness of the proposed approach.

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance.