This paper presents an admittance controller based on the passivity theory for a powered upper-limb exoskeleton robot which is governed by the nonlinear equation of motion. Passivity allows us to include a human operator and environmental interaction in the control loop. The robot interacts with the human operator via F/T sensor and interacts with the environment mainly via end-effectors. Although the environmental interaction cannot be detected by any sensors (hence unknown), passivity allows us to have natural interaction. An analysis shows that the behavior of the actual system mimics that of a nominal model as the control gain goes to infinity, which implies that the proposed approach is an admittance controller. However, because the control gain cannot grow infinitely in practice, the performance limitation according to the achievable control gain is also analyzed. The result of this analysis indicates that the performance in the sense of infinite norm increases linearly with the control gain. In the experiments, the proposed properties were verified using 1 degree-of-freedom testbench, and an actual powered upper-limb exoskeleton was used to lift and maneuver the unknown payload.

We present an entirely new geometric and probabilistic approach to synchronization of correspondences across multiple sets of objects or images. In particular, we present two algorithms: (1) Birkhoff-Riemannian L-BFGS for optimizing the relaxed version of the combinatorially intractable cycle consistency loss in a principled manner, (2) Birkhoff-Riemannian Langevin Monte Carlo for generating samples on the Birkhoff Polytope and estimating the confidence of the found solutions. To this end, we first introduce the very recently developed Riemannian geometry of the Birkhoff Polytope. Next, we introduce a new probabilistic synchronization model in the form of a Markov Random Field (MRF). Finally, based on the first order retraction operators, we formulate our problem as simulating a stochastic differential equation and devise new integrators. We show on both synthetic and real datasets that we achieve high quality multi-graph matching results with faster convergence and reliable confidence/uncertainty estimates.

The last fifty years have seen an impressive development of mathematical methods for the analysis and processing of digital images, mostly in the context of photography, biomedical imaging and various forms of engineering. The arts have been mostly overlooked in this process, apart from a few exceptional works in the last ten years. With the rapid emergence of digitisation in the arts, however, the arts domain is becoming increasingly receptive to digital image processing methods and the importance of paying attention to this therefore increases. In this paper we discuss a range of mathematical methods for digital image restoration and digital visualisation for illuminated manuscripts. The latter provide an interesting opportunity for digital manipulation because they traditionally remain physically untouched. At the same time they also serve as an example for the possibilities mathematics and digital restoration offer as a generic and objective toolkit for the arts.

Despite the widespread use of machine learning algorithms to solve problems of technological, economic, and social relevance, provable guarantees on the performance of these data-driven algorithms are critically lacking, especially when the data originates from unreliable sources and is transmitted over unprotected and easily accessible channels. In this paper we take an important step to bridge this gap and formally show that, in a quest to optimize their accuracy, binary classification algorithms -- including those based on machine-learning techniques -- inevitably become more sensitive to adversarial manipulation of the data. Further, for a given class of algorithms with the same complexity (i.e., number of classification boundaries), the fundamental tradeoff curve between accuracy and sensitivity depends solely on the statistics of the data, and cannot be improved by tuning the algorithm.

Recent breakthroughs in the reinforcement learning (RL) community have made significant advances towards learning and deploying policies on real world robotic systems. However, even with the current state-of-the-art algorithms and computational resources, these algorithms are still plagued with high sample complexity, and thus long training times, especially for high degree of freedom (DOF) systems. There are also concerns arising from lack of perceived stability or robustness guarantees from emerging policies. This paper aims at mitigating these drawbacks by: (1) modeling a complex, high DOF system with a representative simple one, (2) making explicit use of forward and inverse kinematics without forcing the RL algorithm to "learn" them on its own, and (3) learning locomotion policies in Cartesian space instead of joint space. In this paper these methods are applied to JPL's Robosimian, but can be readily used on any system with a base and end effector(s). These locomotion policies can be produced in just a few minutes, trained on a single laptop. We compare the robustness of the resulting learned policies to those of other control methods. An accompanying video for this paper can be found at https://youtu.be/xDxxSw5ahnc .

Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. Our recently introduced topological belief space planning t-bsp instead performs decision making considering only topologies of factor graphs that correspond to posterior future beliefs. In this paper we contribute to this body of work a novel method for efficiently determining error bounds of t-bsp, thereby providing global optimality guarantees or uncertainty margin of its solution. The bounds are given with respect to an optimal solution of information theoretic BSP considering the previously introduced topological metric which is based on the number of spanning trees. In realistic and synthetic simulations, we analyze tightness of these bounds and show empirically how this metric is closely related to another computationally more efficient t-bsp metric, an approximation of the von Neumann entropy of a graph, which can achieve online performance.

Biological studies show that hummingbirds can perform extreme aerobatic maneuvers during fast escape. Given a sudden looming visual stimulus at hover, a hummingbird initiates a fast backward translation coupled with a 180-degree yaw turn, which is followed by instant posture stabilization in just under 10 wingbeats. Consider the wingbeat frequency of 40Hz, this aggressive maneuver is carried out in just 0.2 seconds. Inspired by the hummingbirds' near-maximal performance during such extreme maneuvers, we developed a flight control strategy and experimentally demonstrated that such maneuverability can be achieved by an at-scale 12-gram hummingbird robot equipped with just two actuators. The proposed hybrid control policy combines model-based nonlinear control with model-free reinforcement learning. We use model-based nonlinear control for nominal flight control, as the dynamic model is relatively accurate for these conditions. However, during extreme maneuver, the modeling error becomes unmanageable. A model-free reinforcement learning policy trained in simulation was optimized to 'destabilize' the system and maximize the performance during maneuvering. The hybrid policy manifests a maneuver that is close to that observed in hummingbirds. Direct simulation-to-real transfer is achieved, demonstrating the hummingbird-like fast evasive maneuvers on the at-scale hummingbird robot.

This paper presents two novel control methodologies for the cooperative manipulation of an object by N robotic agents. Firstly, we design an adaptive control protocol which employs quaternion feedback for the object orientation to avoid potential representation singularities. Secondly, we propose a control protocol that guarantees predefined transient and steady-state performance for the object trajectory. Both methodologies are decentralized, since the agents calculate their own signals without communicating with each other, as well as robust to external disturbances and model uncertainties. Moreover, we consider that the grasping points are rigid, and avoid the need for force/torque measurements. Load distribution is also included via a grasp matrix pseudo-inverse to account for potential differences in the agents' power capabilities. Finally, simulation and experimental results with two robotic arms verify the theoretical findings.

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces $\mathscr{U}=\underset{i=1}{\overset{M}\bigcup}S_i$. The similarity matrices thus constructed give the exact clustering in the noise-free case. Additionally, this decomposition gives rise to many distinct similarity matrices from a given set of data, which allow enough flexibility to perform accurate clustering of noisy data. We also show that two known methods for subspace clustering can be derived from the CUR decomposition. An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method. Additionally, an adaptation of our CUR based similarity matrices is utilized to provide a heuristic algorithm for subspace clustering; this algorithm yields the best overall performance to date for clustering the Hopkins155 motion segmentation dataset.

Robotic systems are increasingly relying on distributed feedback controllers to tackle complex and latency-prone sensing and decision problems. These demands come at the cost of a growing computational burden and, as a result, larger controller latencies. To maximize robustness to mechanical disturbances and achieve high control performance, we emphasize the necessity for executing damping feedback in close proximity to the control plant while allocating stiffness feedback in a latency-prone centralized control process. Additionally, series elastic actuators (SEAs) are becoming prevalent in torque-controlled robots during recent years to achieve compliant interactions with environments and humans. However, designing optimal impedance controllers and characterizing impedance performance for SEAs with time delays and filtering are still under-explored problems. The presented study addresses the optimal controller design problem by devising a critically-damped gain design method for a class of SEA cascaded control architectures, which is composed of outer-impedance and inner-torque feedback loops. Via the proposed controller design criterion, we adopt frequency-domain methods to thoroughly analyze the effects of time delays, filtering and load inertia on SEA impedance performance. These results are further validated through the analysis, simulation, and experimental testing on high-performance actuators and on an omnidirectional mobile base.

Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from signal temporal logic (STL) specifications. Existing approaches, however, either consider some a priori discretization of the state-space, deal only with a convex fragment of STL, or are not provably complete. We propose a scalable, provably complete algorithm that directly synthesizes continuous trajectories to satisfy non-convex STL specifications. We separate discrete task planning and continuous motion planning on the fly and harness highly efficient satisfiability modulo theories (SMT) and linear programming (LP) solvers to find dynamically feasible trajectories for high dimensional systems that satisfies non-convex STL specifications. The proposed design algorithms are proved sound and complete, and simulation results demonstrate the scalability of our approach.

Target localization is a critical task for mobile sensors and has many applications. However, generating informative trajectories for these sensors is a challenging research problem. A common method uses information maps that estimate the value of taking measurements from any point in the sensor state space. These information maps are used to generate trajectories; for example, a trajectory might be designed so its distribution of measurements matches the distribution of the information map. Regardless of the trajectory generation method, generating information maps as new observations are made is critical. However, it can be challenging to compute these maps in real-time. We propose using convolutional neural networks to generate information maps from a target estimate and sensor model in real-time. Simulations show that maps are accurately rendered while offering orders of magnitude reduction in computation time.

Body weight support (BWS) is a fundamental technique in rehabilitation. Along with the dramatic progressing of rehabilitation science and engineering, BWS is quickly evolving with new initiatives and has attracted deep research effort in recent years. We have built up a novel gravity offloading system, in which the patient is allowed to move freely in the three-dimensional Cartesian space and receives support against gravity. Thus, the patients, especially for those that suffer from neurological injury such as stroke or spinal cord injury, can focus their residual motor control capabilities on essential therapeutic trainings of balance and gait. The real-time force control performance is critical for the BWS unit to provide suitable support and avoid disturbance. In this work, we have re-designed our BWS unit with a series elastic actuation structure to improve the human-robot interaction performance. Further, the 2 degrees of freedom (2-DOF) control approach was taken for accurate and robust BWS force control. Both simulation and experimental results have validated the efficacy of the BWS design and real-time control methods.

This paper describes a new method for low rank kernel approximation called IKA. The main advantage of IKA is that it produces a function $ψ(x)$ defined as a linear combination of arbitrarily chosen functions. In contrast the approximation produced by Nyström method is a linear combination of kernel evaluations. The proposed method consistently outperformed Nyström method in a comparison on the STL-10 dataset. Numerical results are reproducible using the source code available at https://gitlab.com/matteo-ronchetti/IKA

Automated vehicles can change the society by improved safety, mobility and fuel efficiency. However, due to the higher cost and change in business model, over the coming decades, the highly automated vehicles likely will continue to interact with many human-driven vehicles. In the past, the control/design of the highly automated (robotic) vehicles mainly considers safety and efficiency but failed to address the "driving culture" of surrounding human-driven vehicles. Thus, the robotic vehicles may demonstrate behaviors very different from other vehicles. We study this "driving etiquette" problem in this paper. As the first step, we report the key behavior parameters of human driven vehicles derived from a large naturalistic driving database. The results can be used to guide future algorithm design of highly automated vehicles or to develop realistic human-driven vehicle behavior model in simulations.

Practical bipedal robot locomotion needs to be both energy efficient and robust to variability and uncertainty. In this paper, we build upon recent works in trajectory optimization for robot locomotion with two primary goals. First, we wish to demonstrate the importance of (a) considering and quantifying not only energy efficiency but also robustness of gaits, and (b) optimization not only of nominal motion trajectories but also of robot design parameters and feedback control policies. As a second, complementary focus, we present results from optimization studies on a 5-link planar walking model, to provide preliminary data on particular trade-offs and general trends in improving efficiency versus robustness. In addressing important, open challenges, we focus in particular on discussions of the effects of choices made (a) in formulating what is always, necessarily only an approximate optimization, in choosing metrics for performance, and (b) in structuring and tuning feedback control.

This paper presents a novel Nonlinear Model Predictive Control (NMPC) scheme for underwater robotic vehicles operating in a constrained workspace including static obstacles. The purpose of the controller is to guide the vehicle towards specific way points. Various limitations such as: obstacles, workspace boundary, thruster saturation and predefined desired upper bound of the vehicle velocity are captured as state and input constraints and are guaranteed during the control design. The proposed scheme incorporates the full dynamics of the vehicle in which the ocean currents are also involved. Hence, the control inputs calculated by the proposed scheme are formulated in a way that the vehicle will exploit the ocean currents, when these are in favor of the way-point tracking mission which results in reduced energy consumption by the thrusters. The performance of the proposed control strategy is experimentally verified using a $4$ Degrees of Freedom (DoF) underwater robotic vehicle inside a constrained test tank with obstacles.

The balance between exploration and exploitation is a key problem for reinforcement learning methods, especially for Q-learning. In this paper, a fidelity-based probabilistic Q-learning (FPQL) approach is presented to naturally solve this problem and applied for learning control of quantum systems. In this approach, fidelity is adopted to help direct the learning process and the probability of each action to be selected at a certain state is updated iteratively along with the learning process, which leads to a natural exploration strategy instead of a pointed one with configured parameters. A probabilistic Q-learning (PQL) algorithm is first presented to demonstrate the basic idea of probabilistic action selection. Then the FPQL algorithm is presented for learning control of quantum systems. Two examples (a spin- 1/2 system and a lamda-type atomic system) are demonstrated to test the performance of the FPQL algorithm. The results show that FPQL algorithms attain a better balance between exploration and exploitation, and can also avoid local optimal policies and accelerate the learning process.

In search applications, autonomous unmanned vehicles must be able to efficiently reacquire and localize mobile targets that can remain out of view for long periods of time in large spaces. As such, all available information sources must be actively leveraged -- including imprecise but readily available semantic observations provided by humans. To achieve this, this work develops and validates a novel collaborative human-machine sensing solution for dynamic target search. Our approach uses continuous partially observable Markov decision process (CPOMDP) planning to generate vehicle trajectories that optimally exploit imperfect detection data from onboard sensors, as well as semantic natural language observations that can be specifically requested from human sensors. The key innovation is a scalable hierarchical Gaussian mixture model formulation for efficiently solving CPOMDPs with semantic observations in continuous dynamic state spaces. The approach is demonstrated and validated with a real human-robot team engaged in dynamic indoor target search and capture scenarios on a custom testbed.

Urban-oriented autonomous vehicles require a reliable perception technology to tackle the high amount of uncertainties. The recently introduced compact 3D LIDAR sensor offers a surround spatial information that can be exploited to enhance the vehicle perception. We present a real-time integrated framework of multi-target object detection and tracking using 3D LIDAR geared toward urban use. Our approach combines sensor occlusion-aware detection method with computationally efficient heuristics rule-based filtering and adaptive probabilistic tracking to handle uncertainties arising from sensing limitation of 3D LIDAR and complexity of the target object movement. The evaluation results using real-world pre-recorded 3D LIDAR data and comparison with state-of-the-art works shows that our framework is capable of achieving promising tracking performance in the urban situation.

We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties. Provable robustness to noise and other perturbations is receiving recent interest in vision, from obtaining immunity to adversarial attacks to assessing and describing failure modes of algorithms in mission critical applications. Further, many blind deconvolution methods based on deep architectures internally make use of or optimize the basic formulation, so a clearer understanding of how this sub-module behaves, when it can be solved, and what noise injection it can tolerate is a first order requirement. We derive new insights into the theoretical underpinnings of blind deconvolution. The algorithm that emerges has nice convergence guarantees and is provably robust in a sense we formalize in the paper. Interestingly, these technical results play out very well in practice, where on standard datasets our algorithm yields results competitive with or superior to the state of the art. Keywords: blind deconvolution, robust continuous optimization

The study of human-robot interaction (HRI) has received increasing research attention for robot navigation in pedestrian crowds. In this paper, we present empirical study of pedestrian-robot interaction in an uni-directional exit corridor. We deploy a mobile robot moving in a direction perpendicular to that of the pedestrian flow, and install a pedestrian motion tracking system to record the collective motion. We analyze both individual and collective motion of pedestrians, and measure the effect of the robot motion on the overall pedestrian flow. The experimental results show the effect of passive HRI, where the pedestrians' overall speed is slowed down in the presence of the robot, and the faster the robot moves, the lower the average pedestrian velocity becomes. Experiment results show qualitative consistency of the collective HRI effect with simulation results that was previously reported. The study can be used to guide future design of robot-assisted pedestrian evacuation algorithms.

The paper describes combinatorial framework for planning of geological exploration for oil-gas fields. The suggested scheme of the geological exploration involves the following stages: (1) building of special 4-layer tree-like model (layer of geological exploration): productive layer, group of productive layers, oil-gas field, oil-gas region (or group of the fields); (2) generations of local design (exploration) alternatives for each low-layer geological objects: conservation, additional search, independent utilization, joint utilization; (3) multicriteria (i.e., multi-attribute) assessment of the design (exploration) alternatives and their interrelation (compatibility) and mapping if the obtained vector estimates into integrated ordinal scale; (4) hierarchical design ('bottom-up') of composite exploration plans for each oil-gas field; (5) integration of the plans into region plans and (6) aggregation of the region plans into a general exploration plan. Stages 2, 3, 4, and 5 are based on hierarchical multicriteria morphological design (HMMD) method (assessment of ranking of alternatives, selection and composition of alternatives into composite alternatives). The composition problem is based on morphological clique model. Aggregation of the obtained modular alternatives (stage 6) is based on detection of a alternatives 'kernel' and its extension by addition of elements (multiple choice model). In addition, the usage of multiset estimates for alternatives is described as well. The alternative estimates are based on expert judgment. The suggested combinatorial planning methodology is illustrated by numerical examples for geological exploration of Yamal peninsula.

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately, most existing algorithms that guarantee convergence to optimal solutions suffer from the curse of dimensionality: the run time of the algorithm grows exponentially with the dimension of the state space of the system. We propose novel dynamic programming algorithms that alleviate the curse of dimensionality in problems that exhibit certain low-rank structure. The proposed algorithms are based on continuous tensor decompositions recently developed by the authors. Essentially, the algorithms represent high-dimensional functions (e.g., the value function) in a compressed format, and directly perform dynamic programming computations (e.g., value iteration, policy iteration) in this format. Under certain technical assumptions, the new algorithms guarantee convergence towards optimal solutions with arbitrary precision. Furthermore, the run times of the new algorithms scale polynomially with the state dimension and polynomially with the ranks of the value function. This approach realizes substantial computational savings in "compressible" problem instances, where value functions admit low-rank approximations. We demonstrate the new algorithms in a wide range of problems, including a simulated six-dimensional agile quadcopter maneuvering example and a seven-dimensional aircraft perching example. In some of these examples, we estimate computational savings of up to ten orders of magnitude over standard value iteration algorithms. We further demonstrate the algorithms running in real time on board a quadcopter during a flight experiment under motion capture.

We consider the problem of controlling an aerial robot connected to the ground by a passive cable or a passive rigid link. We provide a thorough characterization of this nonlinear dynamical robotic system in terms of fundamental properties such as differential flatness, controllability, and observability. We prove that the robotic system is differentially flat with respect to two output pairs: elevation of the link and attitude of the vehicle; elevation of the link and longitudinal link force (e.g., cable tension, or bar compression). We show the design of an almost globally convergent nonlinear observer of the full state that resorts only to an onboard accelerometer and a gyroscope. We also design two almost globally convergent nonlinear controllers to track any sufficiently smooth time-varying trajectory of the two output pairs. Finally we numerically test the robustness of the proposed method in several far-from-nominal conditions: nonlinear cross-coupling effects, parameter deviations, measurements noise and non ideal actuators.

Anatomical structures are rarely static during a surgical procedure due to breathing, heartbeats, and peristaltic movements. Inspired by observing an expert surgeon, we propose an intermittent synchronization with the extrema of the rhythmic motion (i.e., the lowest velocity windows). We performed 2 experiments: (1) pattern cutting, and (2) debridement. In (1), we found that the intermittent synchronization approach, while 1.8x slower than tracking motion, was significantly more robust to noise and control latency, and it reduced the max cutting error by 2.6x In (2), a baseline approach with no synchronization achieves 62% success rate for each removal, while intermittent synchronization achieves 80%.

Predictable Feature Analysis (PFA) (Richthofer, Wiskott, ICMLA 2015) is an algorithm that performs dimensionality reduction on high dimensional input signal. It extracts those subsignals that are most predictable according to a certain prediction model. We refer to these extracted signals as predictable features. In this work we extend the notion of PFA to take supplementary information into account for improving its predictions. Such information can be a multidimensional signal like the main input to PFA, but is regarded external. That means it won't participate in the feature extraction - no features get extracted or composed of it. Features will be exclusively extracted from the main input such that they are most predictable based on themselves and the supplementary information. We refer to this enhanced PFA as PFAx (PFA extended). Even more important than improving prediction quality is to observe the effect of supplementary information on feature selection. PFAx transparently provides insight how the supplementary information adds to prediction quality and whether it is valuable at all. Finally we show how to invert that relation and can generate the supplementary information such that it would yield a certain desired outcome of the main signal. We apply this to a setting inspired by reinforcement learning and let the algorithm learn how to control an agent in an environment. With this method it is feasible to locally optimize the agent's state, i.e. reach a certain goal that is near enough. We are preparing a follow-up paper that extends this method such that also global optimization is feasible.

We study an adaptive anisotropic Huber functional based image restoration scheme. By using a combination of L2-L1 regularization functions, an adaptive Huber functional based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrate that the best convergence rates are obtained for our algorithm.

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For high-dimensional SPD matrices, directly using manifold learning algorithms to reduce the dimension of matrix-form data is impossible. The SPD matrix must first be transformed into a long vector, and then the dimension of this vector must be reduced. However, this approach breaks the spatial structure of the SPD matrix space. To overcome this limitation, we propose a new dimension reduction algorithm on SPD matrix space to transform high-dimensional SPD matrices into low-dimensional SPD matrices. Our work is based on the fact that the set of all SPD matrices with the same size has a Lie group structure, and we aim to transform the manifold learning to the SPD matrix Lie group. We use the basic idea of the manifold learning algorithm called locality preserving projection (LPP) to construct the corresponding Laplacian matrix on the SPD matrix Lie group. Thus, we call our approach Lie-LPP to emphasize its Lie group character. We present a detailed algorithm analysis and show through experiments that Lie-LPP achieves effective results on human action recognition and human face recognition.

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated using regression techniques. We propose as regression method a tensor decomposition model that exploits the inherent three-way interaction of positions x velocities x accelerations. Most work in tensor factorization has addressed the decomposition of dense tensors. In this paper, we build upon the decomposition of sparse tensors, with only small amounts of nonzero entries. The decomposition of sparse tensors has successfully been used in relational learning, e.g., the modeling of large knowledge graphs. Recently, the approach has been extended to multi-class classification with discrete input variables. Representing the data in high dimensional sparse tensors enables the approximation of complex highly non-linear functions. In this paper we show how the decomposition of sparse tensors can be applied to regression problems. Furthermore, we extend the method to continuous inputs, by learning a mapping from the continuous inputs to the latent representations of the tensor decomposition, using basis functions. We evaluate our proposed model on a dataset with trajectories from a seven degrees of freedom SARCOS robot arm. Our experimental results show superior performance of the proposed functional tensor model, compared to challenging state-of-the art methods.