Learning generalizable insertion skills in a data-efficient manner has long been a challenge in the robot learning community. While the current state-of-the-art methods with reinforcement learning (RL) show promising performance in acquiring manipulation skills, the algorithms are data-hungry and hard to generalize. To overcome the issues, in this paper we present Prim-LAfD, a simple yet effective framework to learn and adapt primitive-based insertion skills from demonstrations. Prim-LAfD utilizes black-box function optimization to learn and adapt the primitive parameters leveraging prior experiences. Human demonstrations are modeled as dense rewards guiding parameter learning. We validate the effectiveness of the proposed method on eight peg-hole and connector-socket insertion tasks. The experimental results show that our proposed framework takes less than one hour to acquire the insertion skills and as few as fifteen minutes to adapt to an unseen insertion task on a physical robot.

Surrogate algorithms such as Bayesian optimisation are especially designed for black-box optimisation problems with expensive objectives, such as hyperparameter tuning or simulation-based optimisation. In the literature, these algorithms are usually evaluated with synthetic benchmarks which are well established but have no expensive objective, and only on one or two real-life applications which vary wildly between papers. There is a clear lack of standardisation when it comes to benchmarking surrogate algorithms on real-life, expensive, black-box objective functions. This makes it very difficult to draw conclusions on the effect of algorithmic contributions and to give substantial advice on which method to use when. A new benchmark library, EXPObench, provides first steps towards such a standardisation. The library is used to provide an extensive comparison of six different surrogate algorithms on four expensive optimisation problems from different real-life applications. This has led to new insights regarding the relative importance of exploration, the evaluation time of the objective, and the used model. We also provide rules of thumb for which surrogate algorithm to use in which situation. A further contribution is that we make the algorithms and benchmark problem instances publicly available, contributing to more uniform analysis of surrogate algorithms. Most importantly, we include the performance of the six algorithms on all evaluated problem instances. This results in a unique new dataset that lowers the bar for researching new methods as the number of expensive evaluations required for comparison is significantly reduced.

This paper considers theoretical solutions for path planning problems under non-probabilistic uncertainty used in the travel salesman problems under uncertainty. The uncertainty is on the paths between the cities as nodes in a travelling salesman problem. There is at least one path between two nodes/stations where the travelling time between the nodes is not precisely known. This could be due to environmental effects like crowdedness (rush period) in the path, the state of the charge of batteries, weather conditions, or considering the safety of the route while travelling. In this work, we consider two different advanced uncertainty models (i) probabilistic-precise uncertain model: Probability distributions and (ii) non-probabilistic--imprecise uncertain model: Intervals. We investigate what theoretical results can be obtained for two different optimality criteria: maximinity and maximality in the travelling salesman problem.

Optimization equips engineers and scientists in a variety of fields with the ability to transcribe their problems into a generic formulation and receive optimal solutions with relative ease. Industries ranging from aerospace to robotics continue to benefit from advancements in optimization theory and the associated algorithmic developments. Nowadays, optimization is used in real time on autonomous systems acting in safety critical situations, such as self-driving vehicles. It has become increasingly more important to produce robust solutions by incorporating uncertainty into optimization programs. This paper provides a short survey about the state of the art in optimization under uncertainty. The paper begins with a brief overview of the main classes of optimization without uncertainty. The rest of the paper focuses on the different methods for handling both aleatoric and epistemic uncertainty. Many of the applications discussed in this paper are within the domain of control. The goal of this survey paper is to briefly touch upon the state of the art in a variety of different methods and refer the reader to other literature for more in-depth treatments of the topics discussed here.

The Traffic Alert Collision Avoidance System (TCAS) has been an integral part of the increased safety of air transport since it was federally mandated in the 1991 for all passenger carrying aircraft with more than 30 seats flying in U.S. airspace [1, 2]. TCAS led to a dramatic reduction in the occurrence of mid air collisions in modern aviation; however the heuristic based approach undertaken in TCAS has made it difficult to adapt the system to the evolving complexity of the National Airspace System (NAS), which includes new cooperative surveillance systems (e.g., ADS-B) and new vehicle entrants. In response, the Federal Aviation Administration (FAA) commissioned the development of a replacement for TCAS. This new system, referred to as the Next Generation Airborne Collision Avoidance System X (ACAS X), which is currently in development at MIT Lincoln Laboratory and John Hopkins Applied Physics Laboratory, is expected to integrate into multiple aircraft platforms and reduce nuisance alerts as well as reduce the risk of Near Mid Air Collisions (NMAC) [3]. ACAS X introduced several variants designed to reduce the risk of NMAC for a particular operation, such as commercial aviation (ACAS Xa) [4], large uncrewed aerial systems (ACAS Xu) [5], smaller uncrewed aerial vehicles (ACAS sXu) [6], and ACAS Xr which is under development for advanced air mobility and helicopter operations. Each variant adds capabilities and design considerations for the operational environment and platforms that will be commonly seen by the ACAS X equipped vehicle. For example, ACAS sXu introduced vehicle to vehicle surveillance to accommodate a future link that sUAS may use to interrogate and coordinate with each other. While, ACAS Xu added Remain Well Clear alerting due to its use in remotely piloted or autonomous UAS.

We consider the nonlinear inverse problem of learning a transition operator $\mathbf{A}$ from partial observations at different times, in particular from sparse observations of entries of its powers $\mathbf{A},\mathbf{A}^2,\cdots,\mathbf{A}^{T}$. This Spatio-Temporal Transition Operator Recovery problem is motivated by the recent interest in learning time-varying graph signals that are driven by graph operators depending on the underlying graph topology. We address the nonlinearity of the problem by embedding it into a higher-dimensional space of suitable block-Hankel matrices, where it becomes a low-rank matrix completion problem, even if $\mathbf{A}$ is of full rank. For both a uniform and an adaptive random space-time sampling model, we quantify the recoverability of the transition operator via suitable measures of incoherence of these block-Hankel embedding matrices. For graph transition operators these measures of incoherence depend on the interplay between the dynamics and the graph topology. We develop a suitable non-convex iterative reweighted least squares (IRLS) algorithm, establish its quadratic local convergence, and show that, in optimal scenarios, no more than $\mathcal{O}(rn \log(nT))$ space-time samples are sufficient to ensure accurate recovery of a rank-$r$ operator $\mathbf{A}$ of size $n \times n$. This establishes that spatial samples can be substituted by a comparable number of space-time samples. We provide an efficient implementation of the proposed IRLS algorithm with space complexity of order $O(r n T)$ and per-iteration time complexity linear in $n$. Numerical experiments for transition operators based on several graph models confirm that the theoretical findings accurately track empirical phase transitions, and illustrate the applicability and scalability of the proposed algorithm.

The performance of individual evolutionary optimization algorithms is mostly measured in terms of statistics such as mean, median and standard deviation etc., computed over the best solutions obtained with few trails of the algorithm. To compare the performance of two algorithms, the values of these statistics are compared instead of comparing the solutions directly. This kind of comparison lacks direct comparison of solutions obtained with different algorithms. For instance, the comparison of best solutions (or worst solution) of two algorithms simply not possible. Moreover, ranking of algorithms is mostly done in terms of solution quality only, despite the fact that the convergence of algorithm is also an important factor. In this paper, a direct comparison approach is proposed to analyze the performance of evolutionary optimization algorithms. A direct comparison matrix called \emph{Prasatul Matrix} is prepared, which accounts direct comparison outcome of best solutions obtained with two algorithms for a specific number of trials. Five different performance measures are designed based on the prasatul matrix to evaluate the performance of algorithms in terms of Optimality and Comparability of solutions. These scores are utilized to develop a score-driven approach for comparing performance of multiple algorithms as well as for ranking both in the grounds of solution quality and convergence analysis. Proposed approach is analyzed with six evolutionary optimization algorithms on 25 benchmark functions. A non-parametric statistical analysis, namely Wilcoxon paired sum-rank test is also performed to verify the outcomes of proposed direct comparison approach.

Control of light through high numerical aperture (N.A.) objectives is a common requirement in microscopy, for example for engineering specific point spread functions for super-resolution imaging [1, 2], for generating target light distributions for optical stimulation [3, 4, 5], for optical tweezers [6, 7], or for aberration corrections in adaptive optics [8, 9, 10]. For controlling light in all these situations, computational modeling is the most versatile approach for finding a phase pattern that, when displayed on a spatial light modulator (SLM), results in the desired target light distribution in the focal volume. Light propagation through a microscope objective with high N.A. can accurately be described with the vectorial Debye-Wolf diffraction integral [11]. The Debye-Wolf integral takes into account the orientation of the electromagnectic field vector (polarization) which contributes to the shape of the focus in high N.A. objectives. Such effects can be exploited for high resolution imaging, for example with diffraction limited objects, such as single molecules or nanostructures [1, 12, 2]. However, inversion of the Debye-Wolf integral does not have a general closed-form solution [13], and one therefore typically resorts to numerical approaches for applications that aim to generate an intended target light distribution. A fast method for calculating the Debye-Wolf integral would therefore be useful across a range of applications, for example vectorial imaging [14], vectorial beam shaping for tight focusing [2] or superresolution computational imaging [15], as well as any light shaping or imaging applications also at lower resolution, that is where polarization effects have less of an impact.

In today's uncertain and competitive market, where enterprises are subjected to increasingly shortened product life-cycles and frequent volume changes, reconfigurable manufacturing systems (RMS) applications play a significant role in the manufacturing industry's success. Despite the advantages offered by RMS, achieving a high-efficiency degree constitutes a challenging task for stakeholders and decision-makers when they face the trade-off decisions inherent in these complex systems. This study addresses work tasks and resource allocations to workstations together with buffer capacity allocation in RMS. The aim is to simultaneously maximize throughput and minimize total buffer capacity under fluctuating production volumes and capacity changes while considering the stochastic behavior of the system. An enhanced simulation-based multi-objective optimization (SMO) approach with customized simulation and optimization components is proposed to address the abovementioned challenges. Apart from presenting the optimal solutions subject to volume and capacity changes, the proposed approach support decision-makers with discovered knowledge to further understand the RMS design. In particular, this study presents a problem-specific customized SMO combined with a novel flexible pattern mining method for optimizing RMS and conducting post-optimal analyzes. To this extent, this study demonstrates the benefits of applying SMO and knowledge discovery methods for fast decision-support and production planning of RMS.

This paper proposes embedded Gaussian Process Barrier States (GP-BaS), a methodology to safely control unmodeled dynamics of nonlinear system using Bayesian learning. Gaussian Processes (GPs) are used to model the dynamics of the safety-critical system, which is subsequently used in the GP-BaS model. We derive the barrier state dynamics utilizing the GP posterior, which is used to construct a safety embedded Gaussian process dynamical model (GPDM). We show that the safety-critical system can be controlled to remain inside the safe region as long as we can design a controller that renders the BaS-GPDM's trajectories bounded (or asymptotically stable). The proposed approach overcomes various limitations in early attempts at combining GPs with barrier functions due to the abstention of restrictive assumptions such as linearity of the system with respect to control, relative degree of the constraints and number or nature of constraints. This work is implemented on various examples for trajectory optimization and control including optimal stabilization of unstable linear system and safe trajectory optimization of a Dubins vehicle navigating through an obstacle course and on a quadrotor in an obstacle avoidance task using GP differentiable dynamic programming (GP-DDP). The proposed framework is capable of maintaining safe optimization and control of unmodeled dynamics and is purely data driven.