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We develop an algorithmic framework that finds an optimal solution by enumerating some feasible solutions, which number is bounded by a specially derived Variable Parameter (VP) with a favorable asymptotic behavior. We build a VP algorithm for a strongly $\mathsf{NP}$-hard single-machine scheduling problem. The target VP $\nu$ is the number of jobs with some special properties, the so-called emerging jobs. At phase 1 a partial solution including $n-\nu$ non-emerging jobs is constructed in a low degree polynomial time. At phase 2 less than $\nu!$ permutations of the $\nu$ emerging jobs are considered, each of them being incorporated into the partial schedule of phase 1. Based on an earlier conducted experimental study, in practice, $\nu/n$ varied from $1/4$ for small problem instances to $1/10$ for the largest tested instances. We illustrate how the proposed method can be used to build a polynomial-time approximation scheme (PTAS) with the worst-case time complexity $O(\kappa!\kappa k n \log n)$, where $\kappa$, $\kappa<\nu< n$, is a VP and the corresponding approximation factor is $1+1/k$, with $k\kappa<k$. This is better than the time complexity of the earlier known approximation schemes. Using an intuitive probabilistic model, we give more realistic bounds on the running time of the VP algorithm and the PTAS, which are far below the worst-case bounds $\nu!$ and $\kappa!$.

This paper proposes a framework for generating fast, smooth and predictable braking manoeuvers for a controlled robot. The proposed framework integrates two approaches to obtain feasible modal limits for designing braking trajectories. The first approach is real-time capable but conservative considering the usage of the available feasible actuator control region, resulting in longer braking times. In contrast, the second approach maximizes the used braking control inputs at the cost of requiring more time to evaluate larger, feasible modal limits via optimization. Both approaches allow for predicting the robot's stopping trajectory online. In addition, we also formulated and solved a constrained, nonlinear final-time minimization problem to find optimal torque inputs. The optimal solutions were used as a benchmark to evaluate the performance of the proposed predictable braking framework. A comparative study was compiled in simulation versus a classical optimal controller on a 7-DoF robot arm with only three moving joints. The results verified the effectiveness of our proposed framework and its integrated approaches in achieving fast robot braking manoeuvers with accurate online predictions of the stopping trajectories and distances under various braking settings.

Owing to uncertainties in both kinematics and dynamics, the current trajectory tracking framework for mobile robots like spherical robots cannot function effectively on multiple terrains, especially uneven and unknown ones. Since this is a prerequisite for robots to execute tasks in the wild, we enhance our previous hierarchical trajectory tracking framework to handle this issue. First, a modified adaptive RBF neural network (RBFNN) is proposed to represent all uncertainties in kinodynamics. Then the Lyapunov function is utilized to design its adaptive law, and a variable step-size algorithm is employed in the weights update procedure to accelerate convergence and improve stability. Hence, a new adaptive model prediction control-based instruction planner (VAN-MPC) is proposed. Without modifying the bottom controllers, we finally develop the multi-terrain trajectory tracking framework by employing the new instruction planner VAN-MPC. The practical experiments demonstrate its effectiveness and robustness.

Force modulation of robotic manipulators has been extensively studied for several decades. However, it is not yet commonly used in safety-critical applications due to a lack of accurate interaction contact modeling and weak performance guarantees - a large proportion of them concerning the modulation of interaction forces. This study presents a high-level framework for simultaneous trajectory optimization and force control of the interaction between a manipulator and soft environments, which is prone to external disturbances. Sliding friction and normal contact force are taken into account. The dynamics of the soft contact model and the manipulator are simultaneously incorporated in a trajectory optimizer to generate desired motion and force profiles. A constrained optimization framework based on Alternative Direction Method of Multipliers (ADMM) has been employed to efficiently generate real-time optimal control inputs and high-dimensional state trajectories in a Model Predictive Control fashion. Experimental validation of the model performance is conducted on a soft substrate with known material properties using a Cartesian space force control mode. Results show a comparison of ground truth and real-time model-based contact force and motion tracking for multiple Cartesian motions in the valid range of the friction model. It is shown that a contact model-based motion planner can compensate for frictional forces and motion disturbances and improve the overall motion and force tracking accuracy. The proposed high-level planner has the potential to facilitate the automation of medical tasks involving the manipulation of compliant, delicate, and deformable tissues.

The widespread adoption of edge computing has emerged as a prominent trend for alleviating task processing delays and reducing energy consumption. However, the dynamic nature of network conditions and the varying computation capacities of edge servers (ESs) can introduce disparities between computation loads and available computing resources in edge computing networks, potentially leading to inadequate service quality. To address this challenge, this paper investigates a practical scenario characterized by dynamic task offloading. Initially, we examine traditional Multi-armed Bandit (MAB) algorithms, namely the $\varepsilon$-greedy algorithm and the UCB1-based algorithm. However, both algorithms exhibit certain weaknesses in effectively addressing the tidal data traffic patterns. Consequently, based on MAB, we propose an adaptive task offloading algorithm (ATOA) that overcomes these limitations. By conducting extensive simulations, we demonstrate the superiority of our ATOA solution in reducing task processing latency compared to conventional MAB methods. This substantiates the effectiveness of our approach in enhancing the performance of edge computing networks and improving overall service quality.

In this paper, we propose a model averaging approach for addressing model uncertainty in the context of partial linear functional additive models. These models are designed to describe the relation between a response and mixed-types of predictors by incorporating both the parametric effect of scalar variables and the additive effect of a functional variable. The proposed model averaging scheme assigns weights to candidate models based on the minimization of a multi-fold cross-validation criterion. Furthermore, we establish the asymptotic optimality of the resulting estimator in terms of achieving the lowest possible square prediction error loss under model misspecification. Extensive simulation studies and an application to a near infrared spectra dataset are presented to support and illustrate our method.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices \citep{lauritzen2019maximum,slawski2015estimation} and even one observation for diagonally dominant M-matrices \citep{truell2021maximum}. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted $\ell_1$-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

Ancestry-specific proteome-wide association studies (PWAS) based on genetically predicted protein expression can reveal complex disease etiology specific to certain ancestral groups. These studies require ancestry-specific models for protein expression as a function of SNP genotypes. In order to improve protein expression prediction in ancestral populations historically underrepresented in genomic studies, we propose a new penalized maximum likelihood estimator for fitting ancestry-specific joint protein quantitative trait loci models. Our estimator borrows information across ancestral groups, while simultaneously allowing for heterogeneous error variances and regression coefficients. We propose an alternative parameterization of our model which makes the objective function convex and the penalty scale invariant. To improve computational efficiency, we propose an approximate version of our method and study its theoretical properties. Our method provides a substantial improvement in protein expression prediction accuracy in individuals of African ancestry, and in a downstream PWAS analysis, leads to the discovery of multiple associations between protein expression and blood lipid traits in the African ancestry population.

Accurate trajectory prediction of nearby vehicles is crucial for the safe motion planning of automated vehicles in dynamic driving scenarios such as highway merging. Existing methods cannot initiate prediction for a vehicle unless observed for a fixed duration of two or more seconds. This prevents a fast reaction by the ego vehicle to vehicles that enter its perception range, thus creating safety concerns. Therefore, this paper proposes a novel transformer-based trajectory prediction approach, specifically trained to handle any observation length larger than one frame. We perform a comprehensive evaluation of the proposed method using two large-scale highway trajectory datasets, namely the highD and exiD. In addition, we study the impact of the proposed prediction approach on motion planning and control tasks using extensive merging scenarios from the exiD dataset. To the best of our knowledge, this marks the first instance where such a large-scale highway merging dataset has been employed for this purpose. The results demonstrate that the prediction model achieves state-of-the-art performance on highD dataset and maintains lower prediction error w.r.t. the constant velocity across all observation lengths in exiD. Moreover, it significantly enhances safety, comfort, and efficiency in dense traffic scenarios, as compared to the constant velocity model.

Over the past decade, domain adaptation has become a widely studied branch of transfer learning that aims to improve performance on target domains by leveraging knowledge from the source domain. Conventional domain adaptation methods often assume access to both source and target domain data simultaneously, which may not be feasible in real-world scenarios due to privacy and confidentiality concerns. As a result, the research of Source-Free Domain Adaptation (SFDA) has drawn growing attention in recent years, which only utilizes the source-trained model and unlabeled target data to adapt to the target domain. Despite the rapid explosion of SFDA work, yet there has no timely and comprehensive survey in the field. To fill this gap, we provide a comprehensive survey of recent advances in SFDA and organize them into a unified categorization scheme based on the framework of transfer learning. Instead of presenting each approach independently, we modularize several components of each method to more clearly illustrate their relationships and mechanics in light of the composite properties of each method. Furthermore, we compare the results of more than 30 representative SFDA methods on three popular classification benchmarks, namely Office-31, Office-home, and VisDA, to explore the effectiveness of various technical routes and the combination effects among them. Additionally, we briefly introduce the applications of SFDA and related fields. Drawing from our analysis of the challenges facing SFDA, we offer some insights into future research directions and potential settings.