Trajectory replanning for quadrotors is essential to enable fully autonomous flight in unknown environments. Hierarchical motion planning frameworks, which combine path planning with path parameterization, are popular due to their time efficiency. However, the path planning cannot properly deal with non-static initial states of the quadrotor, which may result in non-smooth or even dynamically infeasible trajectories. In this paper, we present an efficient kinodynamic replanning framework by exploiting the advantageous properties of the B-spline, which facilitates dealing with the non-static state and guarantees safety and dynamical feasibility. Our framework starts with an efficient B-spline-based kinodynamic (EBK) search algorithm which finds a feasible trajectory with minimum control effort and time. To compensate for the discretization induced by the EBK search, an elastic optimization (EO) approach is proposed to refine the control point placement to the optimal location. Systematic comparisons against the state-of-the-art are conducted to validate the performance. Comprehensive onboard experiments using two different vision-based quadrotors are carried out showing the general applicability of the framework.

It has always been a research hotspot to use geographic information to assist the navigation of unmanned aerial vehicles. In this paper, a road-network-based localization method is proposed. We match roads in the measurement images to the reference road vector map, and realize successful localization on areas as large as a whole city. The road network matching problem is treated as a point cloud registration problem under two-dimensional projective transformation, and solved under a hypothesise-and-test framework. To deal with the projective point cloud registration problem, a global projective invariant feature is proposed, which consists of two road intersections augmented with the information of their tangents. We call it two road intersections tuple. We deduce the closed-form solution for determining the alignment transformation from a pair of matching two road intersections tuples. In addition, we propose the necessary conditions for the tuples to match. This can reduce the candidate matching tuples, thus accelerating the search to a great extent. We test all the candidate matching tuples under a hypothesise-and-test framework to search for the best match. The experiments show that our method can localize the target area over an area of 400 within 1 second on a single cpu.

We consider the problem of learning rules from a data set that support a proof of a given query, under Valiant's PAC-Semantics. We show how any backward proof search algorithm that is sufficiently oblivious to the contents of its knowledge base can be modified to learn such rules while it searches for a proof using those rules. We note that this gives such algorithms for standard logics such as chaining and resolution.

Then, start the search for the best hyperparameter configuration. The call to search has the same signature as model.fit(). Here's what happens in search: models are built iteratively by calling the model-building function, which populates the hyperparameter space (search space) tracked by the hp object. The tuner progressively explores the space, recording metrics for each configuration.

Mixed Integer Programming (MIP) is one of the most widely used modeling techniques to deal with combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model structures and solution appearances but differing in formulation coefficients. This offers the opportunity for machine learning method to explore the correlations between model structures and the resulting solution values. To address this issue, we propose to represent an MIP instance using a tripartite graph, based on which a Graph Convolutional Network (GCN) is constructed to predict solution values for binary variables. The predicted solutions are used to generate a local branching cut to the model which accelerate the solution process for MIP. Computational evaluations on 8 distinct types of MIP problems show that the proposed framework improves the performance of a state-of-the-art open source MIP solver significantly in terms of running time and solution quality.

In a commonly-used version of the Simple Assembly Line Balancing Problem (SALBP-1) tasks are assigned to stations along an assembly line with a fixed cycle time in order to minimize the required number of stations. It has traditionally been assumed that the total work needed for each product unit has been partitioned into economically indivisible tasks. However, in practice, it is sometimes possible to divide particular tasks in limited ways at additional time penalty cost. Despite the penalties, task division where possible, now and then leads to a reduction in the minimum number of stations. Deciding which allowable tasks to divide creates a new assembly line balancing problem, TDALBP (Task Division Assembly Line Balancing Problem). We propose a mathematical model of the TDALBP, an exact solution procedure for it and present promising computational results for the adaptation of some classical SALBP instances from the research literature. The results demonstrate that the TDALBP sometimes has the potential to significantly improve assembly line performance.

Max-affine regression refers to a model where the unknown regression function is modeled as a maximum of $k$ unknown affine functions for a fixed $k \geq 1$. This generalizes linear regression and (real) phase retrieval, and is closely related to convex regression. Working within a non-asymptotic framework, we study this problem in the high-dimensional setting assuming that $k$ is a fixed constant, and focus on estimation of the unknown coefficients of the affine functions underlying the model. We analyze a natural alternating minimization (AM) algorithm for the non-convex least squares objective when the design is random. We show that the AM algorithm, when initialized suitably, converges with high probability and at a geometric rate to a small ball around the optimal coefficients. In order to initialize the algorithm, we propose and analyze a combination of a spectral method and a random search scheme in a low-dimensional space, which may be of independent interest. The final rate that we obtain is near-parametric and minimax optimal (up to a poly-logarithmic factor) as a function of the dimension, sample size, and noise variance. In that sense, our approach should be viewed as a direct and implementable method of enforcing regularization to alleviate the curse of dimensionality in problems of the convex regression type. As a by-product of our analysis, we also obtain guarantees on a classical algorithm for the phase retrieval problem under considerably weaker assumptions on the design distribution than was previously known. Numerical experiments illustrate the sharpness of our bounds in the various problem parameters.

Sequential decision problems in applications such as manipulation in warehouses, multi-step meal preparation, and routing in autonomous vehicle networks often involve reasoning about uncertainty, planning over discrete modes as well as continuous states, and reacting to dynamic updates. To formalize such problems generally, we introduce a class of Markov Decision Processes (MDPs) called Dynamic Multimodal Stochastic Shortest Paths (DMSSPs). Much of the work in these domains solves deterministic variants, which can yield poor results when the uncertainty has downstream effects. We develop a Hybrid Stochastic Planning (HSP) algorithm, which uses domain-agnostic abstractions to efficiently unify heuristic search for planning over discrete modes, approximate dynamic programming for stochastic planning over continuous states, and hierarchical interleaved planning and execution.

Abstract-- For planning rearrangements of objects in a clutter, it is required to know the goal configuration of the objects. The intermediate local search relies I. INTRODUCTION For instance, typical human environments, object movements. RELATED WORK are usually cluttered; and manipulating the environment to deal with such clutter is integral to performing everyday Related work in robotics Rearrangement of multiple movable chores in social environments, whether that means rearranging objects, a challenging problem that involves planning, objects upon a surface or across multiple surfaces. In particular, planning for geometric a surface is a difficult problem, because it requires the rearrangement with multiple movable objects and its variations, manipulation of existing objects on the surface, as well as such as navigation among movable obstacles [1], [2], the placement of new objects to be put on the surface. To have been studied using various approaches. Since even a solve such a problem, in general, task planning is required simplified variant the rearrangement problem with only one to decide for the order of manipulation actions (e.g., when to movable obstacle has been proved to be NPhard [3], [4], pick, place, move objects), and feasibility checks are required most studies introduce several important restrictions to the to check the execution of each manipulation action against problem, like monotonicity of plans [5]-[9], where each geometric/kinematic constraints (e.g., to avoid collisions).

Recent advances in Neural Architecture Search (NAS) have produced state-of-the-art architectures on several tasks. NAS shifts the efforts of human experts from developing novel architectures directly to designing architecture search spaces and methods to explore them efficiently. The search space definition captures prior knowledge about the properties of the architectures and it is crucial for the complexity and the performance of the search algorithm. However, different search space definitions require restarting the learning process from scratch. We propose a novel agent based on the Transformer that supports joint training and efficient transfer of prior knowledge between multiple search spaces and tasks.