Sampling-based Algorithm Research Articles

A LODBO algorithm for multi-UAV search and rescue path planning in disaster areas

In disaster relief operations, multiple UAVs can be used to search for trapped people. In recent years, many researchers have proposed machine le arning-based algorithms, sampling-based algorithms, and heuristic algorithms to solve the problem of multi-UAV path planning. The Dung Beetle Optimization (DBO) algorithm has been widely applied due to its diverse search patterns in the above algorithms. However, the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic, potentially leading to an inability to fully explore the search space and a tendency to converge to local optima, thereby not guaranteeing the discovery of the optimal path. To address these issues, we propose an improved DBO algorithm guided by the Landmark Operator (LODBO). Specifically, we first use tent mapping to update the population strategy, which enables the algorithm to generate initial solutions with enhanced diversity within the search space. Second, we expand the search range of the rolling ball dung beetle by using the landmark factor. Finally, by using the adaptive factor that changes with the number of iterations., we improve the global search ability of the stealing dung beetle, making it more likely to escape from local optima. To verify the effectiveness of the proposed method, extensive simulation experiments are conducted, and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm (GA), the Gray Wolf Optimizer (GWO), the Whale Optimization Algorithm (WOA) and the original DBO algorithm in the disaster search and rescue task set.

A partitioning Monte Carlo approach for consensus tasks in crowdsourcing

The planner’s role in crowdsourcing involves determining the time to stop collecting information (i.e., timed decision, TD). Previous studies have modeled the uncertain crowdsourcing environment as Partially Observable Markov Decision Processes (POMDPs) and utilized the value of information (VOI) to balance the utilities and costs of information collection. However, there is still room for optimization in solving the TD problem within single-agent POMDPs. In this paper, we propose a partitioning Monte Carlo approach for consensus tasks based on the option-candidate (OC) model partitioning. We simplify the state representation for the OC model and introduce a multi-agent POMDP representation. We establish a correspondence between the single-agent and multi-agent models using two consistency theorems. We propose three progressively improved partitioning Monte Carlo (PMC) algorithms to solve the TD problem within the multi-agent POMDP. We conducted experiments in synthetic domains and a citizen science project, demonstrating that the proposed algorithms exhibit continuous improvements in runtime advantages and consistently outperform the SOTA single-agent Monte Carlo sampling-based algorithm while providing nearly consistent output results.

Trajectory optimization and obstacle avoidance of autonomous robot using Robust and Efficient Rapidly Exploring Random Tree.

One of the key challenges in robotics is the motion planning problem. This paper presents a local trajectory planning and obstacle avoidance strategy based on a novel sampling-based path-finding algorithm designed for autonomous vehicles navigating complex environments. Although sampling-based algorithms have been extensively employed for motion planning, they have notable limitations, such as sluggish convergence rate, significant search time volatility, a vast, dense sample space, and unsmooth search routes. To overcome the limitations, including slow convergence, high computational complexity, and unnecessary search while sampling the whole space, we have proposed the RE-RRT* (Robust and Efficient RRT*) algorithm. This algorithm adapts a new sampling-based path-finding algorithm based on sampling along the displacement from the initial point to the goal point. The sample space is constrained during each stage of the random tree's growth, reducing the number of redundant searches. The RE-RRT* algorithm can converge to a shorter path with fewer iterations. Furthermore, the Choose Parent and Rewire processes are used by RE-RRT* to improve the path in succeeding cycles continuously. Extensive experiments under diverse obstacle settings are performed to validate the effectiveness of the proposed approach. The results demonstrate that the proposed approach outperforms existing methods in terms of computational time, sampling space efficiency, speed, and stability.

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

An efficient constraint method for solving planning problems under end-effector constraints

Purpose In response to the challenge of reduced efficiency or failure of robot motion planning algorithms when faced with end-effector constraints, this study aims to propose a new constraint method to improve the performance of the sampling-based planner. Design/methodology/approach In this work, a constraint method (TC method) based on the idea of cross-sampling is proposed. This method uses the tangent space in the workspace to approximate the constrained manifold pattern and projects the entire sampling process into the workspace for constraint correction. This method avoids the need for extensive computational work involving multiple iterations of the Jacobi inverse matrix in the configuration space and retains the sampling properties of the sampling-based algorithm. Findings Simulation results demonstrate that the performance of the planner when using the TC method under the end-effector constraint surpasses that of other methods. Physical experiments further confirm that the TC-Planner does not cause excessive constraint errors that might lead to task failure. Moreover, field tests conducted on robots underscore the effectiveness of the TC-Planner, and its excellent performance, thereby advancing the autonomy of robots in power-line connection tasks. Originality/value This paper proposes a new constraint method combined with the rapid-exploring random trees algorithm to generate collision-free trajectories that satisfy the constraints for a high-dimensional robotic system under end-effector constraints. In a series of simulation and experimental tests, the planner using the TC method under end-effector constraints efficiently performs. Tests on a power distribution live-line operation robot also show that the TC method can greatly aid the robot in completing operation tasks with end-effector constraints. This helps robots to perform tasks with complex end-effector constraints such as grinding and welding more efficiently and autonomously.

MPTree: A Sampling-based Vehicle Motion Planner for Real-time Obstacle Avoidance

This paper presents a novel and modular framework, named MPTree, for real-time vehicle motion planning with dynamic obstacle avoidance. MPTree adopts a sampling-based algorithm, to explore a tree of Motion Primitives (MPs) and return near-optimal trajectories. Specifically, MPTree builds motion primitives to connect the tree nodes (waypoints), sampled in a mesh of waylines on the local planning horizon. The tree exploration is based on a semi-structured RRTa, with an application-specific cost function (e.g., minimum-jerk or minimum-time) and high-level behavioral policy. We show examples of MPTREE’s specialization for urban environments and autonomous racing, using fast-to-evaluate motion primitives to accelerate the tree exploration phase. A prototype implementation is tested in a closed-loop simulation environment. Our preliminary results show that MPTree provides feasible collision-free trajectories while ensuring low computational times.

Operating Strategy of LNG Terminal in Interdependent Electricity and Natural Gas Markets

With the ever strengthening interdependence between electricity and natural gas (NG) systems, the outcomes of the two energy markets could be affected by market entities from both markets. The existing studies mainly discuss the strategic behaviors of market entities participating in directly the two energy markets, lacking the concentration on the market entities participating in one single market while they could still pose impacts on the other market via the interdependence between the two markets. This paper studies the operating strategy of liquified NG (LNG) terminal, by describing the problem as a NG market game and an electricity market game. The problem is then reformulated as a bi-level single-leader multi-follower mix-integer programming (MIP) model where the LNG terminal acts as the leader while the NG fired power plants (NGPPs) as the followers. The model could be converted to a single-level one with the value-function method, and the interaction between the leader and followers is addressed with the sample-based algorithm, combined with the diagonalization algorithm to find the equilibrium among followers. The case studies further demonstrate the feasibility and effectiveness of the proposed methodology and illustrate the outcomes of the interdependent electricity and NG markets with the strategic LNG terminal.

Motion planning around obstacles with convex optimization.

From quadrotors delivering packages in urban areas to robot arms moving in confined warehouses, motion planning around obstacles is a core challenge in modern robotics. Planners based on optimization can design trajectories in high-dimensional spaces while satisfying the robot dynamics. However, in the presence of obstacles, these optimization problems become nonconvex and very hard to solve, even just locally. Thus, when facing cluttered environments, roboticists typically fall back to sampling-based planners that do not scale equally well to high dimensions and struggle with continuous differential constraints. Here, we present a framework that enables convex optimization to efficiently and reliably plan trajectories around obstacles. Specifically, we focus on collision-free motion planning with costs and constraints on the shape, the duration, and the velocity of the trajectory. Using recent techniques for finding shortest paths in Graphs of Convex Sets (GCS), we design a practical convex relaxation of the planning problem. We show that this relaxation is typically very tight, to the point that a cheap postprocessing of its solution is almost always sufficient to identify a collision-free trajectory that is globally optimal (within the parameterized class of curves). Through numerical and hardware experiments, we demonstrate that our planner, which we name GCS, can find better trajectories in less time than widely used sampling-based algorithms and can reliably design trajectories in high-dimensional complex environments.

A Distributed Block-Split Gibbs Sampler with Hypergraph Structure for High-Dimensional Inverse Problems

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods hardly scale to high dimensional problems, they have recently been paired with optimization techniques, such as proximal and splitting approaches, to address this issue. Such approaches pave the way to distributed samplers, splitting computations to make inference more scalable and faster. We introduce a distributed Split Gibbs sampler (SGS) to efficiently solve such problems involving distributions with multiple smooth and non-smooth functions composed with linear operators. The proposed approach leverages a recent approximate augmentation technique reminiscent of primal-dual optimization methods. It is further combined with a block-coordinate approach to split the primal and dual variables into blocks, leading to a distributed block-coordinate SGS. The resulting algorithm exploits the hypergraph structure of the involved linear operators to efficiently distribute the variables over multiple workers under controlled communication costs. It accommodates several distributed architectures, such as the Single Program Multiple Data and client-server architectures. Experiments on a large image deblurring problem show the performance of the proposed approach to produce high quality estimates with credibility intervals in a small amount of time. Supplementary material to reproduce the experiments is available online.

Sampling-Based Path Planning Algorithm for a Plug & Produce Environment

The purpose of this article is to investigate a suitable path planning algorithm for a multi-agent-based Plug & Produce system that can run online during manufacturing. This is needed since in such systems, resources can move around frequently, making it hard to manually create robot paths. To find a suitable algorithm and verify that it can be used online in a Plug & Produce system, a comparative study between various existing sampling-based path planning algorithms was conducted. Much research exists on path planning carried out offline; however, not so much is performed in online path planning. The specific requirements for Plug & Produce are to generate a path fast enough to eliminate manufacturing delays, to make the path energy efficient, and that it run fast enough to complete the task. The paths are generated in a simulation environment and the generated paths are tested for robot configuration errors and errors due to the target being out of reach. The error-free generated paths are then tested on an industrial test bed environment, and the energy consumed by each path was measured and validated with an energy meter. The results show that all the implemented optimal sampling-based algorithms can be used for some scenarios, but that adaptive RRT and adaptive RRT* are more suitable for online applications in multi-agent systems (MAS) due to a faster generation of paths, even though the environment has more constraints. For each generated path the computational time of the algorithm, move-along time and energy consumed are measured, evaluated, compared, and presented in the article.

Modelling recall-based competing risks data with k different models

In competing risks model, subjects are exposed to failure due to more than one cause. In this study, we develop a model for recall-based competing risks data when the causes associated with time to event are assumed to follow different distributions respectively. The chances of an individual recalling an event will be high if elapsed time between monitoring time and time to event is less. This information is utilized by taking non-recall probability as a function of this elapsed time. For point estimation, an expectation-maximization based algorithm is developed. For interval estimation, we construct the observed Fisher information matrix by using the missing information principle. The study is further extended to the Bayesian paradigm under suitable choices of prior distributions. The samples from full conditionals are drawn using a Gibbs sampling-based algorithm. To assess the performance of proposed estimators, an extensive simulation study is carried out for different proportions of non-recall and censored data with varying sample sizes under uniform and exponential monitoring patterns. Finally, the median duration of breastfeeding cessation for US women is estimated.

Research on robot path planning methods

Mobile robots are used extensively across a variety of industries and fields. How to discover a start-to-end path without colliding has become a hot topic in recent years due to the complexity and uncertainty of the workplace. In various environments, a path planning technique should demonstrate high efficiency and speed. And this can reduce the energy consumption of the robots and greatly increase their working efficiency. This paper will conclude the presently popular path planning algorithm. Based on the different features of these algorithms, they are divided into three types: traditional path planning algorithm, neural-work-based algorithm, and sampling-based algorithm. Based on the new papers in these years, detailed introduction of the algorithms and their variants will be given. At the end of the paper, the thesis is summarized and the future research trend is prospected.

A Novel Sampling-Based Optimal Motion Planning Algorithm for Energy-Efficient Robotic Pick and Place

Energy usage in robotic applications is rapidly increasing as industrial robot installations grow. This research introduces a novel approach, using the rapidly exploring random tree (RRT)-based scheme for optimizing the robot’s motion planning and minimizing energy consumption. Sampling-based algorithms for path planning, such as RRT and its many other variants, are widely used in robotic motion planning due to their efficiency in solving complex high-dimensional problems efficiently. However, standard versions of these algorithms cannot guarantee that the generated trajectories are always optimum and mostly ignore the energy consumption in robotic applications. This paper proposes an energy-efficient industrial robotics motion planning approach using the novel flight cost-based RRT (FC-RRT*) algorithm in pick-and-place operation to generate nodes in a predetermined direction and then calculate energy consumption using the circle point method. After optimizing the motion trajectory, power consumption is computed for the rotary axes of a six degree of freedom (6DOF) serial type of industrial robot using the work–energy hypothesis for the rotational motion of a rigid body. The results are compared to the traditional RRT and RRT* (RRT-star) algorithm as well as the kinematic solutions. The experimental results of axis indexing tests indicate that by employing the sampling-based FC-RRT* algorithm, the robot joints consume less energy (1.6% to 16.5% less) compared to both the kinematic solution and the conventional RRT* algorithm.

A heuristic tomato-bunch harvest manipulator path planning method based on a 3D-CNN-based position posture map and rapidly-exploring random tree

The environment of tomato bunches is complex, and the fruit volume is relatively large, so manipulator picking-harvest motion planning should consider not only how to pick, but also how to avoid obstacles after picking tomato bunches and harvesting them from the complex environment, which puts forward strict requirements for picking-harvest motion performance. However, existing sampling-based algorithms still have problems of blind expansion and low efficiency. To solve these problems, a heuristic tomato-bunch harvest manipulator path planning method based on a 3D-CNN (convolution neural network)-based position posture map (PPM) and rapidly-exploring random tree (RRT) is proposed in this paper. This method comprehensively considers the sampling effectiveness of the whole process of picking and harvesting, search speed, path cost and manipulability of the manipulator, combining a sampling-based path planning algorithm and deep learning framework. The method utilizes CNN and FCN(Fully Connected Neural Networks) for generating a heuristic cost map where each voxel has a cost-to-go value toward the target and an optimal target posture value to guide the expansion tree. In addition, the sampling space of obstacle avoidance planning is reduced by a spatial partition method, and the difficulty caused by the increase in the volume of the end-effector clamping fruit is solved by prioritizing the planning of the fruit harvest path and then planning the picking path. On the basis of the above research, a large number of harvest experiments have verified the effectiveness of the proposed algorithm. Research and experimental results show that, based on the PPM-RRT algorithm, the picking-harvest time of a single tomato bunch is 13 s, and the success rate is close to 100%. Compared with state-of-the-art sampling algorithms, the planning time is reduced by more than 70%, the path length is reduced by more than 24%, and the manipulability of the manipulator is increased by 38.9%. The proposed path planning method is effective in complex environments.

Robust Controller Design for a Generic Helicopter Model: An AI-Aided Application for Terrain Avoidance

This paper focuses on robust controller design for a generic helicopter model and terrain avoidance problem via artificial intelligence (AI). The helicopter model is presented as a hybrid system that covers hover and forward dynamics. By defining a set of easily accessible parameters, it can be used to simulate the motion of different helicopter types. A robust control structure based on reinforcement learning is proposed to ensure the system is robust against model parameter uncertainties. The developed generic model can be utilized in many helicopter applications that have been attempted to be solved with sampling-based algorithms or reinforcement learning approaches that take the dynamical constraints into consideration. This study also focuses on the helicopter terrain avoidance problem to illustrate how the model can be useful in these types of applications and provide an artificial intelligence-aided solution to terrain avoidance.

SOF-RRT*: An improved path planning algorithm using spatial offset sampling

Recently, sampling-based algorithms have demonstrated advantages in complex and high-dimensional environments. The RRT* algorithm, as the best variant of RRT, provides progressive optimality. It is shown that the RRT* algorithm has a slow convergence speed and a high initial path cost that result in the low efficiency of the algorithm, due to the low probability of adequate sampling caused by the invalid expansion of the tree and redundant sampling. To overcome these limitations, the SOF-RRT* algorithm is proposed to generate better initial solutions with higher stability and faster convergence. The SOF-RRT* algorithm is an improvement on the F-RRT* algorithm. The SOF-RRT* algorithm introduces a spatial probability weight sampling strategy into sampling, which makes the sampling probability higher in the area with a large feasible area. It reduces redundant sampling and increases the effective sampling rate. In the aspect of tree expansion, the strategy of target bias and obstacle tangential bias is introduced to improve the tree expansion efficiency, which makes tree expansion away from obstacles and bias to the target point. The proposed algorithm improves the expansion efficiency of sampling and tree. Finally, the initial path generation and convergence speed are simulated and compared, which proves that the algorithm has been greatly optimized in terms of the number of iterations, path quality, and convergence speed.

A Hierarchical Motion Planning Method for Mobile Manipulator.

This paper focuses on motion planning for mobile manipulators, which includes planning for both the mobile base and the manipulator. A hierarchical motion planner is proposed that allows the manipulator to change its configuration autonomously in real time as needed. The planner has two levels: global planning for the mobile base in two dimensions and local planning for both the mobile base and the manipulator in three dimensions. The planner first generates a path for the mobile base using an optimized A* algorithm. As the mobile base moves along the path with the manipulator configuration unchanged, potential collisions between the manipulator and the environment are checked using the environment data obtained from the on-board sensors. If the current manipulator configuration is in a potential collision, a new manipulator configuration is searched. A sampling-based heuristic algorithm is used to effectively find a collision-free configuration for the manipulator. The experimental results in simulation environments proved that our heuristic sampling-based algorithm outperforms the conservative random sampling-based method in terms of computation time, percentage of successful attempts, and the quality of the generated configuration. Compared with traditional methods, our motion planning method could deal with 3D obstacles, avoid large memory requirements, and does not require a long time to generate a global plan.

Hierarchical market-based optimal planning of transmission network and wind-storage hybrid power plant

Coupling renewable energy sources (RES) such as wind farms with energy storage systems (ESSs) to form a hybrid power plant (HPP) has gained increasing attention. However, its investment profitability is closely associated with its capacity configuration, site location, grid network, and market-clearing outcomes. To study the HPP’s planning strategy and its interaction with the transmission system operator (TSO), this paper proposes a tri-level coordinated planning scheme for transmission networks and a profit-driven wind-storage hybrid power plant (WSHPP) in the electricity market. The upper level is the transmission network expansion problem managed by the TSO, which responds to the investment decision of the WSHPP. The middle level determines the optimal capacity and site location of the WSHPP to maximize net benefits given transmission expansion schemes and prices from the third level. In the third level, the independent system operator (ISO) solves a scenario-based economic dispatch problem to provide locational marginal prices with fixed upper-level and middle-level decisions. The proposed tri-level hierarchical optimization model is computationally intractable because of its multi-level structure and binary/integer variables at the upper/middle level. A value-function reformulation and sample-based algorithm is implemented to solve the tri-level planning model and the convergence is proved. Numerical experiments on two typical test systems show the effectiveness of the proposed planning scheme and the tractability of the solution algorithm.

HPO-RRT*: a sampling-based algorithm for UAV real-time path planning in a dynamic environment

AbstractThe real-time path planning of unmanned aerial vehicles (UAVs) in dynamic environments with moving threats is a difficult problem. To solve this problem, this paper proposes a time-based rapidly exploring random tree (time-based RRT*) algorithm, called the hierarchical rapidly exploring random tree algorithm based on potential function lazy planning and low-cost optimization (HPO-RRT*). The HPO-RRT* algorithm can guarantee path homotopy optimality and high planning efficiency. This algorithm uses a hierarchical architecture comprising a UAV perception system, path planner, and path optimizer. After the UAV perception system predicts moving threats and updates world information, the path planner obtains the heuristic path. First, the path planner uses the bias sampling method based on the artificial potential field function proposed in this paper to guide sampling to improve the efficiency and quality of sampling. Then, the tree is efficiently extended by the improved time-based lazy collision checking RRT* algorithm to obtain the heuristic path. Finally, a low-cost path optimizer quickly optimizes the heuristic path directly to optimize the path while avoiding additional calculations. Simulation results show that the proposed algorithm outperforms the three existing advanced algorithms in terms of addressing the real-time path-planning problem of UAVs in a dynamic environment.

The Plausibility of Sampling as an Algorithmic Theory of Sentence Processing.

Words that are more surprising given context take longer to process. However, no incremental parsing algorithm has been shown to directly predict this phenomenon. In this work, we focus on a class of algorithms whose runtime does naturally scale in surprisal-those that involve repeatedly sampling from the prior. Our first contribution is to show that simple examples of such algorithms predict runtime to increase superlinearly with surprisal, and also predict variance in runtime to increase. These two predictions stand in contrast with literature on surprisal theory (Hale, 2001; Levy, 2008a) which assumes that the expected processing cost increases linearly with surprisal, and makes no prediction about variance. In the second part of this paper, we conduct an empirical study of the relationship between surprisal and reading time, using a collection of modern language models to estimate surprisal. We find that with better language models, reading time increases superlinearly in surprisal, and also that variance increases. These results are consistent with the predictions of sampling-based algorithms.