3D Grid Research Articles

3DWS: reliable segmentation on intelligent welding systems with 3D convolutions

AbstractAutomated industrial welding processes depend on a large number of factors interacting with high complexity resulting in some sporadic and random variability of the manufactured product that may affect its quality. It is therefore very important to have an accurate and stable quality control. In this work, a deep learning (DL) model is developed for semantic segmentation of weld seams using 3D stereo images of the seam. The objective is to correctly identify the shape and volume of the weld seam as this is the basic problem of quality control. To achieve this, a model called UNet$${\mathcal {L}}$$ L ++ has been developed, based on the UNet and UNet++ architectures, with a more complex topology and a simple encoder to achieve a good adaptation to the specific characteristics of the 3D data. The proposed model receives as input a voxelized 3D point cloud of the freshly welded part where noise is abundantly visible, and generates as output another 3D voxel grid where each voxel is semantically labeled. The experiments performed with parts built by a real weld line show a correct identification of the weld seams, obtaining values between 0.935 and 0.941 for the Dice Similarity Coefficient (DSC). As far as the authors are aware, this is the first 3D analysis proposal capable of generating shape and volume information of weld seams with almost perfect noise filtering.

Online Multi-Contact Motion Replanning for Humanoid Robots with Semantic 3D Voxel Mapping: ExOctomap.

This study introduces a rapid motion-replanning technique driven by a semantic 3D voxel mapping system, essential for humanoid robots to autonomously navigate unknown territories through online environmental sensing. Addressing the challenges posed by the conventional approach based on polygon mesh or primitive extraction for mapping, we adopt semantic voxel mapping, utilizing our innovative Extended-Octomap (ExOctomap). This structure archives environmental normal vectors, outcomes of Euclidean Cluster Extraction, and principal component analysis within an Octree structure, facilitating an O(log N) efficiency in semantic accessibility from a position query x∈R3. This strategy reduces the 6D contact pose search to simple 3D grid sampling. Moreover, voxel representation enables the search of collision-free trajectories online. Through experimental validation based on simulations and real robotic experiments, we demonstrate that our framework can efficiently adapt multi-contact motions across diverse environments, achieving near real-time planning speeds that range from 13.8 ms to 115.7 ms per contact.

2D score-based estimation of heterogeneous treatment effects

Abstract Statisticians show growing interest in estimating and analyzing heterogeneity in causal effects in observational studies. However, there usually exists a trade-off between accuracy and interpretability for developing a desirable estimator for treatment effects, especially in the case when there are a large number of features in estimation. To make efforts to address the issue, we propose a score-based framework for estimating the conditional average treatment effect (CATE) function in this article. The framework integrates two components: (i) leverage the joint use of propensity and prognostic scores in a matching algorithm to obtain a proxy of the heterogeneous treatment effects for each observation and (ii) utilize nonparametric regression trees to construct an estimator for the CATE function conditioning on the two scores. The method naturally stratifies treatment effects into subgroups over a 2d grid whose axis are the propensity and prognostic scores. We conduct benchmark experiments on multiple simulated data and demonstrate clear advantages of the proposed estimator over state-of-the-art methods. We also evaluate empirical performance in real-life settings, using two observational data from a clinical trial and a complex social survey, and interpret policy implications following the numerical results.

3D-print as a template for reassembly of skull fragments in a homicide case

In this technical note we report a case where 3D-printing aided the reassembly of skull fragments in a homicide with severe tampering of the bones. A young male was shot, the body was incinerated and crushed with garden tools resulting in hundreds of brittle, calcine bone fragments from the skull. An antemortem computed tomography (CT)-scan of the skull was available from a previous assault of the victim. To aid the process of reassembly we used the antemortem CT-data to develop a 3D fixture-grid of the cranial cavity. The 3D grid was utilized as an anatomically correct template for bone reconstruction. This novel technique was based solely on open-source software including 3D Slicer and Blender and could have the potential to aid similar cases.

А particle model of interaction between weakly non-spherical bubbles

A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed. It is a system оf the second order ODEs in the radii of bubbles, the position vectors of their centers and the amplitudes of their small deformations in the form of spherical harmonics. Compared to the available analogs, the proposed model equations are more accurate in terms of the ratio of the radii of bubbles to the distance between their centers. This allows one to study bubble-bubble interaction at smaller distances between the bubbles. The model equations are quite compact, which simplifies their theoretical analysis and construction of algorithms of their solution. Five problems (dynamics of a single bubble under harmonic excitation, bubble collapse near a plane rigid wall, interaction of three synchronized and nonsynchronized bubbles located in line, and interaction between sixteen bubbles with the centers located on a plane surface) are considered for validation. It is shown that in all cases the proposed model results well agree with the corresponding available experimental data and numerical solutions. For demonstration of the applicability, the proposed model is used to analyze radial oscillations, spatial movements and surface deformations of the bubbles in rectilinear, planar and spatial clusters under harmonic forcing. Initially 125, 121 and 125 bubbles of the clusters are located at the nodes of 1D, 2D and 3D uniform grids, respectively. It is found that the monotonically decaying radial oscillations of the 1D cluster bubbles during one period of forcing are quite similar to those of a single bubble. Unlike this, the attenuation of the radial oscillations of the central bubbles in the 2D and 3D clusters is essentially non-monotonic. The maximum pressures in the central bubbles of the 2D and 3D clusters are significantly higher than in the single and 1D cluster bubbles. In all clusters the maximum deformations of bubbles are in the form of the second spherical harmonics, except for the central bubble of the 3D cluster, the maximum deformations of which are in the form of the fourth harmonics.

Generally Genius: A Generals.io Agent Development and Data Collection Framework

We present an agent development and data collection framework for Generals.io (GIO)--a real-time strategy game with imperfect information in which players attempt to gain control of opponents' starting positions within a 2D grid world. The framework provides event-based communication amongst several modules implemented as microservices, enabling real-time data collection from GIO's streaming data. Its modular design facilitates rapid bot development and testing, while the emphasis on data collection makes it easy to analyze agent performance. We use this framework in a case study of a top-performing GIO agent called Flobot. Our analysis demonstrates that Flobot's performance varies based on its starting position. Based on the analysis performed with our framework, we propose a modification to Flobot's pathfinding algorithm. Statistical tests show that the new algorithm results in a significant reduction in performance variance.

Numerical investigation of high-temperature rapid heating of coal gas in CFB heat exchanger via thermal carrier particles

High-temperature rapid heating technology of coal gas is a crucial issue that urgently needs to be addressed for the recycling of coal gas in the iron manufacturing. Drawing upon circulating fluidized bed principles, this study proposed a high-temperature rapid heating technology of coal gas with employing thermal carrier particles. Numerical simulation studies were conducted to evaluate the heating performance of this method. A 3D grid model was established and the Discrete Particle Model (DPM) was employed to simulate the gas-solid two-phase flow and heat transfer behaviors in the riser. The results demonstrate that the gas-solid flow within the circulating fluidized bed (CFB) heat exchanger is capable of achieving rapid heat transfer. The gas was effectively heated from an inlet temperature of 300 K to 1479 K within a height of 4.2 m and within 0.68 s. The CFB heat exchanger achieves rapid heat transfer under the designed industrial operating load conditions, with an average duration of heat exchange not exceeding 1.34 s. Moreover, the axial and radial particle size distribution was investigated during the gas-solid heat transfer process in the CFB heat exchanger and analyze the relationship between particle size distribution and the velocity and temperature of particles. To evaluate the operational flexibility of the riser, the gas-solid two-phase flow patterns, temperature distribution and particle residence time distribution were examined under different operating loads.

ViTScore: a novel three-dimensional Vision Transformer method for accurate prediction of protein-ligand docking poses.

Protein-ligand interactions (PLIs) are essential for cellular activities and drug discovery, and due to the complexity and high cost of experimental methods, there is a great demand for computational approaches, such as protein-ligand docking, to decipher PLI patterns. One of the most challenging aspects of protein-ligand docking is to identify near-native conformations from a set of poses, but traditional scoring functions still have limited accuracy. Therefore, new scoring methods are urgently needed for methodological and/or practical implications. We present a novel deep learning-based scoring function for ranking protein-ligand docking poses based on Vision Transformer (ViT), named ViTScore. To recognize near-native poses from a set of poses, ViTScore voxelizes the protein-ligand interactional pocket into a 3D grid labeled by the occupancy contribution of atoms in different physicochemical classes. This allows ViTScore to capture the subtle differences between spatially and energetically favorable near-native poses and unfavorable non-native poses without needing extra information. After that, ViTScore will output the prediction of the root mean square deviation (rmsd) of a docking pose with reference to the native binding pose. ViTScore is extensively evaluated on diverse test sets including PDBbind2019 and CASF2016, and obtains significant improvements over existing methods in terms of RMSE, R and docking power. Moreover, the results demonstrate that ViTScore is a promising scoring function for protein-ligand docking, and it can be used to accurately identify near-native poses from a set of poses. Furthermore, the results suggest that ViTScore is a powerful tool for protein-ligand docking, and it can be used to accurately identify near-native poses from a set of poses. Additionally, ViTScore can be used to identify potential drug targets and to design new drugs with improved efficacy and safety.

Line‐of‐sight probability for UAV communications in 3D grid urban streets

AbstractIn this letter, the authors present a novel expression for the probability of line‐of‐sight (LoS) between a UAV and ground users situated on a gridded street within urban and dense urban environments. Firstly, this study conducts extensive ray‐tracing simulations, encompassing over 50,000 receivers positioned along streets in Brooklyn and Manhattan, respectively. Moreover, the impact of street width on the probability of LoS is investigated, considering three different average widths. By fitting the LoS probability data corresponding to the UAV's elevation angle in two urban environments obtained by simulations, a unified expression representing the relationship between the LoS probability and the UAV's elevation angle is obtained. This obtained LoS probability expression is compared with three existing expressions. The findings presented in this letter can provide some valuable insights for analytical studies on channel modelling between UAVs and ground‐based street users including vehicles.

Planetesimal formation at the gas pressure bump following a migrating planet

Context. Planetesimal formation is still mysterious. One of the ways to form planetesimals is to invoke a gas pressure bump in a protoplanetary disc. In our previous paper, we proposed a new scenario in which the piled-up dust at a gas pressure bump created by a migrating planet forms planetesimals by streaming instability in a wide region of the disc as the planet migrates inwards. Aims. In the present work, we consider the global time evolution of dust and investigate the detailed conditions and results of the planetesimal formation in our scenario. Methods. We used a 1D grid single-sized dust evolution model, which can follow the growth of the particles in terms of their mutual collision and their radial drift and diffusion. We calculated the time-evolution of the radial distribution of the peak mass and surface density of the dust in a gas disc perturbed by an embedded migrating planet and investigated whether or not the dust satisfies the condition for planetesimal formation. Results. We find that planetesimals form in a belt-like region between the snowline and the position where the planet reaches its pebble-isolation mass when the strength of turbulence is 10−4 ≤ α ≤ 10−3, which is broadly consistent with the observed value of α. Whether the mechanism of the formation is streaming instability or mutual collision depends on the timescale of the streaming instability. The total mass of planetesimals formed in this scenario also depends on α; it is about 30–100 ME if the planetary core already exists at the beginning of the simulation and grows by gas accretion, but decreases as the timing of the formation of the planetary core gets later. We also provide simple approximate expressions for the surface density and total mass of the planetesimals and find that the total planetesimal mass strongly depends on the dust mass. Conclusions. We show that planetesimals form in a belt-like region by a combination of dust pile-up at the gas pressure bump formed by a planet and its inward migration.

Radio-Immune Response of Spatially Fractionated Radiotherapy for VMAT Lattice Plans

To evaluate radio-immune response of spatially fractionated radiotherapy (SFRT) for large tumors using VMAT Lattice technique in terms of tumor volume under irradiation and dose fractionation schemes after SFRT. Eleven patients treated with SFRT from a single institution were retrospectively replanned to deliver 15Gy in single fraction using Lattice technique. High dose regions are defined by multiple spheres with the diameter of 1.25 to 1.5cm and their vertex space of 3.0 to 4.0cm inside of GTV. VMAT plans with multiple arcs were developed for SFRT. Four palliative fractionation regimens of 200cGy x 12 (EQD2 = 24Gy with a/b of 10Gy), 400cGy x 5 (23.3Gy), 600cGy x 3 (24Gy) and 800cGy x2 (24Gy) and four definitive regimens of 200cGy x 24 (EQD2 = 48Gy), 400cGy x 10 (46.7Gy), 600cGy x 6 (48Gy) and 800cGy x 4 (48Gy) were considered for radiotherapy to follow SFRT. Linear quadratic (LQ) model is compared with radio-immune (RI) response model in which the activation of cytotoxic T lymphocytes, tumor immune suppression capability and immunotherapy drugs can be considered. Tumor regrowth time (TRT, time to tumor regrowth to the original volume after treatment) from each model was compared as a measure of benefit achieved from the application of SFRT. The average volume of GTVs in this study was 776cc (range 58-2944cc). Three different SFRT plans (2D GRID technique with conventional collimator, 2D GRID with step & shoot IMRT, and 3D Lattice) were developed for each patient but only Lattice plans were considered in this study since they produced comparable dose modulation inside the tumor but only Lattice significantly reduced skin and critical organ dose. Radio-immune response model always expects longer TRT than LQ model. For palliative regimens, TRT of RI model is longer than that of LQ model by 14.5±9.9, 15.1±10.6, 17.2±12.4, 17.5±12.8 days for each fractionation scheme. When Lattice plan of 15Gy is delivered before the palliative treatment, the difference becomes 25.9±15.3, 31.5±23.3, 36.7±27.6, 37.5±28.5 days. The benefit of SFRT from RI response is only about 10-20 days. Interestingly, RI response is inversely proportional to tumor volume. When curative dose is considered, the difference of TRT is drastically changed from 25.9±9.8, 460.7±285.8, 1180.8±985.7, 1512.0±1327.5 days to 20.7±4.4, 449.0±411.7, 1725.4±2171.0, 3517.7±4531.7 days. The benefit of SFRT from RI response appears larger for large tumor with hypo-fractionation in definitive regimens. The benefit of SFRT is significant for large tumors with hypo fractionation in the definitive regimens when radio-immune response model is considered which is not apparent in LQ model. Radio-immune response model may help to guide the development of successful treatment scheme large tumor volumes.

Lifetime based pressure and temperature sensitive paint measurement on a civil aircraft wing under conditions near the onset of shock-induced separation

Lifetime-based pressure- and temperature-sensitive paint (PSP and TSP) measurements were conducted in a large-scale industrial transonic wind tunnel to obtain high-quality pressure data for validation of computational fluid dynamics (CFD) simulations. A wind tunnel test was performed using the NASA common research model in the JAXA 2 m × 2 m transonic wind tunnel. The freestream Mach number was varied in the range of 0.70–0.89, and aerodynamic forces and moments were acquired in order to obtain the pitch break condition related to the onset of shock-induced separation. Polymer-based PSP was coated on a main wing of the model, and TSP was used in tandem with PSP to correct the temperature dependence of PSP. The two-gate lifetime-based method was applied to obtain the PSP and TSP emissions. An a-priori/in-situ hybrid calibration was conducted to convert ratio-of-ratios to pressure, and measured pressure distributions were mapped onto a three-dimensional (3D) model grid. The root-mean-square error for the pressure measurements was evaluated by pressure tap data and was approximated to be 0.8 kPa for all Mach numbers tested. The obtained pressure distributions exhibited a significantly high signal-to-noise ratio and were used for comparison with CFD results on a 3D grid. The high-spatial-resolution PSP measurements helped to accurately localize the differences from the CFD simulation results and showed that the prediction of the shock location along the main wing is still a relevant challenge.

Robust Localization for Underground Mining Vehicles: An Application in a Room and Pillar Mine.

Most autonomous navigation systems used in underground mining vehicles such as load-haul-dump (LHD) vehicles and trucks use 2D light detection and ranging (LIDAR) sensors and 2D representations/maps of the environment. In this article, we propose the use of 3D LIDARs and existing 3D simultaneous localization and mapping (SLAM) jointly with 2D mapping methods to produce or update 2D grid maps of underground tunnels that may have significant elevation changes. Existing mapping methods that only use 2D LIDARs are shown to fail to produce accurate 2D grid maps of the environment. These maps can be used for robust localization and navigation in different mine types (e.g., sublevel stoping, block/panel caving, room and pillar), using only 2D LIDAR sensors. The proposed methodology was tested in the Werra Potash Mine located at Philippsthal, Germany, under real operational conditions. The obtained results show that the enhanced 2D map-building method produces a superior mapping performance compared with a 2D map generated without the use of the 3D LIDAR-based mapping solution. The 2D map generated enables robust 2D localization, which was tested during the operation of an autonomous LHD, performing autonomous navigation and autonomous loading over extended periods of time.

A self-calibration scheme for two-dimensional free-form probing measurement under the assumption of rigid-body machine kinematic model

A major uncertainty contributor to the on-machine probing is linear axis kinematic errors. This paper proposes a novel self-calibration scheme to separate the workpiece geometry and machine tool kinematic errors from the probed profiles. Many self-calibration schemes have been well developed, but they are limited to either of the straightness, roundness, and two-dimensional (2D) grid point positions, since they require the probed points being in a closed set, as the workpiece is rotated or translated. This paper proposes its extension to a free-form 2D geometry. A key idea is on the assumption that the machine tool’s positioning error is in accordance with the rigid-body kinematic model. It makes linear axis error motions, represented in a look-up table format, be in a closed set. Two experimental case studies are presented. The uncertainty assessment is essential to investigate the effectiveness of the proposed scheme for the given workpiece geometry.

An Improved Harris Hawks Optimization Algorithm and Its Application in Grid Map Path Planning.

Aimed at the problems of the Harris Hawks Optimization (HHO) algorithm, including the non-origin symmetric interval update position out-of-bounds rate, low search efficiency, slow convergence speed, and low precision, an Improved Harris Hawks Optimization (IHHO) algorithm is proposed. In this algorithm, a circle map was added to replace the pseudo-random initial population, and the population boundary number was reduced to improve the efficiency of the location update. By introducing a random-oriented strategy, the information exchange between populations was increased and the out-of-bounds position update was reduced. At the same time, the improved sine-trend search strategy was introduced to improve the search performance and reduce the out-of-bound rate. Then, a nonlinear jump strength combining escape energy and jump strength was proposed to improve the convergence accuracy of the algorithm. Finally, the simulation experiment was carried out on the test function and the path planning application of a 2D grid map. The results show that the Improved Harris Hawks Optimization algorithm is more competitive in solving accuracy, convergence speed, and non-origin symmetric interval search efficiency, and verifies the feasibility and effectiveness of the Improved Harris Hawks Optimization in the path planning of a grid map.

RIS Partitioning Based Scalable Beamforming Design for Large-Scale MIMO: Asymptotic Analysis and Optimization

In next-generation wireless networks, reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems are foreseeable to support a large number of antennas at the transceiver as well as a large number of reflecting elements at the RIS. To fully unleash the potential of RIS, the phase shifts of RIS elements should be carefully designed, resulting in a high-dimensional non-convex optimization problem that is hard to solve with affordable computational complexity. In this paper, we address this scalability issue by partitioning RIS into sub-surfaces, so as to optimize the phase shifts in sub-surface levels to reduce complexity. Specifically, each sub-surface employs a linear phase variation structure to anomalously reflect the incident signal to a desired direction, and the sizes of sub-surfaces can be adaptively adjusted according to channel conditions. We formulate the achievable rate maximization problem by jointly optimizing the transmit covariance matrix and the RIS phase shifts. Under the RIS partitioning framework, the RIS phase shifts optimization reduces to the manipulation of the sub-surface sizes, the phase gradients of sub-surfaces, as well as the common phase shifts of sub-surfaces. Then, we characterize the asymptotic behavior of the system with an infinitely large number of transceiver antennas and RIS elements. The asymptotic analysis provides useful insights on the understanding of the fundamental performance-complexity tradeoff in RIS partitioning design. We show that in the asymptotic domain, the achievable rate maximization problem has a rather simple form with an explicit physical meaning of optimization variables. We develop an efficient algorithm to find an approximately optimal solution to the asymptotic problem via a one-dimensional (1D) grid search. Moreover, we discuss the insights and impacts of the asymptotic result on finite-size system design. By applying the asymptotic result to a finite-size system with necessary modifications, we show by numerical results that the proposed design achieves a favorable tradeoff between system performance and computational complexity.

Cost-effective, portable, patient-dedicated three-dimensional automated breast ultrasound for point-of-care breast cancer screening

Breast cancer screening has substantially reduced mortality across screening populations. However, a clinical need persists for more accessible, cost-effective, and robust approaches for increased-risk and diverse patient populations, especially those with dense breasts where screening mammography is suboptimal. We developed and validated a cost-effective, portable, patient-dedicated three-dimensional (3D) automated breast ultrasound (ABUS) system for point-of-care breast cancer screening. The 3D ABUS system contains a wearable, rapid-prototype 3D-printed dam assembly, a compression assembly, and a computer-driven 3DUS scanner, adaptable to any commercially available US machine and transducer. Acquisition is operator-agnostic, involves a 40-second scan time, and provides multiplanar 3D visualization for whole-breast assessment. Geometric reconstruction accuracy was evaluated with a 3D grid phantom and tissue-mimicking breast phantoms, demonstrating linear measurement and volumetric reconstruction errors < 0.2 mm and < 3%, respectively. The system’s capability was demonstrated in a healthy male volunteer and two healthy female volunteers, representing diverse patient geometries and breast sizes. The system enables comfortable ultrasonic coupling and tissue stabilization, with adjustable compression to improve image quality while alleviating discomfort. Moreover, the system effectively mitigates breathing and motion, since its assembly affixes directly onto the patient. While future studies are still required to evaluate the impact on current clinical practices and workflow, the 3D ABUS system shows potential for adoption as an alternative, cost-effective, dedicated point-of-care breast cancer screening approach for increased-risk populations and limited-resource settings.

Application of Machine Learning Techniques to Improve Multi-Radar Mosaic Precipitation Estimates in Shanghai

In this study, we applied an explainable machine learning technique based on the LightGBM method, a category of gradient boosting decision tree algorithm, to conduct a quantitative radar precipitation estimation and move to understand the underlying reasons for excellent estimations. By introducing 3D grid radar reflectivity data into the LightGBM algorithm, we constructed three LightGBM models, including 2D and 3D LightGBM models. Ten groups of experiments were carried out to compare the performances of the LightGBM models with traditional Z–R relationship methods. To further assess the performances of the LightGBM models, rainfall events with 11,483 total samples during August-September of 2022 were used for statistical analysis, and two heavy rainfall events were specifically chosen for the spatial distribution evaluation. The results from both the statistical analysis and spatial distribution demonstrate that the performance of the LightGBM 3D model with nine points is the best method for quantitative precipitation estimation in this study. Through analyzing the explainability of the LightGBM models from Shapley additive explanations (SHAP) regression values, it can be inferred that the superior performance of the LightGBM 3D model is mainly attributed to its consideration of the rain gauge station attributes, diurnal variation characteristics, and the influence of spatial offset.

A Cooperative Game Hybrid Optimization Algorithm Applied to UAV Inspection Path Planning in Urban Pipe Corridors

This paper proposes an improved algorithm applied to path planning for the inspection of unmanned aerial vehicles (UAVs) in urban pipe corridors, which introduces a collaborative game between spherical vector particle swarm optimization (SPSO) and differential evolution (DE) algorithms. Firstly, a high-precision 3D grid map model of urban pipe corridors is constructed based on the actual urban situation. Secondly, the cost function is formulated, and the constraints for ensuring the safe and smooth inspection of UAVs are proposed to transform path planning into an optimization problem. Finally, a hybrid algorithm of SPSO and DE algorithms based on the Nash bargaining theory is proposed by introducing a cooperative game model for optimizing the cost function to plan the optimal path of UAV inspection in complex urban pipe corridors. To evaluate the performance of the proposed algorithm (GSPSODE), the SPSO, DE, genetic algorithm (GA), and ant colony optimization (ACO) are compared with GSPSODE, and the results show that GSPSODE is superior to other methods in UAV inspection path planning. However, the selection of algorithm parameters, the difference in the experimental environment, and the randomness of experimental results may affect the accuracy of experimental results. In addition, a high-precision urban pipe corridors scenario is constructed based on the RflySim platform to dynamically simulate the optimal path planning of UAV inspection in real urban pipe corridors.

Improved A* Algorithm for Path Planning of Spherical Robot Considering Energy Consumption.

Spherical robots have fully wrapped shells, which enables them to walk well on complex terrains, such as swamps, grasslands and deserts. At present, path planning algorithms for spherical robots mainly focus on finding the shortest path between the initial position and the target position. In this paper, an improved A* algorithm considering energy consumption is proposed for the path planning of spherical robots. The optimization objective of this algorithm is to minimize both the energy consumption and path length of a spherical robot. A heuristic function constructed with the energy consumption estimation model (ECEM) and the distance estimation model (DEM) is used to determine the path cost of the A* algorithm. ECEM and DCM are established based on the force analysis of the spherical robot and the improved Euclidean distance of the grid map, respectively. The effectiveness of the proposed algorithm is verified by simulation analysis based on a 3D grid map and a spherical robot moving with uniform velocity. The results show that compared with traditional path planning algorithms, the proposed algorithm can minimize the energy consumption and path length of the spherical robot as much as possible.