Non-flat Terrain Research Articles

A theoretical method to characterize the resistance effects of nonflat terrain on wind fields in a parametric wind field model for tropical cyclones

Traditionally, an empirical speed-up factor was introduced to reflect the effects of nonflat terrain on near-surface wind speeds. In this paper, the resistance effects of nonflat terrain are considered by introducing the terrain drag coefficient in the parametric wind field model for tropical cyclones (TCs) with a theoretical method. Terrain effects on wind fields are investigated in complex areas along the coastal zone in China under TC conditions. The results show that the terrain drag coefficient is the function of the slope angle and is sensitive to the spatial resolution. After including the resistance effect of nonflat terrain, the TC intensities weaken overall during landfall, with a slight enhancement near the coastal zone. The wind speeds outside the radius of the maximum wind speed decrease, while the wind speeds within the radius of the maximum wind speed increase. Both the TC eye and the radius of maximum wind speed shrink, which is more obvious when the TC center is entirely over land. As a result, the location and magnitude of the maximum wind speed are affected by the nonflat terrain. The changed structure of the wind fields demonstrates the necessity of considering the effects of nonflat terrain in simulating the wind fields under TC conditions.

Open source robot localization for nonplanar environments

AbstractThe operational environments in which a mobile robot executes its missions often exhibit nonflat terrain characteristics, encompassing outdoor and indoor settings featuring ramps and slopes. In such scenarios, the conventional methodologies employed for localization encounter novel challenges and limitations. This study delineates a localization framework incorporating ground elevation and incline considerations, deviating from traditional two‐dimensional localization paradigms that may falter in such contexts. In our proposed approach, the map encompasses elevation and spatial occupancy information, employing Gridmaps and Octomaps. At the same time, the perception model is designed to accommodate the robot's inclined orientation and the potential presence of ground as an obstacle, besides usual structural and dynamic obstacles. We provide an implementation of our approach fully working with Nav2, ready to replace the baseline Adaptative Monte Carlo Localization (AMCL) approach when the robot is in nonplanar environments. Our methodology was rigorously tested in both simulated environments and through practical application on actual robots, including the Tiago and Summit XL models, across various settings ranging from indoor and outdoor to flat and uneven terrains. Demonstrating exceptional precision, our approach yielded error margins below 10 cm and 0.05 radians in indoor settings and less than 1.0 m in extensive outdoor routes. While our results exhibit a slight improvement over AMCL in indoor environments, the enhancement in performance is significantly more pronounced when compared to three‐dimensional simultaneous localization and mapping algorithms. This underscores the considerable robustness and efficiency of our approach, positioning it as an effective strategy for mobile robots tasked with navigating expansive and intricate indoor/outdoor environments.

Applicability of the generalized wind profile model over mountainous forests.

The analytical equation based on Monin-Obukhov (M-O) similarity theory (i.e., wind profile equation) has been adopted since 1970s for using in the prediction of wind vertical profile over flat terrains, which is mature and accurate. However, its applicability over complex terrains remains unknown. This applicability signifies the accuracy of the estimations of aerodynamic parameters for the boundary layer of non-flat terrain, such as zero-displacement height (d) and aerodynamic roughness length (z0), which will determine the accuracy of frequency correction and source area analysis in calculating carbon, water, and trace gas fluxes based on vorticity covariance method. Therefore, the validation of wind profile model in non-flat terrain is the first step to test whether the flux model needs improvement. We measured three-dimensional wind speed data by using the Ker Towers (three towers in a watershed) at Qingyuan Forest CERN in the Mountainous Region of east Liaoning Province, and compared them with data from Panjin Agricultural Station in the Liaohe Plain, to evaluate the applicability of a generalized wind profile model based on the Monin-Obukhov similarity theory on non-flat terrain. The results showed that the generalized wind profile model could not predict wind speeds accurately of three flux towers separately located in different sites, indicating that wind profile model was not suitable for predicting wind speeds in complex terrains. In the leaf-off and leaf-on periods, the coefficient of determination (R2) between observed and predicted wind speeds ranged from 0.12 to 0.30. Compared to measured values, the standard error of the predicted wind speeds was high up to 2 m·s-1. The predicted wind speeds were high as twice as field-measured wind speed, indicating substantial overestimation. Nevertheless, this model correctly predicted wind speeds in flat agricultural landscape in Panjin Agricultural Station. The R2 between observed wind speeds and predicted wind speed ranged from 0.90 to 0.93. The standard error between observed and predicted values was only 0.5 m·s-1. Results of the F-test showed that the root-mean-square error of the observed and predicted wind speeds in each secondary forest complex terrain was much greater than that in flat agricultural landscape. Terrain was the primary factor affecting the applicability of wind profile model, followed by seasonality (leaf or leafless canopy). The wind profile model was not applicable to the boundary-layer flows over forest canopies in complex terrains, because the d was underestimated or both the d and z0 were underestimated, resulting in inaccurate estimation of aerodynamic height.

Registration of Large Optical and SAR Images with Non-Flat Terrain by Investigating Reliable Sparse Correspondences

Optical and SAR image registration is the primary procedure to exploit the complementary information from the two different image modal types. Although extensive research has been conducted to narrow down the vast radiometric and geometric gaps so as to extract homogeneous characters for feature point matching, few works have considered the registration issue for non-flat terrains, which will bring in more difficulties for not only sparse feature point matching but also outlier removal and geometric relationship estimation. This article addresses these issues with a novel and effective optical-SAR image registration framework. Firstly, sparse feature points are detected based on the phase congruency moment map of the textureless SAR image (SAR-PC-Moment), which helps to identify salient local regions. Then a template matching process using very large local image patches is conducted, which increases the matching accuracy by a significant margin. Secondly, a mutual verification-based initial outlier removal method is proposed, which takes advantage of the different mechanisms of sparse and dense matching and requires no geometric consistency assumption within the inliers. These two procedures will produce a putative correspondence feature point (CP) set with a low outlier ratio and high reliability. In the third step, the putative CPs are used to segment the large input image of non-flat terrain into dozens of locally flat areas using a recursive random sample consensus (RANSAC) method, with each locally flat area co-registered using an affine transformation. As for the mountainous areas with sharp elevation variations, anchor CPs are first identified, and then optical flow-based pixelwise dense matching is conducted. In the experimental section, ablation studies using four precisely co-registered optical-SAR image pairs of flat terrain quantitatively verify the effectiveness of the proposed SAR-PC-Moment-based feature point detector, big template matching strategy, and mutual verification-based outlier removal method. Registration results on four 1 m-resolution non-flat image pairs prove that the proposed framework is able to produce robust and quite accurate registration results.

Collision-Free 3-D Navigation of a UAV Team for Optimal Data Collection in Internet-of-Things Networks With Reconfigurable Intelligent Surfaces

This article considers a time-constrained data collection problem from a network of ground sensors mounted on a nonflat terrain by several unmanned aerial vehicles (UAVs). On an uneven terrain, the line-of-sight (LoS) from the sensors to the UAVs is often occluded. Ground-based reconfigurable intelligent surfaces (RISs) are used to make data collection more effective. Data are transmitted to the UAVs either directly or through the RISs. A model-predictive-control-based algorithm for UAVs navigation and data transmission is developed. The algorithm fully addresses the issue of an uneven terrain. It maximizes the amount of data sent to the UAVs within relatively short times and minimizes the energy expenditure of all the UAVs by establishing LoS connection directly or via RISs as often as possible. We present a mathematically rigorous proof of the optimality of the proposed method.

A Non-Flat Terrain Biped Gait Planner Based on DIRCON.

Various constraints exist in bipedal movement. Due to the natural ability of effectively handling constraints, trajectory optimization has become one of the mainstream methods in biped gait planning, especially when constraints become much more complex on non-flat terrain. In this paper, we propose a multi-modal biped gait planner based on DIRCON, which can generate different gaits for multiple, non-flat terrains. Firstly, a virtual knot is designed to model the state transitions when the swing foot contacts terrain and is inserted as the first knot of the target trajectory of the current support phase. Thus, a complete gait or multi-modal gaits sequence can be generated at one time. Then, slacked complementary constraints, which can avoid undesired trajectories, are elaborated to describe the coupling relationships between terrain information and bipedal motion for trajectory optimization based gait planning. The concrete form of the gait planner is also delivered. Finally, we verify the performance of the planner, as well as the structural design of our newly designed biped robot in CoppeliaSim through flat terrain walking, stairs terrain walking and quincuncial piles walking. The three experiments show that the gaits planned by the proposed planner can enable the robot to walk stably over non-flat terrains, even through simple PD control.

Minimizing the Utilized Area of PV Systems by Generating the Optimal Inter-Row Spacing Factor

In mounted photovoltaic (PV) facilities, energy output losses due to inter-row shading are unavoidable. In order to limit the shadow cast by one module row on another, sufficient inter-row space must be planned. However, it is not uncommon to see PV plants with such close row spacing that energy losses occur owing to row-to-row shading effects. Low module prices and high ground costs lead to such configurations, so the maximum energy output per available surface area is prioritized over optimum energy production per peak power. For any applications where the plant power output needs to be calculated, an exact analysis of the influence of inter-row shading on power generation is required. In this paper, an effective methodology is proposed and discussed in detail, ultimately, to enable PV system designers to identify the optimal inter-row spacing between arrays by generating a multiplier factor. The spacing multiplier factor is mathematically formulated and is generated to be a general formula for any geographical location including flat and non-flat terrains. The developed model is implemented using two case studies with two different terrains, to provide a wider context. The first one is in the Kingdome of Saudi Arabia (KSA) provinces, giving a flat terrain case study; the inter-row spacing multiplier factor is estimated for the direct use of a systems designer. The second one is the water pump for agricultural watering using renewable energy sources, giving a non-flat terrain case study in Dhamar, Al-Hada, Yemen. In this case study, the optimal inter-row spacing factor is estimated for limited-area applications. Therefore, the effective area using the proposed formula is minimized so that the shading of PV arrays on each other is avoided, with a simple design using the spacing factor methodology.

Benchmarking Whole-Body Controllers on the TALOS Humanoid Robot.

This article presents a comparison of three control schemes applied on the commercially available TALOS humanoid robot. The aim is to highlight the advantages and drawbacks of each model applied on three locomotion problems: walking on flat and non-flat terrain and climbing stairs. The different models are based on position control (first and second models) or torque control (third model). The first one uses a hierarchical quadratic program at velocity level. The second one uses a weighted quadratic program named Task Space Inverse Dynamic (TSID) at acceleration level. Finally, the last one also uses TSID but at torque level. The controller performances are compared in simulation, using Gazebo, on the accuracy of their tracking, their energy consumption, and their computational time execution.

Path Tracking Strategy for Quadruped Robots Using a Hierarchical Framework

We present a general path tracking strategy, with continuous gaits, for quadruped robots on flat and rigid terrain. We use a hierarchical framework to decompose the task into unique motion templates (actions) such as translation and turning. A Linear Inverted Pendulum Model (LIPM) based algorithm is applied to create physically correct actions while minimizing the sum of squared accelerations of the CoM. These actions are stored in an online action library and are combined using an autonomous steering system that decides when to use which action. The steering system also computes the input parameters for these actions. We also develop transition maneuvers to execute a smooth switching between these actions. This strategy can help reduce the repeated need to perform comprehensive online computation for motion planning. Moreover, one can enrich the action library to execute more complicated tasks involving different gaits and non-flat terrain. We use an 18 DoF quadruped robot model, and simulations are carried out in MATLAB to demonstrate the capabilities of this approach.

Design and Control of a Novel Leg-Arm Multiplexing Mobile Operational Hexapod Robot

A novel legged robot with 6 limbs driven by 20 proprioceptive motors, named SDUHex, is proposed in this letter. The limbs located at the middle of the robot can work as manipulators or locomotors. The topology design of the multi-mode robot is introduced and the kinematics and dynamics of the robot leg is analysed. A hierarchical optimized whole body controller with virtual model active compliance, called VM-WBC, is proposed. This control method unified the foot locomotion and arm operation. The terrain adaptation strategy is proposed to improve the non-flat terrain passability. A series of locomotion and operation experiments are carried out on SDUHex to test the designed robot and control method. Robust locomotion of the robot is verified by lateral impact recovery and slope terrain adaptation experiments. Arm operation of the robot including single-arm pushing and dual-arm picking are experimented to highlight the novel multiplexing function of the robot limbs.

Det6D: A Ground-Aware Full-Pose 3-D Object Detector for Improving Terrain Robustness

Accurate 3D object detection with LiDAR is critical for autonomous driving. Existing research is all based on the flat-world assumption. However, the actual road can be complex with steep sections, which breaks the premise. Current methods suffer from performance degradation in this case due to difficulty correctly detecting objects on sloped terrain. This work presents the first full-degree-of-freedom 3D object detector, Det6D, without spatial and postural limitations to improve terrain robustness.We choose the point-based framework because of its flexible detection range. A ground-aware orientation branch leveraging the local ground constraints is designed to predict full-degree poses, i.e., including pitch and roll. Given the difficulty of long-tail non-flat scene data collection and 6D pose annotation, we present Slope-Aug, a data augmentation method for synthesizing non-flat terrain from existing datasets recorded in flat scenes. Experiments on various datasets demonstrate the effectiveness and robustness of our method on different terrains. The proposed modules are plug-and-play for existing point-based frameworks. The code will be available at https://github.com/HITSZ-NRSL/De6D.

Point cloud segmentation based on Euclidean clustering and multi-plane extraction in rugged field

In this paper, a novel method for point cloud segmentation based on Euclidean clustering and multi-plane extraction is proposed. To cope with overhanging objects, such as tree branches, a hybrid elevation map assisted by Euclidean clustering is designed. By clustering the 3D point clouds falling into the grid cell, the obstacles above a free space are checked and the corresponding traversable regions below are identified. Furthermore, the time consumption is reduced for segmentation by using the multi-resolution grid method. In addition, the multi-plane extraction method based on random sample consensus is well adapted to non-flat terrain. In the simulation, a variety of virtual environments are built on the Gazebo platform to demonstrate the performance of the proposed algorithm. Moreover, it is also evaluated in outdoor environments. The results show that the accuracy as well as efficiency of point cloud segmentation achieves superior performance over existing approaches.

Carbon budget estimation based on different methods of CO2 storage flux in forest ecosystems

Accurate measurement of CO2 storage flux (Fs) in forest ecosystems is of great significance for estimating ecosystem carbon budget by eddy covariance (EC). The errors in the estimation of ecosystem carbon budget caused by different methods for calculating Fs has yet not been comprehensively assessed. Using data from an open-path EC system and an eight-level CO2/H2O profile system (AP100, Campbell Scientific Inc., USA) in a broadleaved deciduous forest at the Maoer-shan in 2018, we evaluated the methodological effect of Fs[2-min mean profile (P2 min), 30-min mean profile (P30 min) and 30-min mean EC single point (Ps)] on the estimation of net ecosystem exchange (NEE), ecosystem respiration (Re), and gross primary productivity (GPP). The results showed that the impact of Fs methods on forest carbon flux generally increased with the increases of time scale, indicating that gap-filling of flux data would further amplify the impacts of Fs estimation methods. At the annual scale, NEE based on P2 min and Ps methods were 36.3% and 29.4% lower than that based on P30 min, while Re based on P2 min was higher than that based on P30 min and Ps by 8.7%. The GPP based on P2 min was 5.4% higher, while that based on Ps was 2.1% lower than that based on P30 min. The traditional P30 min ignored the instantaneous changes in CO2 concentration, Ps missed the changes of CO2 concentration within canopy, and thus both underestimated the actual Re. The approximately instantaneous profile (2-min mean profile) had higher temporal and spatial resolution and could more accurately estimate forest carbon budget with non-flat terrain and complex canopy structure. Our findings had great implications for solving the underestimation of forest Re and GPP as well as the overestimation of net carbon sink on complex conditions with the EC method.

DeepGait: Planning and Control of Quadrupedal Gaits Using Deep Reinforcement Learning

This letter addresses the problem of legged locomotion in non-flat terrain. As legged robots such as quadrupeds are to be deployed in terrains with geometries which are difficult to model and predict, the need arises to equip them with the capability to generalize well to unforeseen situations. In this work, we propose a novel technique for training neural-network policies for terrain-aware locomotion, which combines state-of-the-art methods for model-based motion planning and reinforcement learning. Our approach is centered on formulating Markov decision processes using the evaluation of dynamic feasibility criteria in place of physical simulation. We thus employ policy-gradient methods to independently train policies which respectively plan and execute foothold and base motions in 3D environments using both proprioceptive and exteroceptive measurements. We apply our method within a challenging suite of simulated terrain scenarios which contain features such as narrow bridges, gaps and stepping-stones, and train policies which succeed in locomoting effectively in all cases.

Radar and Visual Odometry Integrated System Aided Navigation for UAVS in GNSS Denied Environment.

Drones are becoming increasingly significant for vast applications, such as firefighting, and rescue. While flying in challenging environments, reliable Global Navigation Satellite System (GNSS) measurements cannot be guaranteed all the time, and the Inertial Navigation System (INS) navigation solution will deteriorate dramatically. Although different aiding sensors, such as cameras, are proposed to reduce the effect of these drift errors, the positioning accuracy by using these techniques is still affected by some challenges, such as the lack of the observed features, inconsistent matches, illumination, and environmental conditions. This paper presents an integrated navigation system for Unmanned Aerial Vehicles (UAVs) in GNSS denied environments based on a Radar Odometry (RO) and an enhanced Visual Odometry (VO) to handle such challenges since the radar is immune against these issues. The estimated forward velocities of a vehicle from both the RO and the enhanced VO are fused with the Inertial Measurement Unit (IMU), barometer, and magnetometer measurements via an Extended Kalman Filter (EKF) to enhance the navigation accuracy during GNSS signal outages. The RO and VO are integrated into one integrated system to help overcome their limitations, since the RO measurements are affected while flying over non-flat terrain. Therefore, the integration of the VO is important in such scenarios. The experimental results demonstrate the proposed system’s ability to significantly enhance the 3D positioning accuracy during the GNSS signal outage.

Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization

We present a single trajectory optimization formulation for legged locomotion that automatically determines the gait sequence, step timings, footholds, swing-leg motions, and six-dimensional body motion over nonflat terrain, without any additional modules. Our phase-based parameterization of feet motion and forces allows to optimize over the discrete gait sequence using only continuous decision variables. The system is represented using a simplified centroidal dynamics model that is influenced by the feet's location and forces. We explicitly enforce friction cone constraints, depending on the shape of the terrain. The nonlinear programming problem solver generates highly dynamic motion plans with full flight phases for a variety of legged systems with arbitrary morphologies in an efficient manner. We validate the feasibility of the generated plans in simulation and on the real quadruped robot ANYmal. Additionally, the entire solver software TOWR , which used to generate these motions is made freely available.

Effectiveness of optimized control strategy and different hub height turbines on a real wind farm optimization

Highlights • An optimized control strategy approach and different hub height turbines are studied. • Means of handling irregular boundaries and wind speed variations over non-flat terrain are developed. • Optimized control strategy yields 9 kW more power per turbine than self-optimum control strategy. • Optimized control strategy reduces cost of energy by 0.08 million dollars per megawatt. • Different hub height turbines are more able to alleviate wake interactions than constant hub height.

Location Accuracy Evaluation of ToA‐Based Lightning Location Systems Over Mountainous Terrain

AbstractIn this paper, we analyze the location error of time of arrival (ToA)‐based lightning location systems (LLSs) caused by propagation effects over mountainous terrain around the Säntis tower located in the Swiss Alps. The study is based on a full‐wave three‐dimensional (3‐D) finite difference time domain approach using the topographic map including the Säntis tower and the nearby sensors belonging to LLSs. It is found that the vertical electric fields are strongly affected by the presence of the mountainous terrain and the finite ground conductivity and that the location error associated with the ToA technique depends strongly on the used onset time estimation technique. The evaluated location errors associated with amplitude thresholds of 10% and 20% and the time of the linear extrapolation of the tangent at maximum field derivative are found to be smallest (about 300 m or less). Finally, we assess the accuracy of two simplified methods (terrain envelope method and tight‐terrain‐fit method) to account for the location error due to propagation over mountainous terrain. These two methods might represent an efficient alternative to estimate the additional time delay due to propagation over a nonflat terrain by using available topographic data. In addition, a possible real‐time location error compensation algorithm using the elongated propagation path method to improve the location error of the LLSs in mountainous regions is presented and discussed.

A computationally-efficient layout optimization method for real wind farms considering altitude variations

In this paper, a novel computationally-efficient optimization scheme is proposed to account for the effect of wind speed variations over non-flat terrain and irregular land plot boundary. In particular, typical analytical wake models are augmented with a wind multiplier (obtained from CFD simulations) to account for the effect of altitude variations, while irregular boundaries are addressed through novel constraint handling method in an unrestricted coordinate optimization formulation. In contrast to the optimization via CFD simulation alone, the augmented wake model provides acceptably accurate results with a reasonable computational burden. The new optimization approach is subsequently applied to two real wind farms with significant altitude variations: the Gokceada Island wind farm and the Grasmere and Albany wind farm. The optimized Gokceada wind farm layout exhibits a significant cost of energy (CoE) reduction when topography is considered (over conventional, flat-terrain optimization). However, the Grasmere and Albany wind farm shows a relatively small decrease in CoE over conventional optimization. This discrepancy can be attributed to the wind characteristics in each location: the Gokceada wind farm has a relatively consistent wind direction and the optimization can use topography to carefully avoid wake interactions. In contrast, the Grasmere and Albany wind farm with less-consistent wind directions leaves no clear method to avoid wakes using topography. These results indicate that the consideration of wind farm topography can yield significant benefits and the wake interactions can be greatly reduced through careful placement of wind turbines in the case where a narrow wind directions is dominant.

Analysis of lightning electromagnetic field propagation in mountainous terrain and its effects on ToA‐based lightning location systems

AbstractIn this paper, we analyze the propagation effects on lightning‐radiated electromagnetic fields over mountainous terrain by using a three‐dimensional (3‐D) finite difference time domain (FDTD) method. We also discuss the time delay error in the time‐of‐arrival (ToA) technique currently used to locate lightning in detection networks, specifically. Furthermore, the accuracy of different approximate methods presented in the literature is discussed and tested by using our 3‐D FDTD method. It is found that (1) the time delays and amplitudes of the lightning‐radiated electromagnetic fields can be significantly affected by the presence of a mountainous terrain and associated diffraction phenomena; (2) for a finitely conducting ground, the time delay shows a slight increase with the increase of the observation distance, but the time delay resulting from the finite ground conductivity appears to be smaller than that caused by the mountainous terrain; and (3) the timing error associated with the ToA technique depends on the threshold times. Threshold times of 10% and 20% of the peak provide very similar results compared to those corresponding to the peak of the first derivative of the magnetic field, and the threshold time exceeds 50% of the initial rising amplitude of the signal. Furthermore, we have assessed the accuracy of two simplified methods (terrain‐envelope method and tight‐terrain fit method) to account for the time delays resulting from the propagation in a mountainous terrain. It is found that both methods result in time delays that are in reasonable agreement but always overestimating the results obtained using the full‐wave 3‐D FDTD approach for the perfectly conducting ground. These two methods represent interesting alternatives to account for the time delay over a nonflat terrain using the terrain model.