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Journal articles on the topic 'Exploration multirobot'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 June 2024

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1

Yliniemi, Logan, Adrian K. Agogino, and Kagan Tumer. "Multirobot Coordination for Space Exploration." AI Magazine 35, no. 4 (2014): 61–74. http://dx.doi.org/10.1609/aimag.v35i4.2556.

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Teams of artificially intelligent planetary rovers have tremendous potential for space exploration, allowing for reduced cost, increased flexibility and increased reliability. However, having these multiple autonomous devices acting simultaneously leads to a problem of coordination: to achieve the best results, the they should work together. This is not a simple task. Due to the large distances and harsh environments, a rover must be able to perform a wide variety of tasks with a wide variety of potential teammates in uncertain and unsafe environments. Directly coding all the necessary rules t

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Fox, D., J. Ko, K. Konolige, B. Limketkai, D. Schulz, and B. Stewart. "Distributed Multirobot Exploration and Mapping." Proceedings of the IEEE 94, no. 7 (2006): 1325–39. http://dx.doi.org/10.1109/jproc.2006.876927.

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Brass, Peter, Flavio Cabrera-Mora, Andrea Gasparri, and Jizhong Xiao. "Multirobot Tree and Graph Exploration." IEEE Transactions on Robotics 27, no. 4 (2011): 707–17. http://dx.doi.org/10.1109/tro.2011.2121170.

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4

Yamauchi, Brian. "Decentralized coordination for multirobot exploration." Robotics and Autonomous Systems 29, no. 2-3 (1999): 111–18. http://dx.doi.org/10.1016/s0921-8890(99)00046-9.

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Cabrera-Mora, F., and Jizhong Xiao. "A Flooding Algorithm for Multirobot Exploration." IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 42, no. 3 (2012): 850–63. http://dx.doi.org/10.1109/tsmcb.2011.2179799.

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Vincent, Regis, Dieter Fox, Jonathan Ko, et al. "Distributed multirobot exploration, mapping, and task allocation." Annals of Mathematics and Artificial Intelligence 52, no. 2-4 (2008): 229–55. http://dx.doi.org/10.1007/s10472-009-9124-y.

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Lewis, Michael, Huadong Wang, Shih Yi Chien, Prasanna Velagapudi, Paul Scerri, and Katia Sycara. "Choosing Autonomy Modes for Multirobot Search." Human Factors: The Journal of the Human Factors and Ergonomics Society 52, no. 2 (2010): 225–33. http://dx.doi.org/10.1177/0018720810366859.

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Objective: The number of robots an operator can supervise increases with the robots’ level of autonomy. The reported study investigates multirobot foraging to identify aspects of the task most suitable for automation. Background: Many envisioned applications of robotics involve multirobot teams. One of the simplest of these applications is foraging, in which robots are operated independently to explore and discover targets. Depending on levels of autonomy and task, operators have been found able to manage 3 to 12 robots. Method: The foraging task can be functionally subdivided into visiting ne

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Xavier A, Jasmine, and Kannan Pauliah Nadar. "Multirobot System to Explore Unknown Environment with Connection Maintenance." Wireless Communications and Mobile Computing 2022 (November 11, 2022): 1–28. http://dx.doi.org/10.1155/2022/1417627.

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This paper addresses the problem of exploring an unknown environment using multiple robots and maintaining the communication among the team of robots. The existing exploration methods assume that the communication is maintained among the team of robots throughout the exploration process. However, this is not possible when the area to be explored is very large and when there is limited communication range. The presented exploration methods provide communication maintenance among the team of robots and maintain coordination. Three different approaches are presented for exploration. They are cent

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Amigoni, Francesco, Jacopo Banfi, and Nicola Basilico. "Multirobot Exploration of Communication-Restricted Environments: A Survey." IEEE Intelligent Systems 32, no. 6 (2017): 48–57. http://dx.doi.org/10.1109/mis.2017.4531226.

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Banfi, Jacopo. "Recent advances in multirobot exploration of communication-restricted environments." Intelligenza Artificiale 13, no. 2 (2020): 203–30. http://dx.doi.org/10.3233/ia-180013.

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Banfi, Jacopo, Alberto Quattrini Li, Ioannis Rekleitis, Francesco Amigoni, and Nicola Basilico. "Strategies for coordinated multirobot exploration with recurrent connectivity constraints." Autonomous Robots 42, no. 4 (2017): 875–94. http://dx.doi.org/10.1007/s10514-017-9652-y.

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Zhou, Xiao, Song Zhou, Xingang Mou, and Yi He. "Multirobot Collaborative Pursuit Target Robot by Improved MADDPG." Computational Intelligence and Neuroscience 2022 (February 25, 2022): 1–10. http://dx.doi.org/10.1155/2022/4757394.

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Policy formulation is one of the main problems in multirobot systems, especially in multirobot pursuit-evasion scenarios, where both sparse rewards and random environment changes bring great difficulties to find better strategy. Existing multirobot decision-making methods mostly use environmental rewards to promote robots to complete the target task that cannot achieve good results. This paper proposes a multirobot pursuit method based on improved multiagent deep deterministic policy gradient (MADDPG), which solves the problem of sparse rewards in multirobot pursuit-evasion scenarios by combin

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Dadvar, Mehdi, Saeed Moazami, Harley R. Myler, and Hassan Zargarzadeh. "Exploration and Coordination of Complementary Multirobot Teams in a Hunter-and-Gatherer Scenario." Complexity 2021 (September 4, 2021): 1–17. http://dx.doi.org/10.1155/2021/9087250.

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The hunter-and-gatherer approach copes with the problem of dynamic multirobot task allocation, where tasks are unknowingly distributed over an environment. This approach employs two complementary teams of agents: one agile in exploring (hunters) and another dexterous in completing (gatherers) the tasks. Although this approach has been studied from the task planning point of view in our previous works, the multirobot exploration and coordination aspects of the problem remain uninvestigated. This paper proposes a multirobot exploration algorithm for hunters based on innovative notions of “expect

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Roehr, Thomas M., Florian Cordes, and Frank Kirchner. "Reconfigurable Integrated Multirobot Exploration System (RIMRES): Heterogeneous Modular Reconfigurable Robots for Space Exploration." Journal of Field Robotics 31, no. 1 (2013): 3–34. http://dx.doi.org/10.1002/rob.21477.

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Lopez-Perez, Jose J., Uriel H. Hernandez-Belmonte, Juan-Pablo Ramirez-Paredes, Marco A. Contreras-Cruz, and Victor Ayala-Ramirez. "Distributed Multirobot Exploration Based on Scene Partitioning and Frontier Selection." Mathematical Problems in Engineering 2018 (June 20, 2018): 1–17. http://dx.doi.org/10.1155/2018/2373642.

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In mobile robotics, the exploration task consists of navigating through an unknown environment and building a representation of it. The mobile robot community has developed many approaches to solve this problem. These methods are mainly based on two key ideas. The first one is the selection of promising regions to explore and the second is the minimization of a cost function involving the distance traveled by the robots, the time it takes for them to finish the exploration, and others. An option to solve the exploration problem is the use of multiple robots to reduce the time needed for the ta

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Kim, Jonghoek. "Multirobot Exploration While Building Power-Efficient Sensor Networks in Three Dimensions." IEEE Transactions on Cybernetics 49, no. 7 (2019): 2771–78. http://dx.doi.org/10.1109/tcyb.2018.2835824.

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Luo, Yandong, Jianwen Guo, Zhenpeng Lao, Shaohui Zhang, and Xiaohui Yan. "Swarm Robot Exploration Strategy for Path Formation Tasks Inspired by Physarum polycephalum." Complexity 2021 (May 19, 2021): 1–17. http://dx.doi.org/10.1155/2021/6698421.

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Physarum polycephalum, a unicellular and multiheaded slime mould, can form highly efficient networks connecting separated food sources during the process of foraging. These adaptive networks exhibit a unique characteristic in that they are optimized without the control of a central consciousness. Inspired by this phenomenon, we present an efficient exploration and navigation strategy for a swarm of robots, which exploits cooperation and self-organisation to overcome the limited abilities of the individual robots. The task faced by the robots consists in the exploration of an unknown environmen

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Dai, Xuefeng, Zhifeng Yao, and Yan Zhao. "A Discrete Adaptive Auction-Based Algorithm for Task Assignments of Multi-Robot Systems." Journal of Robotics and Mechatronics 26, no. 3 (2014): 369–76. http://dx.doi.org/10.20965/jrm.2014.p0369.

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<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260003/10.jpg"" width=""300"" />Teammates trajectories</span></div> For reasons of production cost and differences in manufacturing dates for mobile robots, individual robots on a robot team have different processing, movement, and detection abilities. To maximize the potential ability of individual robots and minimize overall exploration time in unknown environments, this paper proposes a novel discrete adaptive auction-based algorithm for coordinating multirobot systems (MRSs). A utility calculati

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Zhang, Dawei, and Tingting Yang. "Visual Object Tracking Algorithm Based on Biological Visual Information Features and Few-Shot Learning." Computational Intelligence and Neuroscience 2022 (March 3, 2022): 1–8. http://dx.doi.org/10.1155/2022/3422859.

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Eye tracking is currently a research hotspot in the territory of service robotics. There is an urgent need for machine vision technique in the territory of video surveillance, and biological visual object following is one of the important basic research problems. By tracking the object of interest and recording the tracking trajectory, we can extract a structure from a video. It can also analyze the abnormal behavior of groups or individuals in the video or assist the public security organs in inquiring and searching for evidence of criminal suspects, etc. Moving object following has always be

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Lund, Henrik Hautop, and Luigi Pagliarini. "Distributed Robotics Education." Journal of Robotics and Mechatronics 23, no. 5 (2011): 859–70. http://dx.doi.org/10.20965/jrm.2011.p0859.

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Distributed robotics takes many forms, for instance, multirobots, modular robots, and self-reconfigurable robots. The understanding and development of such advanced robotic systems demand extensive knowledge in engineering and computer science. In this paper, we describe the concept of a distributed educational system as a valuable tool for introducing students to interactive parallel and distributed processing programming as the foundation for distributed robotics and human-robot interaction development. This is done by providing an educational tool that enables problem representation to be c

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Lucas, Nathan, and Abhilash Pandya. "Multirobot Confidence and Behavior Modeling: An Evaluation of Semiautonomous Task Performance and Efficiency." Robotics 10, no. 2 (2021): 71. http://dx.doi.org/10.3390/robotics10020071.

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There is considerable interest in multirobot systems capable of performing spatially distributed, hazardous, and complex tasks as a team leveraging the unique abilities of humans and automated machines working alongside each other. The limitations of human perception and cognition affect operators’ ability to integrate information from multiple mobile robots, switch between their spatial frames of reference, and divide attention among many sensory inputs and command outputs. Automation is necessary to help the operator manage increasing demands as the number of robots (and humans) scales up. H

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Yu, Lingli, Zixing Cai, Ping’an Gao, and Xiaoying Liu. "A spatial orthogonal allocation and heterogeneous cultural hybrid algorithm for multirobot exploration mission planning." Journal of Control Theory and Applications 9, no. 2 (2011): 171–76. http://dx.doi.org/10.1007/s11768-011-9109-3.

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23

Huntsberger, T., P. Pirjanian, A. Trebi-Ollennu, et al. "CAMPOUT: a control architecture for tightly coupled coordination of multirobot systems for planetary surface exploration." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 33, no. 5 (2003): 550–59. http://dx.doi.org/10.1109/tsmca.2003.817398.

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Quattrini Li, Alberto, Riccardo Cipolleschi, Michele Giusto, and Francesco Amigoni. "A semantically-informed multirobot system for exploration of relevant areas in search and rescue settings." Autonomous Robots 40, no. 4 (2015): 581–97. http://dx.doi.org/10.1007/s10514-015-9480-x.

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25

Nagatani, Keiji, Yoshito Okada, Naoki Tokunaga, et al. "Multirobot exploration for search and rescue missions: A report on map building in RoboCupRescue 2009." Journal of Field Robotics 28, no. 3 (2011): 373–87. http://dx.doi.org/10.1002/rob.20389.

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Jiang, Zhihong, Xiaolei Cao, Xiao Huang, Hui Li, and Marco Ceccarelli. "Progress and Development Trend of Space Intelligent Robot Technology." Space: Science & Technology 2022 (January 25, 2022): 1–11. http://dx.doi.org/10.34133/2022/9832053.

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Since space intelligent robots are not restricted by physiological conditions, it is an attractive choice for the development of automation technology to use them for space exploration and utilization. It is currently the key development direction of the major space powers over the world. This paper first investigates the robotic manipulators and humanoid robot systems for space station applications and reviews theories and methods for robots to achieve large-range stable motion and intelligent dexterous manipulation. Then, the intelligent robot systems for on-orbit satellite maintenance are r

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Ravankar, Abhijeet, Ankit Ravankar, Yukinori Kobayashi, and Yohei Hoshino. "A Bio-Inspired Algorithm for Autonomous Task Coordination of Multiple Mobile Robots." Proceedings 4, no. 1 (2018): 1. http://dx.doi.org/10.3390/ecsa-5-05760.

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Efficient task co-ordination is an important problem in multirobot systems. The explicit programming of each robot to perform specific tasks (e.g., cleaning) is too cumbersome and inefficient, as the areas to serve in a map may vary with time. Moreover, the number of available robots to serve may also vary, as some of the robots may be charging and not available. Improper task division can cause two or more robots to serve the same areas of the map, which is a waste of computation and resources. Hence, there is a need for a simpler scheme for the autonomous task co-ordination of multiple robot

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Gong, Junghwan, and Seunghwan Lee. "Hierarchical Area-Based and Path-Based Heuristic Approaches for Multirobot Coverage Path Planning with Performance Analysis in Surveillance Systems." Sensors 23, no. 20 (2023): 8533. http://dx.doi.org/10.3390/s23208533.

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In this study, we present a systematic exploration of hierarchical designs for multirobot coverage path planning (MCPP) with a special focus on surveillance applications. Unlike conventional studies centered on cleaning tasks, our investigation delves into the realm of surveillance problems, specifically incorporating the sensing range (SR) factor equipped on the robots. Conventional path-based MCPP strategies considering SR, primarily rely on naive approaches, generating nodes (viewpoints) to be visited and a global path based on these nodes. Therefore, our study proposes a general MCPP frame

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Petrlik, Matej, Pavel Petráček, Vít Krátký, et al. "UAVs Beneath the Surface: Cooperative Autonomy for Subterranean Search and Rescue in DARPA SubT." Field Robotics 3, no. 1 (2023): 1–68. http://dx.doi.org/10.55417/fr.2023001.

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This paper presents a novel approach for autonomous cooperating UAVs in search and rescue operations in subterranean domains with complex topology. The proposed system was ranked second in the Virtual Track of the DARPA SubT Finals as part of the team CTU-CRAS-NORLAB. In contrast to the winning solution that was developed specifically for the Virtual Track, the proposed solution also proved to be a robust system for deployment onboard physical UAVs flying in the extremely harsh and confined environment of the real-world competition. The proposed approach enables fully autonomous and decentrali

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Morisawa, Toma, Kotaro Hayashi, and Ikuo Mizuuchi. "Allocating Multiple Types of Tasks to Heterogeneous Agents Based on the Theory of Comparative Advantage." Journal of Robotics 2018 (2018): 1–18. http://dx.doi.org/10.1155/2018/1408796.

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We present a method to allocate multiple tasks with uncertainty to heterogeneous robots using the theory of comparative advantage: an economic theory that maximizes the benefit of specialization. In real applications, robots often must execute various tasks with uncertainty and future multirobot system will have to work effectively with people as a team. As an example, it may be necessary to explore an unknown environment while executing a main task with people, such as carrying, rescue, military, or construction. The proposed task allocation method is expected to reduce the total makespan (to

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Yatsenko, M. Yu, and V. A. Vorontsov. "To the question of including additional technical means in the Venus exploration program." Spacecrafts & Technologies 6, no. 1 (2022): 5–13. http://dx.doi.org/10.26732/j.st.2022.1.01.

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The current issue of expanding the scheme of the experiment for the contact research of Venus by including a multirotor aircraft as an additional technical means of research in a prospective expedition is considered. The concept is developed by the authors considers the possibility of creating and launching a multi-rotor aircraft (as a complex technical system) into the atmosphere of Venus in order to collect data on the composition and properties of the planet's atmosphere, as well as taking photos and videos of its surface. Such devices will operate for a certain time in the specified altitu

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Yatsenko, M. Yu, V. A. Vorontsov, and V. V. Ryzhkov. "System engineering research of a multirotor aircraft as a prospective technical means of exploring the atmosphere and surface of the planet Venus." Spacecrafts & Technologies 7, no. 3 (2023): 220–26. http://dx.doi.org/10.26732/j.st.2023.3.06.

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Currently, the exploration of the planet Venus is a very relevant and developing direction in space science. The development of rocket and space technologies has expanded the boundaries of accessibility of spacecraft to objects in the Solar System, allow for entire interplanetary expeditions, including flights to terrestrial planets, giant planets, and the outskirts of the Solar System. Currently, a program of planetary exploration for the next decades is being formed. Studying the history of expeditions to Venus and Mars clarifies the need to develop and improve methods for studying the atmos

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LIU, Jian-xin, Hui-peng LIU, Rong LIU, Jian-qiang XUE, Yue-hua LI, and Fang WANG. "Application of aeromagnetic survey to mineral exploration of Jinping, Yunnan, China by using multirotor UAV." Transactions of Nonferrous Metals Society of China 33, no. 5 (2023): 1550–58. http://dx.doi.org/10.1016/s1003-6326(23)66202-8.

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34

Carpenter, Chris. "Dual Heuristic Dynamic Programming Enables Trajectory Tracking Control." Journal of Petroleum Technology 75, no. 05 (2023): 76–78. http://dx.doi.org/10.2118/0523-0076-jpt.

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_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 200271, “Dual Heuristic Dynamic Programming in the Oil and Gas Industry for Trajectory Tracking Control,” by Seaar Al-Dabooni, Basra Oil Company; Alaa Azeez Tawiq, Technical Institute of Basra; and Hussen Alshehab, Basra Oil Company. The paper has not been peer reviewed. _ The complete paper presents an artificial intelligence (AI) algorithm the authors call dual heuristic dynamic programming (DHDP) that is used to solve optimization-control problems. Fast, self-learning control based on DHDP is

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Wang, Hongling, Chengjin Zhang, Yong Song, and Bao Pang. "Information-Fusion Methods Based Simultaneous Localization and Mapping for Robot Adapting to Search and Rescue Postdisaster Environments." Journal of Robotics 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/4218324.

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The first application of utilizing unique information-fusion SLAM (IF-SLAM) methods is developed for mobile robots performing simultaneous localization and mapping (SLAM) adapting to search and rescue (SAR) environments in this paper. Several fusion approaches, parallel measurements filtering, exploration trajectories fusing, and combination sensors’ measurements and mobile robots’ trajectories, are proposed. The novel integration particle filter (IPF) and optimal improved EKF (IEKF) algorithms are derived for information-fusion systems to perform SLAM task in SAR scenarios. The information-fu

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Jayaweera, Herath M. P. C., and Samer Hanoun. "UAV Path Planning for Reconnaissance and Look-Ahead Coverage Support for Mobile Ground Vehicles." Sensors 21, no. 13 (2021): 4595. http://dx.doi.org/10.3390/s21134595.

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Path planning of unmanned aerial vehicles (UAVs) for reconnaissance and look-ahead coverage support for mobile ground vehicles (MGVs) is a challenging task due to many unknowns being imposed by the MGVs’ variable velocity profiles, change in heading, and structural differences between the ground and air environments. Few path planning techniques have been reported in the literature for multirotor UAVs that autonomously follow and support MGVs in reconnaissance missions. These techniques formulate the path planning problem as a tracking problem utilizing gimbal sensors to overcome the coverage

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Chengqi Zhang*, Ling Guan**, and Zheru Chi. "Introduction to the Special Issue on Learning in Intelligent Algorithms and Systems Design." Journal of Advanced Computational Intelligence and Intelligent Informatics 3, no. 6 (1999): 439–40. http://dx.doi.org/10.20965/jaciii.1999.p0439.

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Learning has long been and will continue to be a key issue in intelligent algorithms and systems design. Emulating the behavior and mechanisms of human learning by machines at such high levels as symbolic processing and such low levels as neuronal processing has long been a dominant interest among researchers worldwide. Neural networks, fuzzy logic, and evolutionary algorithms represent the three most active research areas. With advanced theoretical studies and computer technology, many promising algorithms and systems using these techniques have been designed and implemented for a wide range

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Cao, C., H. Zhu, Z. Ren, H. Choset, and J. Zhang. "Representation granularity enables time-efficient autonomous exploration in large, complex worlds." Science Robotics 8, no. 80 (2023). http://dx.doi.org/10.1126/scirobotics.adf0970.

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We propose a dual-resolution scheme to achieve time-efficient autonomous exploration with one or many robots. The scheme maintains a high-resolution local map of the robot’s immediate vicinity and a low-resolution global map of the remaining areas of the environment. We believe that the strength of our approach lies in this low- and high-resolution representation of the environment: The high-resolution local map ensures that the robots observe the entire region in detail, and because the local map is bounded, so is the computation burden to process it. The low-resolution global map directs the

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Yatsenko, M. Yu, V. A. Vorontsov, and V. V. Ryzhkov. "Review of problematic issues in creation of a multirotor aircraft for Venus exploration." Engineering Journal: Science and Innovation, no. 2 (134) (February 2023). http://dx.doi.org/10.18698/2308-6033-2023-2-2255.

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The paper considers problematic issues that could arise in the process of studying design situations when creating a multirotor aircraft, which was first proposed as the technical means in studying the planet Venus as part of the promising Venusian spacecraft. The course of work identified a number of critical situations that should be analyzed already at the early stages of designing and developing the multirotor aircraft being a complex technical system in Venus exploration and taken into account when developing a program for its direct operation on the planet. The summary matrix of problems

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Dutta, Abhishek. "Robust design of a multirotor aerial vehicle." Scientific Reports 11, no. 1 (2021). http://dx.doi.org/10.1038/s41598-021-00413-4.

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AbstractThis paper introduces the methodology of systematic robust design of a multirotor vehicle as an example of how to carry out the robust design of a physical system. Robustness in aerial vehicles is highly desirable as it guarantees a desired level of performance even under environmental uncertainties. Thus far, robustness has been considered in terms of active control in the space of multirotor vehicles, but exploration of the design space itself is lacking. In this work, a conceptual design followed by a robust design is performed to come up with the specifications that lead to least u

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Lin, Tzu-Jui, and Karl A. Stol. "Faster navigation of semi-structured forest environments using multirotor UAVs." Robotica, November 4, 2022, 1–21. http://dx.doi.org/10.1017/s0263574722001564.

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Abstract Modern approaches for exploration path planning generally do not assume any structural information regarding the operational area. Therefore, they offer good performance when the region of interest is entirely unknown. However, for some applications such as plantation forest surveying, partial information regarding the survey area is known before the exploration process. Because the region of interest consists only of the lower portions of the tree stems themselves, the ground and high-elevation sections of the environment are unimportant and do not need to be observed. Due to these u

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Prieto, Samuel A., Nikolaos Giakoumidis, and Borja García de Soto. "Multiagent robotic systems and exploration algorithms: Applications for data collection in construction sites." Journal of Field Robotics, March 22, 2024. http://dx.doi.org/10.1002/rob.22316.

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AbstractThe construction industry has been notoriously slow to adopt new technology and embrace automation. This has resulted in lower efficiency and productivity compared to other industries where automation has been widely adopted. However, recent advancements in robotics and artificial intelligence offer a potential solution to this problem. In this study, a methodology is proposed to integrate multirobotic systems in construction projects with the aim of increasing efficiency and productivity. The proposed approach involves the use of multiple robot and human agents (HA) working collaborat

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Amorim, Thulio, Tiago Nascimento, Akash Chaudhary, Eliseo Ferrante, and Martin Saska. "A Minimalistic 3D Self-Organized UAV Flocking Approach for Desert Exploration." Journal of Intelligent & Robotic Systems 110, no. 2 (2024). http://dx.doi.org/10.1007/s10846-024-02108-0.

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AbstractIn this work, we propose a minimalistic swarm flocking approach for multirotor unmanned aerial vehicles (UAVs). Our approach allows the swarm to achieve cohesively and aligned flocking (collective motion), in a random direction, without externally provided directional information exchange (alignment control). The method relies on minimalistic sensory requirements as it uses only the relative range and bearing of swarm agents in local proximity obtained through onboard sensors on the UAV. Thus, our method is able to stabilize and control the flock of a general shape above a steep terrai

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