封面
市场调查报告书
商品编码
1679326

2030 年机器人技术市场预测:按类型、组件、技术、应用和地区进行的全球分析

Robotics Technology Market Forecasts to 2030 - Global Analysis By Type (Industrial Robots, Service Robots, Collaborative Robots, Mobile Robots, Humanoid Robots, and Other Types), Component, Technology, Application and By Geography

出版日期: | 出版商: Stratistics Market Research Consulting | 英文 200+ Pages | 商品交期: 2-3个工作天内

价格

根据 Stratistics MRC 的数据,全球机器人技术市场规模预计在 2024 年达到 1,200.5 亿美元,到 2030 年将达到 3,111.2 亿美元,复合年增长率为 17.2%。

机器人技术涉及机器人的设计、开发和应用,以执行通常由人类执行的任务。它涵盖机械工程、电气工程、电脑科学和人工智慧等多个学科,以创造能够准确、高效、快速地执行自动化任务的机器。机器人技术正在应用于製造业、医疗保健、物流和国防等行业,以提高生产力、降低人事费用、提高安全性并在复杂和危险的环境中提供创新解决方案。

根据国际机器人联合会发布的《世界机器人报告》,预计2021年,全球工业机器人运作数量将达到378.8万台。根据俄罗斯情报局的资料,2018年,共有35,880台机器人运往加拿大、美国和墨西哥,比前一年成长了7%。

协作机器人 (Cobots) 的采用日益广泛

协作机器人安全、适应性强且具有简单的程式设计能力,使其成为各种规模企业的理想选择。此外,人工智慧和机器学习的进步正在增强协作机器人执行复杂任务的能力。製造、航运和医疗保健领域对自动化的需求也推动了协作机器人的采用。随着各行各业寻求降低人事费用并提高业务效率,协作机器人变得越来越受欢迎。

技术纯熟劳工短缺

机器人技术的快速发展需要专业知识和专业技能,但这些技能却供不应求。许多行业在吸引和留住操作、维护和编程机器人系统的技术人员方面面临挑战。此外,技能差距导致营运成本增加和机器人解决方案的采用速度变慢。需要对教育和培训计划进行投资来解决这一问题并培养一支具备不断扩展的机器人领域所需技能的劳动力。技术纯熟劳工的短缺仍然是机器人技术广泛应用的重大障碍。

电子商务和物流业蓬勃发展

对网路购物和快速送货服务的需求不断增长,推动了仓库和配送中心自动化的需求。自动导引车(AGV)和机器人分类系统等机器人解决方案提高了物流业务的效率和准确性。人工智慧和物联网技术的整合将进一步优化供应链管理和库存控制。随着电子商务领域的不断扩大,机器人技术在物流领域的应用预计将迅速成长。这一趋势为机器人技术提供者提供了巨大的成长机会。

某些应用程式缺乏灵活性

机器人非常适合执行重复性的常规任务,但难以执行需要灵活性或复杂决策的任务。在需要高度客製化和不可预测性的行业中,传统的机器人解决方案可能不够用。此外,将机器人技术融入现有程序可能会成本高昂且困难。为了克服这些缺陷,机器人硬体和软体必须不断发展,变得更加灵活和多功能。机器人技术市场的不断扩大,要求其具有广泛的应用适应性。

COVID-19 的影响

COVID-19 疫情对机器人市场产生了重大影响。由于劳动力短缺和安全问题,疫情加速了自动化和机器人技术的采用。非接触式操作和远端监控的需求不断增长,进一步推动了机器人市场的发展。然而,疫情期间的供应链中断和经济不确定性给该行业带来了挑战。儘管面临这些挑战,但这场疫情凸显了机器人技术在提高营运弹性和效率方面的重要性。

工业机器人市场预计在预测期内成为最大的市场

预计工业机器人将在预测期内占据最大的市场占有率,因为它们具有在製造业、汽车和电子行业中执行各种任务的多功能性。对精度、速度和生产率的需求正在推动工业机器人的应用。此外,协作机器人和人工智慧机器人等机器人技术的进步正在进一步增强其功能。工业机器人的巨大市场占有率凸显了其在现代化製造流程中的关键作用。

预测期内,农业部门预计将实现最高复合年增长率

预计预测期内农业部门将出现最高成长率。这是因为精密农业和自动化的需求日益增长,以提高生产力并降低人事费用。人工智慧和物联网技术的融合将使农民能够优化资源利用率并提高作物产量。政府推动智慧农业的措施进一步推动了机器人技术在农业领域的应用。高复合年增长率反映了机器人技术在应对现代农业挑战方面日益增长的重要性。

比最大的地区

在预测期内,亚太地区预计将凭藉其快速的经济成长和不断扩大的工业基础占据最大的市场占有率。中国、日本和韩国等国家是机器人技术市场的主要贡献者。主要机器人製造商的存在和对自动化的不断增加的投资正在推动该地区市场的成长。此外,政府推动工业 4.0 和智慧製造的措施进一步推动了机器人技术的应用。

复合年增长率最高的地区:

由于各行各业迅速采用先进的机器人技术,预计北美在预测期内将呈现最高的复合年增长率。该地区拥有发达的医疗保健基础设施和不断增长的老龄人口,对医疗机器人和辅助技术的需求日益增长。此外,製造业和物流行业对自动化数位化的日益关注也促进了市场的成长。领先的科技公司和研究机构的存在进一步加速了该地区的机器人创新。

免费客製化服务:

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  • 公司简介
    • 对其他市场公司(最多 3 家公司)进行全面分析
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  • 地理细分
    • 根据客户兴趣对主要国家进行的市场估计、预测和复合年增长率(註:基于可行性检查)
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    • 根据产品系列、地理分布和策略联盟对主要企业基准化分析

目录

第一章执行摘要

第 2 章 前言

  • 概述
  • 相关利益者
  • 研究范围
  • 调查方法
    • 资料探勘
    • 资料分析
    • 资料检验
    • 研究途径
  • 研究资讯来源
    • 主要研究资讯来源
    • 二手研究资料资讯来源
    • 先决条件

第三章 市场走势分析

  • 驱动程式
  • 限制因素
  • 机会
  • 威胁
  • 技术分析
  • 应用分析
  • 新兴市场
  • COVID-19 的影响

第 4 章 波特五力分析

  • 供应商的议价能力
  • 买家的议价能力
  • 替代品的威胁
  • 新进入者的威胁
  • 竞争对手之间的竞争

5. 全球机器人技术市场按类型划分

  • 工业机器人
    • 关节机器人
    • SCARA机器人
    • Delta机器人
    • 直角坐标机器人
  • 服务机器人
    • 个人机器人
    • 专业机器人
  • 协作机器人
  • 移动机器人
  • 人形机器人
  • 其他类型

6. 全球机器人技术市场(按组件划分)

  • 软体
  • 硬体
  • 服务

7. 全球机器人市场(依技术划分)

  • 工业IoT(IIoT)
  • 机器人领域的人工智慧和机器学习
  • 视觉系统和感测器
  • 云端机器人

8. 全球机器人市场(按应用)

  • 製造业
    • 电子产品
    • 航太和国防
  • 卫生保健
    • 手术机器人
    • 復健机器人
  • 物流和仓储
  • 农业
  • 饮食
  • 零售
  • 建造
  • 其他用途

9. 全球机器人技术市场(按地区)

  • 北美洲
    • 美国
    • 加拿大
    • 墨西哥
  • 欧洲
    • 德国
    • 英国
    • 义大利
    • 法国
    • 西班牙
    • 欧洲其他地区
  • 亚太地区
    • 日本
    • 中国
    • 印度
    • 澳洲
    • 纽西兰
    • 韩国
    • 其他亚太地区
  • 南美洲
    • 阿根廷
    • 巴西
    • 智利
    • 南美洲其他地区
  • 中东和非洲
    • 沙乌地阿拉伯
    • 阿拉伯聯合大公国
    • 卡达
    • 南非
    • 其他中东和非洲地区

第十章 主要进展

  • 协议、伙伴关係、合作和合资企业
  • 收购与合併
  • 新产品发布
  • 业务扩展
  • 其他关键策略

第十一章 公司概况

  • ABB Ltd.
  • KUKA AG
  • Fanuc Corporation
  • Yaskawa Electric Corporation
  • Universal Robots A/S
  • iRobot Corporation
  • Teradyne Inc.
  • Boston Dynamics
  • Honda Motor Co., Ltd.
  • Siemens AG
  • Epson Robots
  • Denso Corporation
  • Comau SpA
  • Rockwell Automation, Inc.
  • Adept Technology
Product Code: SMRC28909

According to Stratistics MRC, the Global Robotics Technology Market is accounted for $120.05 billion in 2024 and is expected to reach $311.12 billion by 2030 growing at a CAGR of 17.2% during the forecast period. Robotics technology involves the design, development, and application of robots to perform tasks that are typically carried out by humans. It encompasses various fields including mechanical engineering, electrical engineering, computer science, and artificial intelligence to create machines capable of performing automated tasks with precision, efficiency, and speed. Robotics technology is applied across industries such as manufacturing, healthcare, logistics, and defense, aiming to enhance productivity, reduce labor costs, improve safety, and enable innovative solutions in complex or hazardous environments.

According to the World Robotics report presented by the International Federation of Robotics, operational stock of industrial robots is expected to reach 3788 thousand units by 2021. According to the RIA's data, 35,880 robots were shipped, in 2018, to Canada, along with the United States and Mexico, an increase of 7% from the previous year.

Market Dynamics:

Driver:

Rising adoption of Collaborative Robots (Cobots)

Cobots are perfect for companies of all sizes because of their safe, adaptable, and simple programming features. Additionally, advancements in AI and machine learning enhance the capabilities of cobots, enabling them to perform complex tasks. Cobot adoption is also fuelled by the need for automation in the manufacturing, shipping, and healthcare sectors. Cobots are becoming more and more popular as industries want to cut labor expenses and increase operational efficiency.

Restraint:

Lack of skilled workforce

The rapid advancement of robotics technologies requires specialized knowledge and expertise, which is in short supply. Many industries face challenges in finding and retaining qualified personnel to operate, maintain, and program robotic systems. Additionally, the gap in skills can lead to increased operational costs and delays in the implementation of robotics solutions. Investment in educational and training initiatives is necessary to address this problem and create a workforce with the necessary skills to serve the expanding robotics sector. The lack of skilled workers remains a critical barrier to the widespread adoption of robotics technology.

Opportunity:

Growing E-commerce and logistics sector

The increasing demand for online shopping and fast delivery services drives the need for automation in warehouses and distribution centers. Robotics solutions, such as automated guided vehicles (AGVs) and robotic sortation systems, enhance the efficiency and accuracy of logistics operations. The integration of AI and IoT technologies further optimizes supply chain management and inventory control. As the e-commerce sector continues to expand, the adoption of robotics technology in logistics is expected to grow rapidly. This trend offers substantial growth opportunities for robotics technology providers.

Threat:

Limited flexibility in some applications

Robots are great at repeated, predetermined activities, but they can find it difficult to do tasks that call for flexibility and intricate decision-making. Conventional robotic solutions might not be sufficient for industries that demand a high degree of customisation and unpredictability. Furthermore, incorporating robots into current procedures might be expensive and difficult. Robotics hardware and software must continuously progress to increase flexibility and variety in order to defeat this danger. Adaptability to a wide range of applications is essential for the robotics technology market's continued expansion.

Covid-19 Impact

The Covid-19 pandemic has had a profound impact on the robotics technology market. The pandemic accelerated the adoption of automation and robotics due to labor shortages and safety concerns. The increased demand for contactless operations and remote monitoring further boosted the robotics market. However, supply chain disruptions and economic uncertainties during the pandemic posed challenges for the industry. Despite these challenges, the pandemic underscored the importance of robotics in enhancing operational resilience and efficiency.

The industrial robots segment is expected to be the largest during the forecast period

The industrial robots segment is expected to account for the largest market share during the forecast period, due to their versatility and ability to perform a wide range of tasks in manufacturing, automotive, and electronics industries. The demand for high precision, speed, and productivity drives the adoption of industrial robots. Additionally, advancements in robotic technologies, such as collaborative and AI-powered robots, further enhance their capabilities. The significant market share of industrial robots highlights their critical role in modernizing manufacturing processes.

The agriculture segment is expected to have the highest CAGR during the forecast period

Over the forecast period, the agriculture segment is predicted to witness the highest growth rate, due to the increasing need for precision agriculture and automation to enhance productivity and reduce labor costs. The integration of AI and IoT technologies enables farmers to optimize resource usage and improve crop yields. Government initiatives to promote smart farming practices further drive the adoption of robotics in agriculture. The high CAGR reflects the growing importance of robotics in addressing the challenges of modern agriculture.

Region with largest share:

During the forecast period, Asia Pacific region is expected to hold the largest market share, due to the region's rapid economic growth and expanding industrial base. Countries like China, Japan, and South Korea are major contributors to the robotics technology market. The presence of leading robotics manufacturers and increasing investment in automation drive the market's growth in the region. Additionally, government initiatives to promote Industry 4.0 and smart manufacturing further support the adoption of robotics.

Region with highest CAGR:

Over the forecast period, the North America region is anticipated to exhibit the highest CAGR, owing to the rapid adoption of advanced robotics technologies in various industries. The region's developed healthcare infrastructure and growing senior population drive the demand for medical robots and assistive technologies. Additionally, the increasing focus on automation and digitalization in manufacturing and logistics sectors contributes to market growth. The presence of leading technology companies and research institutions further accelerates innovation in robotics in this region.

Key players in the market

Some of the key players profiled in the Robotics Technology Market include ABB Ltd., KUKA AG, Fanuc Corporation, Yaskawa Electric Corporation, Universal Robots A/S, iRobot Corporation, Teradyne Inc., Boston Dynamics, Honda Motor Co., Ltd., Siemens AG, Epson Robots, Denso Corporation, Comau S.p.A., Rockwell Automation, Inc., and Adept Technology.

Key Developments:

In January 2025, ABB is acquiring Sensorfact BV, a fast-growing energy management company headquartered in Utrecht, Netherlands. The acquisition further expands ABB's digital energy management offering and is expected to close in Q1 2025. Financial terms were not disclosed.

In January 2025, Yaskawa Electric Corporation announces that the Company signed a MOU with Astellas Pharma Inc. to start discussion to build an innovative cell therapy platform by combining robotics and pharmaceutical technologies. The MOU is a legally non-binding agreement on a partnership between the two companies, and specific discussions will proceed.

Types Covered:

  • Industrial Robots
  • Service Robots
  • Collaborative Robots
  • Mobile Robots
  • Humanoid Robots
  • Other Types

Components Covered:

  • Software
  • Hardware
  • Services

Technologies Covered:

  • Industrial IoT (IIoT)
  • AI and Machine Learning in Robotics
  • Vision Systems and Sensors
  • Cloud Robotics

Applications Covered:

  • Manufacturing
  • Healthcare
  • Logistics & Warehousing
  • Agriculture
  • Food & Beverage
  • Retail
  • Construction
  • Other Applications

Regions Covered:

  • North America
    • US
    • Canada
    • Mexico
  • Europe
    • Germany
    • UK
    • Italy
    • France
    • Spain
    • Rest of Europe
  • Asia Pacific
    • Japan
    • China
    • India
    • Australia
    • New Zealand
    • South Korea
    • Rest of Asia Pacific
  • South America
    • Argentina
    • Brazil
    • Chile
    • Rest of South America
  • Middle East & Africa
    • Saudi Arabia
    • UAE
    • Qatar
    • South Africa
    • Rest of Middle East & Africa

What our report offers:

  • Market share assessments for the regional and country-level segments
  • Strategic recommendations for the new entrants
  • Covers Market data for the years 2022, 2023, 2024, 2026, and 2030
  • Market Trends (Drivers, Constraints, Opportunities, Threats, Challenges, Investment Opportunities, and recommendations)
  • Strategic recommendations in key business segments based on the market estimations
  • Competitive landscaping mapping the key common trends
  • Company profiling with detailed strategies, financials, and recent developments
  • Supply chain trends mapping the latest technological advancements

Free Customization Offerings:

All the customers of this report will be entitled to receive one of the following free customization options:

  • Company Profiling
    • Comprehensive profiling of additional market players (up to 3)
    • SWOT Analysis of key players (up to 3)
  • Regional Segmentation
    • Market estimations, Forecasts and CAGR of any prominent country as per the client's interest (Note: Depends on feasibility check)
  • Competitive Benchmarking
    • Benchmarking of key players based on product portfolio, geographical presence, and strategic alliances

Table of Contents

1 Executive Summary

2 Preface

  • 2.1 Abstract
  • 2.2 Stake Holders
  • 2.3 Research Scope
  • 2.4 Research Methodology
    • 2.4.1 Data Mining
    • 2.4.2 Data Analysis
    • 2.4.3 Data Validation
    • 2.4.4 Research Approach
  • 2.5 Research Sources
    • 2.5.1 Primary Research Sources
    • 2.5.2 Secondary Research Sources
    • 2.5.3 Assumptions

3 Market Trend Analysis

  • 3.1 Introduction
  • 3.2 Drivers
  • 3.3 Restraints
  • 3.4 Opportunities
  • 3.5 Threats
  • 3.6 Technology Analysis
  • 3.7 Application Analysis
  • 3.8 Emerging Markets
  • 3.9 Impact of Covid-19

4 Porters Five Force Analysis

  • 4.1 Bargaining power of suppliers
  • 4.2 Bargaining power of buyers
  • 4.3 Threat of substitutes
  • 4.4 Threat of new entrants
  • 4.5 Competitive rivalry

5 Global Robotics Technology Market, By Type

  • 5.1 Introduction
  • 5.2 Industrial Robots
    • 5.2.1 Articulated Robots
    • 5.2.2 SCARA Robots
    • 5.2.3 Delta Robots
    • 5.2.4 Cartesian Robots
  • 5.3 Service Robots
    • 5.3.1 Personal Robots
    • 5.3.2 Professional Robots
  • 5.4 Collaborative Robots
  • 5.5 Mobile Robots
  • 5.6 Humanoid Robots
  • 5.7 Other Types

6 Global Robotics Technology Market, By Component

  • 6.1 Introduction
  • 6.2 Software
  • 6.3 Hardware
  • 6.4 Services

7 Global Robotics Technology Market, By Technology

  • 7.1 Introduction
  • 7.2 Industrial IoT (IIoT)
  • 7.3 AI and Machine Learning in Robotics
  • 7.4 Vision Systems and Sensors
  • 7.5 Cloud Robotics

8 Global Robotics Technology Market, By Application

  • 8.1 Introduction
  • 8.2 Manufacturing
    • 8.2.1 Automotive
    • 8.2.2 Electronics
    • 8.2.3 Aerospace & Defense
  • 8.3 Healthcare
    • 8.3.1 Surgical Robots
    • 8.3.2 Rehabilitation Robots
  • 8.4 Logistics & Warehousing
  • 8.5 Agriculture
  • 8.6 Food & Beverage
  • 8.7 Retail
  • 8.8 Construction
  • 8.9 Other Applications

9 Global Robotics Technology Market, By Geography

  • 9.1 Introduction
  • 9.2 North America
    • 9.2.1 US
    • 9.2.2 Canada
    • 9.2.3 Mexico
  • 9.3 Europe
    • 9.3.1 Germany
    • 9.3.2 UK
    • 9.3.3 Italy
    • 9.3.4 France
    • 9.3.5 Spain
    • 9.3.6 Rest of Europe
  • 9.4 Asia Pacific
    • 9.4.1 Japan
    • 9.4.2 China
    • 9.4.3 India
    • 9.4.4 Australia
    • 9.4.5 New Zealand
    • 9.4.6 South Korea
    • 9.4.7 Rest of Asia Pacific
  • 9.5 South America
    • 9.5.1 Argentina
    • 9.5.2 Brazil
    • 9.5.3 Chile
    • 9.5.4 Rest of South America
  • 9.6 Middle East & Africa
    • 9.6.1 Saudi Arabia
    • 9.6.2 UAE
    • 9.6.3 Qatar
    • 9.6.4 South Africa
    • 9.6.5 Rest of Middle East & Africa

10 Key Developments

  • 10.1 Agreements, Partnerships, Collaborations and Joint Ventures
  • 10.2 Acquisitions & Mergers
  • 10.3 New Product Launch
  • 10.4 Expansions
  • 10.5 Other Key Strategies

11 Company Profiling

  • 11.1 ABB Ltd.
  • 11.2 KUKA AG
  • 11.3 Fanuc Corporation
  • 11.4 Yaskawa Electric Corporation
  • 11.5 Universal Robots A/S
  • 11.6 iRobot Corporation
  • 11.7 Teradyne Inc.
  • 11.8 Boston Dynamics
  • 11.9 Honda Motor Co., Ltd.
  • 11.10 Siemens AG
  • 11.11 Epson Robots
  • 11.12 Denso Corporation
  • 11.13 Comau S.p.A.
  • 11.14 Rockwell Automation, Inc.
  • 11.15 Adept Technology

List of Tables

  • Table 1 Global Robotics Technology Market Outlook, By Region (2022-2030) ($MN)
  • Table 2 Global Robotics Technology Market Outlook, By Type (2022-2030) ($MN)
  • Table 3 Global Robotics Technology Market Outlook, By Industrial Robots (2022-2030) ($MN)
  • Table 4 Global Robotics Technology Market Outlook, By Articulated Robots (2022-2030) ($MN)
  • Table 5 Global Robotics Technology Market Outlook, By SCARA Robots (2022-2030) ($MN)
  • Table 6 Global Robotics Technology Market Outlook, By Delta Robots (2022-2030) ($MN)
  • Table 7 Global Robotics Technology Market Outlook, By Cartesian Robots (2022-2030) ($MN)
  • Table 8 Global Robotics Technology Market Outlook, By Service Robots (2022-2030) ($MN)
  • Table 9 Global Robotics Technology Market Outlook, By Personal Robots (2022-2030) ($MN)
  • Table 10 Global Robotics Technology Market Outlook, By Professional Robots (2022-2030) ($MN)
  • Table 11 Global Robotics Technology Market Outlook, By Collaborative Robots (2022-2030) ($MN)
  • Table 12 Global Robotics Technology Market Outlook, By Mobile Robots (2022-2030) ($MN)
  • Table 13 Global Robotics Technology Market Outlook, By Humanoid Robots (2022-2030) ($MN)
  • Table 14 Global Robotics Technology Market Outlook, By Other Types (2022-2030) ($MN)
  • Table 15 Global Robotics Technology Market Outlook, By Component (2022-2030) ($MN)
  • Table 16 Global Robotics Technology Market Outlook, By Software (2022-2030) ($MN)
  • Table 17 Global Robotics Technology Market Outlook, By Hardware (2022-2030) ($MN)
  • Table 18 Global Robotics Technology Market Outlook, By Services (2022-2030) ($MN)
  • Table 19 Global Robotics Technology Market Outlook, By Technology (2022-2030) ($MN)
  • Table 20 Global Robotics Technology Market Outlook, By Industrial IoT (IIoT) (2022-2030) ($MN)
  • Table 21 Global Robotics Technology Market Outlook, By AI and Machine Learning in Robotics (2022-2030) ($MN)
  • Table 22 Global Robotics Technology Market Outlook, By Vision Systems and Sensors (2022-2030) ($MN)
  • Table 23 Global Robotics Technology Market Outlook, By Cloud Robotics (2022-2030) ($MN)
  • Table 24 Global Robotics Technology Market Outlook, By Application (2022-2030) ($MN)
  • Table 25 Global Robotics Technology Market Outlook, By Manufacturing (2022-2030) ($MN)
  • Table 26 Global Robotics Technology Market Outlook, By Automotive (2022-2030) ($MN)
  • Table 27 Global Robotics Technology Market Outlook, By Electronics (2022-2030) ($MN)
  • Table 28 Global Robotics Technology Market Outlook, By Aerospace & Defense (2022-2030) ($MN)
  • Table 29 Global Robotics Technology Market Outlook, By Healthcare (2022-2030) ($MN)
  • Table 30 Global Robotics Technology Market Outlook, By Surgical Robots (2022-2030) ($MN)
  • Table 31 Global Robotics Technology Market Outlook, By Rehabilitation Robots (2022-2030) ($MN)
  • Table 32 Global Robotics Technology Market Outlook, By Logistics & Warehousing (2022-2030) ($MN)
  • Table 33 Global Robotics Technology Market Outlook, By Agriculture (2022-2030) ($MN)
  • Table 34 Global Robotics Technology Market Outlook, By Food & Beverage (2022-2030) ($MN)
  • Table 35 Global Robotics Technology Market Outlook, By Retail (2022-2030) ($MN)
  • Table 36 Global Robotics Technology Market Outlook, By Construction (2022-2030) ($MN)
  • Table 37 Global Robotics Technology Market Outlook, By Other Applications (2022-2030) ($MN)

Note: Tables for North America, Europe, APAC, South America, and Middle East & Africa Regions are also represented in the same manner as above.