The labeled MRPP (Multi-Robot Path Planning) problem involves routing robots from start to goal configurations efficiently while avoiding collisions. Despite progress in solution quality and runtime, its complexity and industrial relevance continue to drive research. This dissertation introduces scalable MRPP methods with provable guarantees and practical heuristics. First, we study dense MRPP on 2D grids, relevant to warehouse and parcel systems. We propose the Rubik Table method, achieving $(1 + δ)$-optimal makespan (with $δ\in (0, 0.5]$) for up to $\frac{m_1 m_2}{2}$ robots, solving large instances efficiently and setting a new theoretical benchmark. Next, we address real-world MRPP. We design optimal layouts for structured environments (e.g., warehouses, parking systems) and propose a puzzle-based system for dense, deadlock-free autonomous vehicle parking. We also extend MRPP to Reeds-Shepp robots, introducing motion primitives and smoothing techniques to ensure feasible, efficient paths under nonholonomic constraints. Simulations and real-world tests validate the approach in urban driving and robotic transport scenarios.

India s operational stock of industrial robots hit all time high. Sales of industrial robots in India reached a new record of 4,945 units installed. This is an increase of 54 percent compared to the previous year (2020: 3,215 units). In terms of annual installations, India now ranks in tenth position worldwide. These are findings of the report World Robotics, presented by the International Federation of Robotics (IFR).

Countries around the world invest in robotics to support developments in industry and society. What are the exact targets of robotics research funding programs (R&D) officially driven by governments in Asia, Europe and America today? This has been researched by the International Federation of Robotics and published in the 2023 update paper of "World Robotics R&D Programs". "The 3rd version of World Robotics R&D Programs covers the latest funding developments including updates in 2022," says Prof. Dr. Jong-Oh Park, Vice-Chairman IFR Research Committee and member of the Executive Board. In China, the "14th Five-Year Plan" for Robot Industry Development, released by the Ministry of Industry and Information Technology (MIIT) in Beijing on 21st December 2021, focuses on promoting innovation.

China's massive investment in industrial robotics has put the country in the top ranking of robot density, surpassing the United States for the first time.

China's massive investment in industrial robotics has put the country in the top ranking of robot density, surpassing the United States for the first time. The number of operational industrial robots relative to the number of workers hit 322 units per 10,000 employees in the manufacturing industry. The world s top 5 most automated countries in manufacturing 2021 are: South Korea, Singapore, Japan, Germany and China. "Robot density is a key indicator of automation adoption in the manufacturing industry around the world," says Marina Bill, President of the International Federation of Robotics. "The new average of global robot density in the manufacturing industry surged to 141 robots per 10,000 employees – more than double the number six years ago. China's rapid growth shows the power of its investment so far, but it still has much opportunity to automate."

China now has more industrial robots per 10,000 workers than the United States, according to the International Federation of Robotics (IFR). This is the first time China has surpassed the United States in robot density. In 2021, China averaged 322 industrial robots for every 10,000 employees. According to the IFR, China saw a huge jump in robot installations in 2021. The country's industrial robotics market saw 243,300 installations last year, a 44% increase from the year before.

For enabling efficient, large-scale coordination of unmanned aerial vehicles (UAVs) under the labeled setting, in this work, we develop the first polynomial time algorithm for the reconfiguration of many moving bodies in three-dimensional spaces, with provable $1.x$ asymptotic makespan optimality guarantee under high robot density. More precisely, on an $m_1\times m_2 \times m_3$ grid, $m_1\ge m_2\ge m_3$, our method computes solutions for routing up to $\frac{m_1m_2m_3}{3}$ uniquely labeled robots with uniformly randomly distributed start and goal configurations within a makespan of $m_1 + 2m_2 +2m_3+o(m_1)$, with high probability. Because the makespan lower bound for such instances is $m_1 + m_2+m_3 - o(m_1)$, also with high probability, as $m_1 \to \infty$, $\frac{m_1+2m_2+2m_3}{m_1+m_2+m_3}$ optimality guarantee is achieved. $\frac{m_1+2m_2+2m_3}{m_1+m_2+m_3} \in (1, \frac{5}{3}]$, yielding $1.x$ optimality. In contrast, it is well-known that multi-robot path planning is NP-hard to optimally solve. In numerical evaluations, our method readily scales to support the motion planning of over $100,000$ robots in 3D while simultaneously achieving $1.x$ optimality. We demonstrate the application of our method in coordinating many quadcopters in both simulation and hardware experiments.

The use of industrial robots in factories around the world is accelerating at a high rate: 126 robots per 10,000 employees is the new average of global robot density in the manufacturing industries – nearly double the number five years ago (2015: 66 units). This is according to the 2021 World Robot Report. By regions, the average robot density in Asia/Australia is 134 units, in Europe 123 units and in the Americas 111 units. The top 5 most automated countries in the world are: South Korea, Singapore, Japan, Germany, and Sweden. "Robot density is the barometer to track the degree of automation adoption in the manufacturing industry around the world," says Milton Guerry, President of the International Federation of Robotics.

Robotics is creating a hot buzz around the world in the field of cutting-edge technologies. Thousands of robots are getting deployed to work for multiple industries to help employees, customers, patients, tourists, and so on. Educational institutes have started offering professional degrees in robotics to highly interested students. Now, these robotics professionals are receiving a plethora of opportunities to work and develop robots in countries with an RPA facility or the best research and development labs. Let's explore some of the top ten countries for robotics professionals to continue the work with robotics.

Research has found a link between higher densities of robots in a population and increased levels of productivity. The study – conducted by supply chain specialists Balloon One – analysed countries with similar levels of manufacturing output and looked at their densities of robots and GDP per hours worked. Balloon One's research found that: "This analysis shows that countries with a robot density of 150 or more are, on average, experiencing higher productivity levels than those with a robot density of 149 or less. While it could be argued that this is a result of some nations being more focused on manufacturing as part of their economy, and therefore having developed better infrastructure to meet demand, higher levels of productivity aren't skewed towards nations that rely more heavily on manufacturing. In fact, manufacturing levels are, on average, higher (17.86% of GDP) in less-robot-dense nations. Because there is a correlation between robot density and higher levels of productivity, it seems that if the UK increased its robot density, it could boost productivity. This begs the question of whether the country should invest more in automation if it wants to see a boost in its manufacturing productivity. It certainly seems to be working for nations of a similar standing."