A Systematic Review of Inverse Kinematics Methods for Fixed-Base Serial Manipulators: Analytical, Numerical, and Machine Learning Methods

Trullo, Hernan Dario
Alban, Oscar Andres Vivas

International Journal of Robotics and Control Systems
Vol 5, No 3 (2025)

Inverse kinematics is essential for precision tasks in fixed-base serial robots, such as surgical robotics or high-speed manufacturing, where delays or errors can have critical consequences. Current inverse kinematic methods face a fundamental trade-off: analytical solutions are fast but limited to spherical-wrist manipulators, while numerical and AI-based approaches sacrifice speed for generality. Despite prior reviews comparing performance metrics, no study provides a unified quantitative framework to guide method selection based on robot structure or application requirements. This systematic review addresses this lack of (1) quantitatively contrasting (response time, accuracy) analytical, numerical, and AI-based methods using studies in fields such as industrial robotics, medicine, and collaborative spaces and (2) identifying optimal hybrid strategies for real-time applications such as path planning. Using PRISMA, we analyzed 47 peer-reviewed articles from Scopus/Web of Science between 2019-2024, excluding algorithms for continuous, parallel, or mobile robots to focus solely on fixed-base serial architectures; selecting topics like ’inverse kinematics and serial robots and analytical or numeric or machine learning methods’. The review reveals that 32% of the analyzed methods are numerical, while 30% are AI-based approaches, reflecting the growing interest in data-driven solutions for IK problems; this scenario highlights the implementation of these methods given the limitations of analytical methods. Moreover, 56% of the nonanalytical approaches achieve an accuracy better than 0.01 mm; and about 70% of these approaches have response times exceeding 20 ms or don´t evaluate the metric, highlighting a critical bottleneck for real-time use. We conclude that hybrid IK methods, combined with standardized validation protocols, are essential for critical applications like robotic surgery. Future work must address benchmarking gaps, especially in AI-based IK, to enable reliable adoption in industry.