Math
The Math section provides resources and tutorials on advanced mathematical concepts that are pivotal in robotics applications. These topics include probabilistic modeling, registration techniques, and optimization methods, which are essential for perception, planning, control, and decision-making in robotic systems.
This section is currently under development, and contributions from individuals with expertise or interest in robotics-related mathematics are highly encouraged.
Key Subsections and Highlights
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Gaussian Process and Gaussian Mixture Model A tutorial covering the fundamentals of Gaussian Processes (GP), Gaussian Mixture Models (GMM), and the Expectation Maximization (EM) algorithm. Discusses applications in robotics, such as environment modeling, motion planning, and state estimation.
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Registration Techniques in Robotics Explains Horn’s closed-form solution for absolute orientation and its applications in robotics, including camera-robot registration and Iterative Closest Point (ICP) for aligning point clouds. This section focuses on transforming between coordinate systems and registering sensor data.
Development Needs
This section aims to become a comprehensive resource for mathematics relevant to robotics. We are actively seeking contributions in the following areas:
- Linear algebra for robotics (e.g., matrix transformations, eigenvalues in rigid body dynamics)
- Optimization techniques used in motion planning and control
- Probability and statistics in robotic perception
- Numerical methods for solving differential equations in robotics
- Advanced geometry and kinematics for robot manipulators
- Tutorials on implementing these concepts using Python, MATLAB, or other tools
Your expertise and input will greatly enrich this resource. If you’re interested in contributing, please reach out or consider submitting content directly.