🚀 9 Essential Math Fundamentals to Build a Humanoid Robot

Robotics Engineering Essentials:

Jan 01, 2024

An Indian boy in his university dorm room, working on math for robotics in the evening. The room is dimly lit with a small desk lamp. Books and robotics parts are scattered on the desk. A laptop is open with mathematical formulas on the screen. The boy, wearing casual clothes, is focused on a notebook, writing equations. The room has typical dormitory features like a bed, a small wardrobe, and posters on the wall. The atmosphere is studious and serene.

The list provided covers many of the key mathematical concepts used in the design and operation of humanoid robots, but it's not exhaustive. The mathematics used in robotics is vast and can span several disciplines depending on the specific area of focus. The goal of this post is to get beginners started with absolutely necessary math and then as you progress in your robotics journey, you will realise that the complexity of the math involved in a robotics project can vary greatly depending on the scope and goals of the project. While it's beneficial to have a broad understanding of many of these areas, specialists often focus on a few areas in depth.

Trigonometry: Key for understanding angles and movement, used in tasks like robotic walking or object manipulation. For example, it helps a robot to calculate the angle it needs to bend its 'knee' to take a step.
Linear Algebra: Powers transformations, rotations, and translations in 3D space - crucial for motion planning and control. It helps a robot to understand where its hand is in relation to its body.
Calculus: Essential for control theory, calculating rates of change, and understanding how systems evolve over time. It allows robots to accurately predict where a thrown ball will land.
Differential Equations: Used to model the behaviour of robotic systems over time, accounting for factors like inertia and forces. It helps in determining how quickly a robot can stop or start moving.
Probability and Statistics: Deals with uncertainty in robotics, used in sensor data fusion, noise filtering, and robot localization (like in SLAM). It helps a robot estimate its position within a map.
Graph Theory: Used in path planning algorithms (e.g., Dijkstra's, A*). It enables a robot to find the most efficient path from point A to point B.
Geometry: Essential in vision systems for object detection, recognition, and also in motion planning and collision detection. It helps a robot to recognize a human face, for example.
Quaternion Algebra: Used in 3D rotation and orientation. It helps a robot to accurately calculate and control its orientation in space, preventing problems like a gimbal lock.
Screw theory: It is a fundamental concept in robotics, and is vital for designing, planning, and controlling robotic movements. It underpins algorithms for tasks like path planning and motion control.

Happy Learning 😌✌️

Mayur’s Robotic's Diary

Discussion about this post