Robotics

Moving is not easy at all! We rarely stop to think about how effortlessly we walk on two feet. Navigating a three‑dimensional environment like the world we live in requires not only a solid understanding of where every object is located relative to our own position, but also a sense of how much effort each action will take. That effort might be something as simple as picking up a mug from the table or as demanding as climbing a rock.

Robotics is a mix or sensing, navigating, and decision making. Let's first focus on navigating.

01

Rotation matrix and angular velocities

To describe a rigid body’s orientation in space, we need to track how its local coordinate axes sit relative to a reference frame. This requires three orthonormal vectors, collected neatly into a 3 × 3 rotation matrix

02

Homogeneous transformation, twists, and screws

By Homogeneous Transformation, we unify rotation and translation displacement, in a 4 × 4 matrix, and by Twist we represent both rotational and translational velocity in one vector. Screw theory provides the geometric framework that ties these together, giving an elegant description of robot motion.

03

Exponential Coordinate of Rigid-Body Motions

By exponential coordinates, we express a finite rigid-body motion through a single screw motion, capturing rotation and translation in one compact form. The matrix logarithm reverses this process.

04

Forward Kinematics

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