Ali K Esfahani
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 and twists
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.
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
About Lie Groups
05
Forward Kinematics: PoE, Relative Twists
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