ASBR (463) and RDKDC (646)

Table of Contents

• Introduction
• ASBR: The Fun Side
• RDKDC: The Harder Side
• Quaternions: The necessary evil?
• Beyond the Class

Introduction

So now I’m onto robotics stuff. These two—ASBR (Algorithms for Sensor-Based Robotics) and RDKDC (Robot Dynamics, Kinematics, and Dynamic Control)—are the core courses for the Robotics MSE at Hopkins.

One leans more algorithmic, the other more mechanical/mathematical. Between the two, I feel like I got both the thrill of making robots “think” and the headache of making robots “move.”

ASBR: The Fun Side

ASBR was fun. I fell in love with Kalman filters and their extended variants—beautiful ways of filtering noise and predicting where things are going, even when your sensors lie to you. And then there’s SLAM (Simultaneous Localization and Mapping). To outsiders, it sounds like robots doing something cinematic. Internally, it’s really about the elegance of closing the loop: using imperfect data to both build a map of the world and figure out where you are inside it. Placeholder for SLAM loop diagram: The “closed loop formula” idea is everywhere in robotics, and SLAM felt like a perfect embodiment of it.

RDKDC: The Harder Side

RDKDC was harder. Not because I dislike linear algebra—I’m “not bad at it, just not good either”—but because the professor chose a very mathematical approach. Enter: Lie groups and Lie algebras.

At one point, I tried to think of them as donuts (technically, a torus) with tangent planes glued on. That mental image was… charming, but mostly useless when it came to actually understanding the special orthogonal group SO(3) and the special Euclidean group SE(3).

In practice, the rules go like this: so(3) –(exp)–> SO(3)
se(3) –(exp)–> SE(3)

A twist lives in so(3), and when you exponentiate it, you get a screw motion in SO(3). Sounds neat, right? It is neat—until you actually try to work with it.

Quaternions: The necessary evil?

Then came quaternions. Why do they exist? Because Euler angles and roll-pitch-yaw angles have singularities—the dreaded gimbal lock that robotists despise. So quaternions add an extra constraint, which lets you describe orientations without those singularities. They’re also a mathematical group, and in some sense they map (many-to-one) back into Cartesian coordinates.

The problem? They’re not exactly intuitive. You don’t see a quaternion and immediately understand what it means in 3D space.

My aerospace friends swear by them (“quaternions or bust”), but robotists are more skeptical. We’ll use them if we have to, but we don’t like the hype. Twists and Screws

Because SO(3) and SE(3) are so abstract, people came up with twists and screws—a much more user-friendly way to think about rigid body motion.

A rigid motion can be decomposed into:

• A translation along an axis
• A rotation around that same axis (counterclockwise, by default)

This feels much nicer to visualize. A screw motion has an axis, a pitch, a direction—it’s a geometric story, not just a 4×4 matrix.

I appreciated this “user feedback” moment from the math community. It’s like they realized: hey, maybe people actually want to picture what’s going on!

Still, the back-and-forth conversions between representations can be annoying. But if I had to rank them: screws > quaternions.

Beyond the Class

These courses gave me two very different flavors of robotics: one where I could feel clever (ASBR), and one where I felt smacked by linear algebra (RDKDC). Both stretched me, both were frustrating at times, but together they shaped how I now think about robots—messy sensors, clean math, and everything in between.