Month: January 2021

Number Bases Stretch The Mind

January 1, 2021 by 22 Comments

Some of us might solve crossword puzzles or Sudoko games to exercise our minds, but [Nathan Nichols] plays with exotic number systems to keep the brain cells in shape. He wrote the Hanoi C99 library while in high school, implementing several of his favorites.

We have all been using decimal (base 10) and duodecimal (base 12, as in clocks) since before grade school. Us computer geeks are also adept at various computer-friendly systems like binary, octal, and hexadecimal. The true nerds among us will be familiar with systems like vigesimal (base 20 Mayan numerals) and sexagesimal (base 60 Babylonian numbers). We ourselves espoused the virtues of seximal (base 6) a couple of years ago. But if you really want to stretch your mind, take a dive into the weird number systems that [Nathan] has been exploring.

Negabinary (base -2)

The lowest level of weirdness in the group, this one is almost normal. Its the same as binary, except the bit weights have alternating signs: { 1, -2, 4, -8, ... }.

Binarions (base -1+i)

Or base -1+j if you studied electrical engineering. The use of complex numbers as radices was proposed by Donald Knuth way back in 1955. We find it really hard to imagine this one being helpful.

Fibonacci base

Numbers can also be represented by the summation of a sequence of Fibonacci numbers. Using this system, a number can sometimes be represented more than one way, so watch out.

Stern-Brocot tree

A number is represented by its path down the Stern-Brocot tree. One feature of this system is that numbers can be exact. For example, the Stern-Brocot tree representation of one-third has a finite number of digits.

While [Nathan]’s library only performs conversion at input or output, we wonder if someone will take this further and implement an arithmetic unit inside an FPGA. Besides being a fun exercise, it would baffle someone casually trying to reverse engineer your secret calculations. Let us know of any strange number systems you have used or encountered.

Transforming Drone Can Be A Square Or A Dragon

January 1, 2021 by 8 Comments

When flying drones in and around structures, the size of the drone is generally limited by the openings you want to fit through. Researchers at the University of Tokyo got around this problem by using an articulating structure for the drone frame, allowing the drone to transform from a large square to a narrow, elongated form to fit through smaller gaps.

The drone is called DRAGON, which is somehow an acronym for the tongue twisting description “Dual-Rotor Embedded Multilink Robot with the Ability of Multi-Degree-of-Freedom Aerial Transformation“. The drone consists of four segments, with a 2-DOF actuated joint between each segment. A pair of ducted fan motors are attached to the middle of each segment with a 2-DOF gimbal that allows it to direct thrust in any direction relative to the segment. For normal flight the segments would be arranged in the square shape, with minimal movement between the segments. When a small gap is encountered, as demonstrated in the video after the break, the segments rearrange into a dragon-like shape, that can pass through a gap in any plane.

Each segment has its own power source and controller, and the control software required to make everything work together is rather complex. The full research paper is unfortunately behind a paywall. The small diameter of the propellers, and all the added components would be a severe limiting factor in terms of lifting capacity and flight time, but the concept is to definitely interesting.

The idea of shape shifting robots has been around for a while, and can become even more interesting when the different segment can detach and reattach themselves to become modular robots. The 2016 Hackaday Grand Prize winner DTTO is a perfect example of this, although it did lack the ability to fly. Continue reading “Transforming Drone Can Be A Square Or A Dragon” →