Coursera: Control of Mobile Robotics

I completed a Coursera course last month on the subject of the Control of Mobile Robotics. The class was sort of a bite-sized introduction to control theory in the flavor of autonomous navigation at the hardware level. This means that no consideration was given to mechanical system design or AI approaches. Magnus Egerstedt of Georgia Tech was the primary instructor and his research and teaching assistants provided supplemental lectures, responded to questions on the forum, and presented programming exercises using their Simiam robotic simulation software (a package of Matlab files). This course was useful for me as my formal experience with a Dynamics Systems and Controls was kind of abstract and didn't possess a strong focus on real-world application.

The first lesson was an introduction to dynamic systems which was embodied by the investigation and design of an automotive cruise controller. The lesson explored some of the primary objectives in control system design for autonomous systems:

• Stability

• Tracking

• Robustness

• Disturbance Rejection

• Optimality 

Project Euler

Portrait of Leonhard Euler (1707-1783)

Fun and challenging problems

I've been working my way through these Project Euler exercises since September 2012. From what I gather, these problems originally spawned off of a thread on mathschallenge.net in 2001 and moved to a seperate domain in 2006. The gist of these tasks is that a problem is presented that requires the derivation of some mathematical truth (such as the number of twin primes below some value or the last 10 digits of !1000). All of the tasks are meant to be performed by algorithms implemented on a modern computer in under one minute.

For instance, the latest problem that I have solved is number fifty. It asks for the prime number less than 1,000,000 which is the sum of the largest chain of consecutive primes.

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Problem 50

The prime 41, can be written as the sum of six consecutive primes:

41 = 2 + 3 + 5 + 7 + 11 + 13

This is the longest sum of consecutive primes that adds to a prime below one-hundred.

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.

Which prime, below one-million, can be written as the sum of the most consecutive primes?

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