PYTHON · NUMPY

Which sense is the best buy?

Attitude channels cost about a third of what the cart-position channels cost per read. Per unit of certified region bought, attitude is:

Price every sensor set in joules per unit of region bought, and identify which vector is cheaper.

01Challenge

You have four channels and a budget. Cart position and velocity cost 0.0090 and 0.0060 joules a read; pole angle and rate cost 0.0030 and 0.0025. Before you run it: which pair buys more region per joule?

Predict firstAttitude channels cost about a third of what the cart-position channels cost per read. Per unit of certified region bought, attitude is:

02Model

Sensors serve two different jobs. Attitude tells the machine whether it is about to leave its box, which is the protective job. Cart position tells it whether it is doing the task, which is the generative one. Those are separate circuits in an animal, running at different rates with different authority, and they turn out to have very different prices per unit of viability bought.

03Guided practice

Run the sweep. Read the joules-per-region column. Then compare the attitude pair against the position pair directly and note the ratio.

04Feedback

PASS WHEN You priced four channels and found the cheap pair is not the one most stacks spend on first.

If your run fails, check:

Attitude alone plus its rate buys region at about 17.6 J per point. Cart position plus its rate buys region at about 279 J per point, roughly sixteen times dearer, and it costs more in absolute joules as well.
Protection is the better buy on both counts. That is what makes an always-on protective layer affordable: it is low bandwidth AND cheap per unit of viability, so it can run continuously while perception is duty-cycled.
Look at the task-error column separately from region. The full suite is the only row that moves task error substantially, from 0.920 to 0.501. Region and task are different denominators and a sensor can be a bargain on one and poor on the other.

05Retrieve & space

Which sensor pair buys certified region more cheaply, and by roughly what factor?
Why can an always-on protective layer be affordable when always-on perception is not?
A sensor improves task error but not region. Which denominator should price it?

06Mastery & project

Price a proposed sensor suite in joules per unit of the region it buys, and say which channels are protective and which are generative.

Take a robot's published sensor list. Sort it into protective and generative, and estimate which half carries the continuous duty cycle.