CS 452/652 Winter 2020 - Lecture 20

February 26, 2020 prev next

Train Modelling - Velocity

Kinematics: area of Mechanics (and thus Physics)
studies "motion of objects without reference to the forces which cause the motion."
model trains emulate real trains
we model the model trains

Goals / Objectives

location tracking
- collision avoidance
- accurate stopping
train efficiency: complete trips as fast as possible

Velocity

inherently an average: distance / time
discussed earlier in class

Experiments and Data

how many speed levels to investigate?
determine minimum speed (per segment?) to avoid getting stuck
stop from lower speed is more accurate
how much data can you feasibly collect?
document and justify decisions!

Measurement

recommendation: use tight polling loop (no kernel)
sensor → timestamp
measurement errors
- signal delivery, Märklin processing: constant (?)
  - constant errors cancel out when subtracting timestamps
- delivery to software: variable (polling loop)
  - statistical modelling (see below)
- processing in software: small (?)
  - ignore small errors

Uncertainty

timestamp uniformly distributed across duration of polling loop (~70ms)
- sample mean/variance are good estimates of real mean/variance
- sum of uniform distributions: triangle distribution
- but: measured data typically forms bimodal distribution
  - why? is that a problem?
but velocity (distance/time) is non-linear in time!
average of time is straightforwarded
average of velocity not so much
- consider simple example: 100m distance, 2 time samples 10s, 20s
- speed: 10m/s, 5m/s → average would be 7.5m/s
- compute average time first, then speed: 100m/15s = 6.66m/s

Dynamic/Continuous Calibration

verify validity of and/or update current estimates
long-term variability: track degradation? (or improvement)
real-world variations (wear and tear): difficult to model
need window of recent measurements
basic technique: Exponentially Weighted Moving Average (EWMA)
- c: current estimate; d: next data sample, a: weighting factor
- c := c * (1 - a) + d * a
- no need to store array of samples
- with appropriate choice of a, can use bitshift instead of division
- can use similar approximation for standard deviation

Earlier Documents

The material covered in class should be sufficient for train modelling. However, during the past years, various documents have described train modelling and calibration in the context of CS 452/652. The various versions are made available below with the caveat that they might or might not be helpful:

Stopping (2016)
The Kinematics of Train Calibration (2017)
The Kinematics of Train Calibration (2015)
Reverse Engineering Acceleration/Deceleration(2011)