16711: Kinematics, Dynamics, & Control
By your TA, Matthew McNaughton
Comments on assignments
Sample code, lecture notes, and readings
 Use the Lagrange method
with the symbolic math features of Matlab to derive dynamics.
Here are a few variations on the theme. For your own
implementations, you can copy the last one.

ldemo.m  This uses a somewhat verbose
way of handling the derivatives.
 ldemo2.m  Clever use of the chain
rule to take the derivatives more compactly. Thanks to
Ben Stephens for pointing this out.
 lagrangian_segway.m 
Final generic implementation.
 udwadiademo.m  Use Uwadia
and Kalaba's method to implement the dynamics.
 Papers on Udwadia and
Kalaba's method of deriving equations of motion for
constrained systems:
Paper 1 (early),
Paper 2,
Paper 3 (handles with nonideal
constraints)
 Uwadia and Kalaba's excellent book on analytical dynamics. Probably the best book ever written on the topic, and easy to understand.
 Wednesday Feb 14:
 Use Matlab's fmincon() for a rough demo
of nonlinear optimal control by direct transcription with a
point mass on a line
(linear constraint version).
 Solution for the point mass example,
and the results of running
the solution run without feedback through simulation.
 Another fmincon() demo, with
some nonlinear constraints. Solution, and result of simulation.
 Some examples of a fullcycle walk for a planar 5link
biped derived with dircol: Example 1,
Example 2,
Example 3,
Example 4.
 ke1.mAnother quick demo of how to
use symbolic math in Matlab to avoid errors in deriving
equations.
 Monday April 2:
 symdyn.m and mycumsum.m, demonstration of using as little effort as possible to derive kinematics and dynamics of an arm.
Lab Instructions
Assignments
Assignment 7