Robotic Systems · Lecture 1

Models, states, and simulation experiments

Simeon Nedelchev

Full notes, practice, and references

Modeling boundary

Bodies, joints, forces, and measurements define the model.

Neglected effects belong in the assumptions.

State-space form

p˙=v,v˙=(u−bv−kp)/m\dot p=v,\qquad \dot v=(u-bv-kp)/m

The initial state and input history define the experiment.

Continuous and discrete systems

x˙=f(x,u)\dot x=f(x,u)
xk+1=FΔt(xk,uk)x_{k+1}=F_{\Delta t}(x_k,u_k)

Numerical updates have their own stability properties.

Dimensional check

m=2m=2, b=0.4b=0.4, k=8k=8, p=0.1p=0.1, v=−0.2v=-0.2, u=1u=1

Net force: 0.28 N

Acceleration: 0.14 m/s2^2

Verification and validation

Verification compares code with the chosen equations.

Validation compares predictions with physical evidence.

First experiment

Compare oscillator trajectories and energy.

A plausible animation cannot quantify numerical error.

Companion: CMU 16-715

Reading

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