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Put All Together

1. Abstractions and Approximations

We have made some assumptions so far

  • Dynamics, $\dot x=u$, NOT even close to being reasonable!
  • Sensors, we can measure distance and angle

Recall teh unicycle model, we want to our system behave like $\dot x=u $

How? A Layered Architercture

  • Navigation system can be decoupled along 3 levels of abstraction:
  • Strategic Level: Where should the goal points be (Not in this course)
  • Dijkstra, A*, D*, RRT…
  • Operational Level: which direction to move (go-to-goal and avoid-obstacles)
  • Tactical Level: How to make the robot move in those direction (control design)

2. Transforming the Unicycle

The unicycle model
$$
\begin{array}{l}
\dot{x}=v \cos \phi \
\dot{y}=v \sin \phi \
\dot{\phi}=\omega
\end{array}
$$
What if we ignored the orientation and picked a different point on the robot as the point we care about

And now the $u_1,u_2$ would directly related to $v$ and $w$

Before: Use a Planner and Tracker

After: Use a Planner and Transformer and DO NOT need a PID controller for lower control


Can this method applied to other kind of robots? YES

Car-Like robots, Segway robot, Fixed-Wing aircraft, Underwater glider

Common: all the robots involves POSE:

  • Position
  • Heading

Almost everything with pose is almost a unicycle

3. Further

Nonlinear system, Optimal Control minimize some specific cost

Machine Learning. good for optimal control

Perception and Mapping

High-Level AI

4. Conclusion

Punchline

  1. We need a model, it should be rich enough to be relevant yet simple enough to be useful
  2. Feedback control should be used to guarantee stability, tracking and robustness
  3. Architectures: plan for simple systems, execute on the real system