LaValle Planning Algorithms, ch 15

Basically deals with control theory

  • (712) Stability characterizes how integral curves of a vector field behave around a goal point
  • Controlability indicates whether a an action traj exists that arrives at a a specified goal
  • In ctrl thry, dynamic programming is in terms of a partial differential eq in terms of optimal cost-to-go
  • (715) If a func is linear the stability question wrt the origin can be answered by checking the eigenvector
    • In other situations this test doesn’t work, and other tests have to be used that aren’t always conclusive
  • (717) “classical” ctrl thry is interested in ctrl in absence of obstacles
  • (718) Small-time locally controllable for control in domains w/obstacles
    • Do plan-and-transform
  • (720) Continuous time dynamic programming (HJB eq)
  • (722) In general, this HJB eq is difficult to solve analytically
  • (734) A holonomic system is completely integrable, nonholonomic isn’t
    • Complete integrability means entire sys can be represented w/o derivatives
  • (740) How to detect complete integrability
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