Previous Work

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Previous Work

• Hamilton-Jacobi-Bellman equation methods globally
  solve complex problems, but high computational
  cost
• DDP provides local feedback controllers and
  exhibit 2nd-order convergence.
• Iterative LQR iteratively linearizes dynamics and
  is more efficient than DDP
• DDP and ILQR cannot handle constraints.
• All methods assume deterministic dynamics

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Features of Iterative LQG

• Nonlinear Dynamics
• Non-quadratic cost function
• Control-dependent noise
• Constraints
• Un-biased nonadaptive linear filter
• Computes optimal feedback control law
• Computes optimal filter given control law

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Overview

• Nonlinear Dynamics
• Linearized about nominal trajectory
• Optimal Control Estimator

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Computing Cost-to-go

• Partially Observable
• Fully Observable

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Controller Design

• Portion of Cost-to-go depending on control
• Expectation over state trajectory
• In absense of control constraints

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Estimator Design

• Given a control law (u1, u2,,uN) and previous
  filter gains, (K1,K2,KN), compute new filter
  gains that minimize estimated error results in
  a minimized expected cost.

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Example ILQR (in MATLAB)

• 3-link Biped ankle, hip, shoulder
• 15Ns Impulse
• 0.01s timestep (Euler)
• N5025150
• Q diag(1e1,1e1,1e1,1e0,1e0,1e0)
• R diag(1e-2,1e-3,1e-3)
• Qf 1e3Q
• Rf 1e1R

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