Fast Solution of Optimal Control Problems with L1 Cost Simon Le - - PowerPoint PPT Presentation

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fast solution of optimal control problems with l1 cost
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Fast Solution of Optimal Control Problems with L1 Cost Simon Le - - PowerPoint PPT Presentation

Feb 05, 2023 402 likes •744 views

Fast Solution of Optimal Control Problems with L1 Cost Simon Le Cleac'h and Zac Manchester Robotjc Exploratjon Lab Motivation Why L1-norm cost? Minimum-fuel, minimum-tjme Bang-ofg-bang control Contribution Solver: Fast

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Fast Solution of Optimal Control Problems with L1 Cost

Simon Le Cleac'h and Zac Manchester Robotjc Exploratjon Lab

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Motivation

Why L1-norm cost?

  • Minimum-fuel, minimum-tjme
  • Bang-ofg-bang control
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Contribution

Solver:

  • Fast
  • Low-memory footprint
  • Nonlinear dynamics
  • State and control constraints

Enables:

  • In fmight sofuware implementatjon
  • Embedded trajectory optjmizatjon
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Trajectory Optimization

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Trajectory Optimization

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Trajectory Optimization

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Trajectory Optimization

Nonsmooth cost functjon

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ADMM

Problem form: f, g are convex Augmented Lagrangian:

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ADMM

Augmented Lagrangian: 3 optjmizatjon steps:

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ADMM

Augmented Lagrangian: 3 optjmizatjon steps: Minimizatjon Minimizatjon Dual ascent

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Trajectory Optimization

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Method

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Method

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Method

Augmented Lagrangian:

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Method

Augmented Lagrangian: Cost

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Method

Augmented Lagrangian: Penalty

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Method

Augmented Lagrangian: Alternatjng Directjon Method of Multjpliers (ADMM)

1. 2. 3.

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Method

Alternatjng Directjon Method of Multjpliers (ADMM)

1.

Optjmal control step <=> LQR, closed-form solutjon

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Method

Alternatjng Directjon Method of Multjpliers (ADMM)

2.

Sofu-threhold step <=> closed-form solutjon

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Method

Alternatjng Directjon Method of Multjpliers (ADMM)

3.

Dual ascent step <=> closed-form solutjon

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Method

Alternatjng Directjon Method of Multjpliers (ADMM)

1. 2. 3.

Optjmal control step <=> LQR, closed-form solutjon Sofu-threhold step <=> closed-form solutjon Dual ascent step <=> closed-form solutjon

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Application

Spacecrafu rendezvous problem

  • Minimum-fuel
  • Small satellite
  • Pathfjnder for Autonomous Navigatjon (PAN)
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Application

Spacecrafu rendezvous problem

  • Nonlinear dynamics (drag etc.)
  • Unbounded control
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Results

  • Nonlinear dynamics (drag etc.)
  • Unbounded control
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Results

  • Nonlinear dynamics (drag etc.)
  • Unbounded control
  • Impulse control
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Results

  • Nonlinear dynamics (drag etc.)
  • Bounded control
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Results

  • Nonlinear dynamics (drag etc.)
  • Bounded control
  • Bang-ofg-bang
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Results

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Spacecraft Rendezvous

L1 cost: Bang-ofg-bang

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Spacecraft Rendezvous

Quadratjc cost: smooth control

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Conclusions

Solver: for L1 control cost problem.

  • Fast and low-memory footprint
  • Broad range of applicatjons in astrodynamics

Enables:

  • In fmight sofuware implementatjon
  • Small satellite rendezvous maneuver
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Questions?

simonlc@stanford.edu rexlab.stanford.edu

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Algorithm