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

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 • Low-memory footprint • Nonlinear dynamics • State and control constraints Enables: • In fmight sofuware implementatjon • Embedded trajectory optjmizatjon

Trajectory Optimization

Trajectory Optimization

Trajectory Optimization

Trajectory Optimization Nonsmooth cost functjon

ADMM Problem form: f, g are convex Augmented Lagrangian:

ADMM Augmented Lagrangian: 3 optjmizatjon steps:

ADMM Augmented Lagrangian: 3 optjmizatjon steps: Minimizatjon Minimizatjon Dual ascent

Trajectory Optimization

Method

Method

Method Augmented Lagrangian:

Method Augmented Lagrangian: Cost

Method Augmented Lagrangian: Penalty

Method Augmented Lagrangian: Alternatjng Directjon Method of Multjpliers (ADMM) 1. 2. 3.

Method Alternatjng Directjon Method of Multjpliers (ADMM) 1. Optjmal control step <=> LQR, closed-form solutjon

Method Alternatjng Directjon Method of Multjpliers (ADMM) 2. Sofu-threhold step <=> closed-form solutjon

Method Alternatjng Directjon Method of Multjpliers (ADMM) 3. Dual ascent step <=> closed-form solutjon

Method Alternatjng Directjon Method of Multjpliers (ADMM) 1. Optjmal control step <=> LQR, closed-form solutjon 2. Sofu-threhold step <=> closed-form solutjon 3. Dual ascent step <=> closed-form solutjon

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

Application Spacecrafu rendezvous problem • Nonlinear dynamics (drag etc.) • Unbounded control

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

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

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

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

Results

Spacecraft Rendezvous L1 cost: Bang-ofg-bang

Spacecraft Rendezvous Quadratjc cost: smooth control

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

Questions? simonlc@stanford.edu rexlab.stanford.edu

Algorithm