1 / 13

Optimization to solve Inverted Pendulum problem

Optimization to solve Inverted Pendulum problem. Zhili Chen. Problem Description. Given a initial Phi>0, Apply F on cart to regain balance (Phi=0). Problem Description. Performance Evaluation Minimum time period before balance, or Minimum cart movement, or Minimum energy used by force F.

caron
Télécharger la présentation

Optimization to solve Inverted Pendulum problem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Optimization to solve Inverted Pendulum problem Zhili Chen

  2. Problem Description • Given a initial Phi>0, Apply F on cart to regain balance (Phi=0)

  3. Problem Description • Performance Evaluation • Minimum time period before balance, or • Minimum cart movement, or • Minimum energy used by force F

  4. Physical Equations Approximate and linearize =>

  5. Solution 1 • Optimization-Based Interactive Motion Synthesis, SUMIT JAIN, YUTING YE, and C. KAREN LIU • Use current joint configuration, get configuration of next time step.

  6. Solution 1 • Variables • Constraints • Where • Upper and lower bounds for

  7. Solution 1 • Objective function • Want to decrease angle using smaller car movement • Initial value • Solution of the last time step is the initial value for current time step • Use ‘fmincon’ in MATLAB • Algorithm: active set (small scale)

  8. Solution 1 • Result • Not good • Constraints are too lax or too strict? • Step by step optimization not suitable for this problem? (optimal solution of whole process does not imply optimal solution for every time step)

  9. Solution 2 • Spacetime Constraints, Andrew Witkin,MichaelKass • Regard the process as a whole (from initial state to balance state)

  10. Solution 2 • Optimization variable • n = T/h (h, length of timestep) • Constraints • => Ay=b • Upper and lower bounds for

  11. Solution 2 • Objective function • Initial value (or boundary condition) • Use ‘fmincon’ in MATLAB • Algorithm: interior-point (large scale, sparse matrix, both inequality and equality)

  12. Solution 2 • Result • Close to result from classic control theory

  13. Thanks

More Related