Modeling & Control of a Longboard-Riding Robot Matt Keeter - PowerPoint PPT Presentation

Modeling & Control of a Longboard-Riding Robot Matt Keeter mkeeter@mit.edu 6.832 Final Project Spring 2012

Inspiration

System Model

Simplified Model

State Variables

Control Inputs

System Parameters

System Summary • q = [ x , y , α ] ′

System Summary • q = [ x , y , α ] ′ • u = [ F , τ ] ′

System Summary • q = [ x , y , α ] ′ • u = [ F , τ ] ′ • Gliding and pushing modes • y toe ≤ 0 → pushing • y toe > 0 → gliding

Dynamics • Wrote tools to automatically solve dynamics

Dynamics • Wrote tools to automatically solve dynamics • Written in Python using Sage

Dynamics • Wrote tools to automatically solve dynamics • Written in Python using Sage • Solves for: • Second derivatives ¨ q • Co-located PFL equations

Dynamics • Wrote tools to automatically solve dynamics • Written in Python using Sage • Solves for: • Second derivatives ¨ q • Co-located PFL equations • Exports as MATLAB scripts

Feedback Linearization • Solve dynamics equations for ¨ x , F , τ

Feedback Linearization • Solve dynamics equations for ¨ x , F , τ • Solutions are in terms of q , ˙ q , ¨ y , ¨ α (as well as constants)

Feedback Linearization • Solve dynamics equations for ¨ x , F , τ • Solutions are in terms of q , ˙ q , ¨ y , ¨ α (as well as constants) • Plug in ¨ y , ¨ α for feedback linearization • ¨ y = ¨ y desired • ¨ α = ¨ α desired

Feedback Linearization • Solve dynamics equations for ¨ x , F , τ • Solutions are in terms of q , ˙ q , ¨ y , ¨ α (as well as constants) • Plug in ¨ y , ¨ α for feedback linearization • ¨ y = ¨ y desired • ¨ α = ¨ α desired • Double integrator control

Controller Strategy High-level strategy breaks motion into stages Swing leg forward Switch to gliding state Stand up Lower self Switch to pushing state Push off

Controller Strategy Swing leg forward Switch to gliding state Stand up Lower self Switch to pushing state Push off

Controller Strategy Swing leg forward Switch to gliding state Stand up Lower self Switch to pushing state Push off

Controller Strategy Swing leg forward Switch to gliding state Stand up Lower self Switch to pushing state Push off

Controller Strategy Swing leg forward Switch to gliding state Stand up Lower self Switch to pushing state Push off

Controller Strategy Swing leg forward Switch to gliding state Stand up Lower self Switch to pushing state Push off

Demo

Controller Parameters Controller is parameterized by three terms: Angle of collision α hit Angle ending push α stand ¨ Swinging acceleration α swing

Controller Parameters Angle of collision α hit Angle ending push α stand ¨ Swinging acceleration α swing

Controller Parameters Angle of collision α hit Angle ending push α stand ¨ Swinging acceleration α swing

Controller Parameters Angle of collision α hit Angle ending push α stand ¨ Swinging acceleration α swing

Stochastic Gradient Descent Optimized for distance travelled in fixed time

Stochastic Gradient Descent Optimized for distance travelled in fixed time 50 48 46 Distance travelled 44 42 40 38 36 0 20 40 60 80 100 Iteration

Optimized Demo

Optimized Demo 20% improvement!

Summary • Developed simplified system model • Wrote dynamics-solving tools • Designed high-level controller behavior • Used gradient descent to optimize parameters

Questions?