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Modeling & Control of a Longboard-Riding Robot Matt Keeter - - PowerPoint PPT Presentation
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 ,
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System Model
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Simplified Model
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State Variables
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Control Inputs
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System Parameters
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System Summary
- q = [x, y, α]′
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System Summary
- q = [x, y, α]′
- u = [F, τ]′
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System Summary
- q = [x, y, α]′
- u = [F, τ]′
- Gliding and pushing modes
- ytoe ≤ 0 → pushing
- ytoe > 0 → gliding
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Dynamics
- Wrote tools to automatically solve dynamics
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Dynamics
- Wrote tools to automatically solve dynamics
- Written in Python using Sage
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Dynamics
- Wrote tools to automatically solve dynamics
- Written in Python using Sage
- Solves for:
- Second derivatives ¨
q
- Co-located PFL equations
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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
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Feedback Linearization
- Solve dynamics equations for ¨
x, F, τ
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Feedback Linearization
- Solve dynamics equations for ¨
x, F, τ
- Solutions are in terms of q, ˙
q, ¨ y, ¨ α (as well as constants)
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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 = ¨ ydesired
- ¨
α = ¨ αdesired
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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 = ¨ ydesired
- ¨
α = ¨ αdesired
- Double integrator control
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Controller Strategy
High-level strategy breaks motion into stages
Push off Stand up Lower self
Switch to pushing state
Swing leg forward
Switch to gliding state
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Controller Strategy
Push off Stand up Lower self
Switch to pushing state
Swing leg forward
Switch to gliding state
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Controller Strategy
Push off Stand up Lower self
Switch to pushing state
Swing leg forward
Switch to gliding state
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Controller Strategy
Push off Stand up Lower self
Switch to pushing state
Swing leg forward
Switch to gliding state
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Controller Strategy
Push off Stand up Lower self
Switch to pushing state
Swing leg forward
Switch to gliding state
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Controller Strategy
Push off Stand up Lower self
Switch to pushing state
Swing leg forward
Switch to gliding state
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Demo
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Controller Parameters
Controller is parameterized by three terms: αhit Angle of collision αstand Angle ending push ¨ αswing Swinging acceleration
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Controller Parameters
αhit Angle of collision αstand Angle ending push ¨ αswing Swinging acceleration
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Controller Parameters
αhit Angle of collision αstand Angle ending push ¨ αswing Swinging acceleration
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Controller Parameters
αhit Angle of collision αstand Angle ending push ¨ αswing Swinging acceleration
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Stochastic Gradient Descent
Optimized for distance travelled in fixed time
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Stochastic Gradient Descent
Optimized for distance travelled in fixed time
20 40 60 80 100 36 38 40 42 44 46 48 50 Iteration Distance travelled
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Optimized Demo
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Optimized Demo
20% improvement!
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Summary
- Developed simplified system model
- Wrote dynamics-solving tools
- Designed high-level controller behavior
- Used gradient descent to optimize parameters
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