Class material vs. Lab material Lab 2, 3 vs. 4 ,5, 6 BeagleBoard / TI / Digilent GoPro
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Transcript of Class material vs. Lab material Lab 2, 3 vs. 4 ,5, 6 BeagleBoard / TI / Digilent GoPro
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• Class material vs. Lab material– Lab 2, 3 vs. 4 ,5, 6
• BeagleBoard / TI / Digilent• GoPro
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• Class material vs. Lab material– Lab 2, 3 vs. 4 ,5, 6
• BeagleBoard / TI / Digilent• GoPro
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There is no ideal drive configuration that simultaneously maximizes stability, maneuverability, and controllability.
For example, typically inverse correlation between controllability and maneuverability.
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Holonomicity • If the controllable degrees of freedom is equal to the total
degrees of freedom then the robot is said to be holonomic. – Holonomic constraints reduce the number of degrees of freedom
of the system
• If the controllable degrees of freedom are less than the total degrees of freedom it is non-holonomic.
• A robot is considered to be redundant if it has more controllable degrees of freedom than degrees of freedom in its task space.
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Why study holonomic constraints?
• How many independent motions can our turtlebot robot produce?– 2 at the most
• How many DOF in the task space does the robot need to control?– 3 DOF
• The difference implies that our system has holonomic constraints
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• Open loop control vs. Closed loop control
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• Open loop control vs. Closed loop control
• Recap– Control Architectures– Sensors & Vision– Control & Kinematics
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Core AI Problem• Mobile robot path planning: identifying a trajectory that,
when executed, will enable the robot to reach the goal location
• Representation– State (state space)– Actions (operators)– Initial and goal states
• Plan:– Sequence of actions/states that achieve desired goal state.
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Model of the world
Compute Path
Smooth it and satisfy differential constraints
Design a trajectory (velocity function) along the
path
Design a feedback
control law that tracks
the trajectory
Execute
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Fundamental Questions
• How is a plan represented?• How is a plan computed?• What does the plan achieve?• How do we evaluate a plan’s quality?
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1) World is known, goal is not
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2) Goal is known, world is not
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3) World is known, goal is known
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4) Finding shortest path?
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5) Finding shortest path with costs
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The World consists of...• Obstacles– Places where the robot can’t (shouldn’t) go
• Free Space– Unoccupied space within the world– Robots “might” be able to go here
• There may be unknown obstacles• The state may be unreachable
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Configuration Space (C-Space)
• Configuration Space: the space of all possible robot configurations.– Data structure that allows us to represent
occupied and free space in the environment
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Configuration Space
For a point robot moving in 2-D plane, C-space is
qgoal
qinit
CCfree
Cobs
2R
Point robot (no constraints)
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What if the robot is not a point?
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Expand obstacle(s)
Reduce robot
What if the robot is not a point?
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Example Workspace
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Example Workspace
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If we want to preserve the angular component…
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Rigid Body Planning
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Transfer in Reinforcement Learning via Shared Features: Konidaris, Scheidwasser, and Barto, 2002
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Back to Path Planning…
• Typical simplifying assumptions for indoor mobile robots:– 2 DOF for representation– robot is round, so that orientation doesn’t matter– robot is holonomic, can move in any direction
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Back to Path Planning…• Now lets assume that someone gave us a map. How do we
plan a path from to
How is a plan represented? How is a plan computed? What does the plan achieve? How do we evaluate a plan’s
quality?
Fundamental Questions
start
goal
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start
goal
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Occupancy Grid
start
goal
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Occupancy Grid, accounting for C-Space
start
goal
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Occupancy Grid, accounting for C-Space
start
goal
Slightly larger grid size can make the goal unreachable.Problem if grid is “too small”?
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