1. Locomotion of Wheeled Robots
3 wheels are sufficient and guarantee stability
Differential drive (Pioneer)
Car drive (Ackerman steering)
Synchronous drive (B21)
Omni-drive: Mecanum wheels, XR4000
[Many slides come from and Steffen Gutmann]
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2. Instantaneous Center of Curvature
ICC
For rolling motion to occur, each wheel has to move along its y-axis
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3. Differential Drive Two driven wheels One passive (castor) wheel
Obot, Erratic, Pioneers…
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4. Differential Drive Kinematics
ICC v l  R
(x,y) y v r
l/2
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5. Differential Drive: Forward Kinematics
ICC R
Compare to PR (5.9), p 127
P(t+t)
For changing velocities, integrate
over small dt.
P(t)
11/16/2018
CS225B Kurt Konolige

6. Need to deal with incremental errors
Odometry
Integrating relative position information
Need to deal with incremental errors
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7. Ackerman Drive One driven wheel Two passive wheels
Similar to front-driven cars
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8. Synchronous Drive All wheels are actuated synchronously by one motor
Defines robot speed
All wheels are steered synchronously by 2nd motor
Sets robot's heading
Orientation of robot frame is always the same
Not possible to control orientation of robot frame
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9. Mecanum Wheels y x forward v1 v2 v0 v3 v1 left v1 v2 v0 v3 v0 v2 v3
turn
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10. Motion planning is the ability for an agent to compute its own motions in order to achieve certain goals. All autonomous robots and digital actors should eventually have this ability　
[Latombe]
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11. Robot Motion Planning
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12. Goal of Motion Planning
Compute motion strategies, e.g.:
Geometric paths
Time-parameterized trajectories
Sequence of sensor-based motion commands
To achieve high-level goals, e.g.:
Go into a room without colliding with obstacles
Assemble/disassemble a car
Explore and build map of our department
Find an object (a person, the soccer ball, etc.)
11/16/2018
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13. Mobile Robot Navigation
Path planning and obstacle avoidance
No clear distinction, but usually:
Path-planning
low-frequency, time-intensive search method for global finding of a path to a goal
Examples: road maps, cell decomposition
Obstacle avoidance
fast, reactive method with local time and space horizon
Examples: Vector field histogram, dynamic window approach
“Gray area”
Fast methods for finding path to goal which can fail if environment contains “local minima”
Example: potential field method
11/16/2018
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14. Path Planning Global vs. Local Path Planning Configuration Space
Each configuration is a point in the space
Obstacles are regions of the space
A freespace path represents valid motion
Hard – PSPACE hard
Local Methods
Potential field
Fuzzy rules
Motor schemas
Vector Field Histogram
Local Methods => Global Method?
LAGR cul-de-sac
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15. Tool: Configuration Space
Articulated object (4DoF)
C-Space (2D cut)
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16. Configuration Space of a Disc
Workspace W
Configuration space C
path y x
Configuration = coordinates (x,y) of robot’s center
Configuration space C = {(x,y)}
Free space F = subset of collision-free configurations
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17. Workspace
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18. Configuration Space
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19. Discretization
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20. Dynamic Window Method [Fox et al.]
Evaluating constant curvature path in configuration space
Window of values based on one-step acceleration
When will the robot crash?
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21. Dynamic Window Method [Fox et al.]
Admissible trajectories: braking before collision
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22. Dynamic Window Method [Fox et al.]
Heading: achieve the goal
Distance: avoid obstacles
Velocity: do it fast
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23. Dynamic Window Method [Fox et al.]
DWA Issues
Computation
Evaluation function tuning: small openings
Longer paths / lower acceleration
Oscillation
LAGR Cul-de-sac
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24. Vector Field Histogram [Borenstein and Koren]
Potential field method
Workspace obstacles
Obstacle probabilities from Cartesian histogram
Polar histogram of good directions
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25. Vector Field Histogram [Borenstein and Koren]
Potential field method
Workspace obstacles
Obstacle probabilities from Cartesian histogram
Polar histogram of good directions
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26. Vector Field Histogram [Borenstein and Koren]
Issues
Width of robot, safety margin
Cost function for handling tradeoffs: safety, progress, etc.
Trajectory and dynamics
Oscillation
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