1. 9/14/2015CS225B Kurt Konolige Locomotion of Wheeled Robots 3 wheels are sufficient and guarantee stability Differential drive (TurtleBot) Car drive (Ackerman steering) Synchronous drive (B21) Omni-drive: Mecanum wheels, PR2 [Many slides come from www.probabilistic-robotics.org and Steffen Gutmann]www.probabilistic-robotics.org x y x

2. 9/14/2015CS225B Kurt Konolige Instantaneous Center of Curvature ICC For rolling motion to occur, each wheel has to move along its y-axis

3. 9/14/2015CS225B Kurt Konolige Differential Drive Two driven wheels One passive (castor) wheel TurtleBot, Erratic, Pioneers …

4. 9/14/2015CS225B Kurt Konolige Differential Drive Kinematics R ICC  (x,y) y l/2  x v l v r

5. 9/14/2015CS225B Kurt Konolige Differential Drive: Forward Kinematics ICC R P(t) P(t+  t) For changing velocities, integrate over small dt. Compare to PR (5.9), p 127

6. 9/14/2015CS225B Kurt Konolige Odometry Integrating relative position information ➔ Need to deal with incremental errors

7. 9/14/2015CS225B Kurt Konolige One driven wheel Two passive wheels Similar to front-driven cars Ackerman Drive

8. 9/14/2015CS225B Kurt Konolige Synchronous Drive All wheels are actuated synchronously by one motor ➔ Defines robot speed All wheels are steered synchronously by 2 nd motor ➔ Sets robot's heading Orientation of robot frame is always the same ➔ Not possible to control orientation of robot frame

9. 9/14/2015CS225B Kurt Konolige Active Casters Rollin’ Justin (DLR) PR2 (Willow Garage)

10. 9/14/2015CS225B Kurt Konolige Mecanum Wheels forward y x v1v1 v2v2 v0v0 v3v3 left v1v1 v2v2 v0v0 v3v3 v2v2 turn v1v1 v0v0 v3v3 Kuka Omni-Drive

11. 9/14/2015CS225B Kurt Konolige 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]

12. 9/14/2015CS225B Kurt Konolige Robot Motion Planning

13. 9/14/2015CS225B Kurt Konolige 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.) Goal of Motion Planning

14. 9/14/2015CS225B Kurt Konolige 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

15. 9/14/2015CS225B Kurt Konolige 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? Borenstein VFH

16. 9/14/2015CS225B Kurt Konolige Vector Field Histogram [Borenstein and Koren] Potential field method Workspace obstacles Obstacle probabilities from Cartesian histogram Polar histogram of good directions

17. 9/14/2015CS225B Kurt Konolige Vector Field Histogram [Borenstein and Koren] Potential field method Workspace obstacles Obstacle probabilities from Cartesian histogram Polar histogram of good directions

18. 9/14/2015CS225B Kurt Konolige Vector Field Histogram [Borenstein and Koren] Issues Width of robot, safety margin Cost function for handling tradeoffs: safety, progress, etc. Trajectory and dynamics Oscillation

19. 9/14/2015CS225B Kurt Konolige Tool: Configuration Space Articulated object (4DoF) C-Space (2D cut)

20. 9/14/2015CS225B Kurt Konolige Workspace W Configuration space C x y Configuration = coordinates (x,y) of robot’s center Configuration space C = {(x,y)} Free space F = subset of collision-free configurations path Configuration Space of a Disc

21. 9/14/2015CS225B Kurt Konolige Workspace

22. 9/14/2015CS225B Kurt Konolige Configuration Space

23. 9/14/2015CS225B Kurt Konolige Discretization

24. 9/14/2015CS225B Kurt Konolige 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?

25. 9/14/2015CS225B Kurt Konolige Dynamic Window Method [Fox et al.] Admissible trajectories: braking before collision

26. 9/14/2015CS225B Kurt Konolige Dynamic Window Method [Fox et al.] Heading: achieve the goal Distance: avoid obstacles Velocity: do it fast

27. 9/14/2015CS225B Kurt Konolige Dynamic Window Method [Fox et al.] DWA Issues Computation Evaluation function tuning: small openings Longer paths / lower acceleration Oscillation