1. Toward Autonomous Free- Climbing Robots Tim Bretl, Jean-Claude Latombe, and Stephen Rock May 2003 Presented by Randall Schuh

2. Motivation Non-specific autonomous rock-climbing robots could benefit several applications: Non-specific autonomous rock-climbing robots could benefit several applications:  Search-and-rescue mountainous terrain mountainous terrain broken urban environments broken urban environments  Exploration Sub-surface environments Sub-surface environments Planetary, especially on Mars Planetary, especially on Mars  New modes of motion for humanoid robots

3. Previous Work Climbing robots Climbing robots  exploit unnatural surface properties, e.g.: Peg into hole Peg into hole Suction pads (grass, steel surfaces) Suction pads (grass, steel surfaces) Track and legged robots Track and legged robots  ascend slopes up to 50 degrees  Few works consider choosing foot placement Grasping Grasping  usually emphasizes force-closure

4. Planar Model 3 identical limbs, 8 dof 3 identical limbs, 8 dof Ignores self-collision Ignores self-collision Coulomb friction Coulomb friction Motion occurs in 4-D subspace of C-space Motion occurs in 4-D subspace of C-space

5. Planar Motion Planning One-Step-Climbing Problem One-Step-Climbing Problem Geometrical insight allows solution path planning in 2 dimensions (pelvis position) Geometrical insight allows solution path planning in 2 dimensions (pelvis position) Uses PRM techniques Uses PRM techniques  Instead of collisions, the planner tests for equilibrium Uses dynamic testing algorithm (Class 3) Uses dynamic testing algorithm (Class 3) Uses a simple smoothing technique Uses a simple smoothing technique

6. Coulomb friction cones F friction ≤ μ N F friction ≤ μ F cos θ Stable if: F sin θ < μ F cos θ Friction cone: tan φ ≤ μ φ ≤ tan –1 μ

7. E Dependent only on x Equilibrium Region += – + = 0 Dependent on x

8. Geometrical Analysis Free space of the free limb consists of 2 connected subsets Free space of the free limb consists of 2 connected subsets

9. Planar Example Planar Example1

10. Planar Example Planar Example2

11. Planar Example Planar Example3

12. Planar Example Planar Example4

13. Planar Example Planar Example5

14. Planar Example Planar Example6

15. Planar Example Planar Example7

16. Planar Example Planar Example8

17. Climbing up mountain (first 15 sec)

18. 3D Model – LEMUR 1 II Each limb has a spherical shoulder and a revolute knee (4 dof); limbs are 30 cm long Each limb has a spherical shoulder and a revolute knee (4 dof); limbs are 30 cm long Joints are mechanically limited Joints are mechanically limited Robot can push or pull from each endpoint Robot can push or pull from each endpoint Motion occurs in 13-D subspace of C-space Motion occurs in 13-D subspace of C-space 1 Limbed Excursion Mobile Utility Robot – developed by JPL

19. 3D Motion Planning Still tests for equilibrium Still tests for equilibrium Uses PQP to test for self-collisions and collisions with environment Uses PQP to test for self-collisions and collisions with environment Uses a more sophisticated technique for sampling closed kinematic chains Uses a more sophisticated technique for sampling closed kinematic chains Not yet reduced dimension of problem with geometrical analysis. Not yet reduced dimension of problem with geometrical analysis.

20. 3D Example 3D Example1

21. 3D Example 3D Example2

22. 3D Example 3D Example3

23. 3D Example 3D Example4

24. 3D Example 3D Example5

25. 3D Example 3D Example6

26. 3D Example 3D Example7

27. 3D Example 3D Example8

28. 3D Example 3D Example9

29. Future Work Apply geometric insight to be able to capture narrow passages more efficiently Apply geometric insight to be able to capture narrow passages more efficiently Add torque constraints Add torque constraints Implement the algorithm on hardware, which will require Implement the algorithm on hardware, which will require  Visual and tactile sensing of grasps  Tactile feedback (slippage detection)  Multi-step planning based on incomplete information

30. Paper Comparison Common Features: Planning from a discrete series of grasps Planning from a discrete series of grasps Applying PRM techniques Applying PRM techniques Differences: Application to real vs. digital environment Application to real vs. digital environment Kinematic & equilibrium vs. kinematic constraints Kinematic & equilibrium vs. kinematic constraints