1 Toward Autonomous Free-Climbing Robots Tim Bretl Jean-Claude Latombe Stephen Rock CS 326 Presentation Winter 2004 Christopher Allocco Special thanks to Eric Baumgartner, Brett Kennedy, and Hrand Aghazarian at the Planetary Robotics Lab, NASA-JPL

2 Goal Develop integrated control, planning, and sensing capabilities to enable a wide class of multi-limbed robots to climb steep natural terrain.

3 Previous Multi-Limbed Climbing Robots Each exploits a specific surface property NINJA II Hirose et al, 1991 Neubauer, 1994 Yim, PARC, 2002

4 Non-Gaited Motion Gaited Non-Gaited Non-Gaited Motion implies one-step approach

5 One-Step-Climbing Problem Given a start configuration of the robot and a hold, compute a path connecting the start configuration to a configuration that places the foot of the free limb at the hold such that the robot remains in equilibrium along the entire path.

6 Hold A hold is defined by a point (x i,y i ) and a direction v i. The reaction force that the hold may exert on the foot spans a cone Fc i —the friction cone at i—of half angle less than or equal to pi/2. Hold

7 Equilibrium For the robot to be in equilibrium, there must exist reaction forces at the supporting holds whose sum exactly compensates for the gravitational force on the robot. Equilibrium

8 Example System

9 Configuration Space For each combination of knee bends: –Position (x P,y P ) of pelvis –Joint angles (  1,  2 ) of free limb

10 Feasible Space 11 22   

11 1.Simple test for the feasibility of (x p,y p ) where… Feasible Space

12 1.Simple test for the feasibility of (x p,y p ) 2.Feasible (  1,  2 ) varying with (x p,y p ), in one half of  f where… ff Feasible Space

13 1.Simple test for the feasibility of (x p,y p ) 2.Feasible (  1,  2 ), varying with (x p,y p ), in one half of  f 3.Switching between halves of  f Feasible Space

14 Motion Planning Basic Approach (Probabilistic Roadmap) –Sample 4D configuration space –Check equilibrium condition –Check (self-)collision –Check torque limit Refined approach –Sample 2D pelvis space, lift to full 4D paths –Narrow passages are found in the 4D space –Does not scale directly to handle DOFs > 2 or constraints such as collision avoidance, joint limits

15 Algorithm 1 One-Step-Climbing 1. V {}, E {} 2. If qs satisfies the equilibrium test, then add qs to V, else exit with failure. 3. (Sample the goal region) Loop N1 times: (a) Sample uniformly at random a combination of knee bends of the contact chain and a pelvis position (xp, yp) within distance 2L from each of the three holds i, k, and g. (b) For each of the corresponding two configurations q where the foot of the free limb is at g, if q satisfies the equilibrium test, then add q to V. 4. If no vertex was added to V at Step 3, then exit with failure. 5. (Sample the feasible space) Loop N2 times: (a) Sample uniformly at random a configuration q 2 Fik. If it satisfies the equilibrium test, then add q to V. (b) For every configuration q0 previously in V that is closer to q than some predefined distance, if the linear path joining q and q0 satisfies the equilibrium test, then add this path to E. (c) If the connected component containing qs also contains a configuration sampled at Step 3 (goal configuration), then exit with a path. 6. Exit with failure. Basic Algorithm

16 1.Achieve  2 =0 2.Move with  2 =0 3.Switch between halves of  f 4.Move with  2 =0 5.Move to goal Refined Algorithm

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18 backstep highsteplieback

19 3-D Four-Limbed Robot 1. The joint limits are such that the inverse kinematics of each limb has at most one solution. Therefore, no decomposition of Cik according to knee bends is needed. 2. Sampling configurations of the contact chain is much harder than in the planar case. 3. The equilibrium test of Section 3.3 is modified since there are three supporting limbs. The friction cone becomes an n-gonal pyramid. 4. Check for both self-collision of the robot and collision with the environment.

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21 Current Work  Terrain sensing and hold detection  Force control and slippage sensing  Uncertainty (hold location, limb positioning)  Motion optimization  Extension of feasible space analysis