1 toward autonomous free-climbing robots tim bretl jean-claude latombe stephen rock cs 326...
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Toward AutonomousFree-Climbing Robots
Tim BretlJean-Claude Latombe
Stephen Rock
CS 326 Presentation Winter 2004Christopher Allocco
Special thanks to Eric Baumgartner, Brett Kennedy, and Hrand Aghazarian at the Planetary Robotics Lab, NASA-
JPL
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GoalDevelop integrated control, planning, and sensing capabilities to enable a wide class of multi-limbed robots to climb steep natural terrain.
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Previous Multi-Limbed Climbing
RobotsEach exploits a specific
surface property
NINJA IIHirose et al, 1991
Neubauer, 1994
Yim, PARC, 2002
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Non-Gaited MotionGaited Non-Gaited
Non-Gaited Motion implies one-step approach
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One-Step-Climbing Problem
Given a start configuration of the robot and a hold,compute a path connecting the start configurationto a configuration that places the foot of the free
limbat the hold such that the robot remains in
equilibrium along the entire path.
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Hold
A hold is defined by a point (xi,yi) and a direction vi .
The reaction force that the hold may exert on the foot spans a cone Fci—the friction cone at i—of half angle less than or equal to pi/2.
Hold
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EquilibriumFor 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.
ˆ f i1ˆ f i2
ˆ f k1ˆ f k2
ri ˆ f i1 ri ˆ f i2 rk ˆ f k1 rk ˆ f k2
0 0
0 0
mg 0
f i1
f i2
fk1
fk 2
xcm
ycm
0
mg
0
Equilibrium
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Example System
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Configuration SpaceConfiguration Space
For each combination of knee bends:– Position (xP,yP) of pelvis
– Joint angles (1,2) of free limb
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Feasible SpaceFeasible Space
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2
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1. Simple test for the feasibility of (xp,yp)
xmin/free x p L
xmax/free x p L
where…
x*/free 3x* 2xCM / chain
Feasible SpaceFeasible Space
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1. Simple test for the feasibility of (xp,yp)
2. Feasible (1,2) varying with (xp,yp), in one half of f
1 cos 1 ˜ x
2 0
where…
˜ x 0.5 * max xmin, free, L min xmax, free ,L
f
Feasible SpaceFeasible Space
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1. Simple test for the feasibility of (xp,yp)
2. Feasible (1,2), varying with (xp,yp), in one half of f
3. Switching between halves of f
Feasible SpaceFeasible Space
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Motion PlanningMotion 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
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Algorithm 1 One-Step-Climbing1. 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 satisfiesthe 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 linearpath 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
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1. Achieve 2=02. Move with 2=03. Switch between
halves of f
4. Move with 2=05. Move to goal
Refined Algorithm
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backstep highstep lieback
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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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Current WorkCurrent Work
Terrain sensing and hold detection Force control and slippage sensing Uncertainty (hold location, limb
positioning) Motion optimization Extension of feasible space analysis
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