MultiLimb Robots on Irregular Terrain NASAJPLs LEMUR Robot
Multi-Limb Robots on Irregular Terrain
NASA/JPL’s LEMUR Robot
Only friction and internal degrees of freedom are used to achieve equilibrium F r e e C l i m b i n g
Other Climbing Robots Cutkosky, Stanford, 2004 NINJA II Hirose et al, 1991 Yim, PARC, 2002
Free climbing is a problem -solving activity § Each step is unique § Where to make contact? § Which body posture to take? § Which forces to exert? § Decisions at one step may affect the ability to perform future steps
ATHLETE (NASA/JPL)
HRP-2 (AIST, Japan)
Motion-Before-Stances Approach Suitable when the terrain is mostly even and horizontal Stances-Before-Motion Approach
Overview goal § Given a terrain model and a goal location § Compute a motion path to reach the goal Sensing Planning waypoint 1 candidate contacts Robot non-gaited motion path 9
Overview § Given a terrain model and a goal location § Compute a motion path to reach the goal Planning Sensing goal waypoint 2 waypoint 1 Execution 10
Key Concept: Stance § Set of fixed robotenvironment contacts § Fs: space of feasible robot configurations at stance s 3 -stance of LEMUR 1. 2. 3. 4. Contacts Quasi-static equilibrium No (self-)collision Torques within bounds Feasible motion at 4 -stance
Inverse Kinematics Problem
Forward Kinematics q 2 d 1 q 1 (x, y) x = d 1 cos q 1 + d 2 cos(q 1+q 2) y = d 1 sin q 1 + d 2 sin(q 1+q 2)
Inverse Kinematics q 2 d 1 (x, y) q 2 = cos-1 q 1 = x 2 + y 2 – d 12 – d 22 2 d 1 d 2 -x(d 2 sinq 2) + y(d 1 + d 2 cosq 2) y(d 2 sinq 2) + x(d 1 + d 2 cosq 2)
Inverse Kinematics d 2 d 1 (x, y) q 2 = cos-1 q 1 = Two solutions x 2 + y 2 – d 12 – d 22 2 d 1 d 2 -x(d 2 sinq 2) + y(d 1 + d 2 cosq 2) y(d 2 sinq 2) + x(d 1 + d 2 cosq 2)
More Complicated Example q 2 d 2 (x, y) d 3 q 3 d 1 q 1 § Redundant linkage § Infinite number of solutions § Self-motion space
More Complicated Example q 2 d 2 (x, y) d 3 q 3 d 1 q 1
More Complicated Example q 2 d 2 (x, y) d 3 q 3 d 1 q 1
Challenge § High-dimensional configuration space C (11 LEMUR, 42 for ATHLETE, 36 for HRP-2, 16 for Stanford robot) § Many possible contacts, hence many stances C Fs
Equilibrium Constraint CM
backstep highstep lieback
Equilibrium Test in 3 D § Assuming infinite torque limits: § Center of mass above convex support polygon
Equilibrium Test § Assuming infinite torque limits: § Center of mass above convex support polygon CM
Equilibrium Test § Assuming infinite torque limits: § Center of mass above convex support polygon
Transition Configuration Zero force
Lazy Search
Lazy Search
Lazy Search
Lazy Search
Lazy Search
Lazy Search
Lazy Search
Configuration Sampling 1. Sample position/orientation of the chassis at random in restricted area 2. Solve IK for each limb making contact 3. Sample DOFs in free limb at random 4. Test equilibrium constraint 34
35
Need for Sensor Feedback
- Slides: 36