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

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

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

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Need for Sensor Feedback