2/26/2012 NASA/JPLs LEMUR Robot Multi-Limb Robots on Irregular - - PDF document

2/26/2012 1 Multi-Limb Robots on Irregular Terrain g

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

NINJA II Hirose et al, 1991 Yim, PARC, 2002 Cutkosky, Stanford, 2004

Free climbing is a problem-solving activity

Each step is unique Where to make contact? Which body posture to t k ? take? Which forces to exert? Decisions at one step may affect the ability to perform future steps ATHLETE (NASA/JPL)

2/26/2012 2 HRP-2 (AIST, Japan) Motion-Before-Stances Approach

Suitable when the terrain is mostly even and horizontal

Stances-Before-Motion Approach

Overview

goal goal

Given a terrain model and a goal location Compute a motion path to reach the goal

9

Sensing Planning Robot

candidate contacts

waypoint 1

non-gaited motion path

Overview

goal goal

Given a terrain model and a goal location Compute a motion path to reach the goal

waypoint 2

10

Sensing Planning Execution waypoint 1

Key Concept: Stance

Set of fixed robot- environment contacts Fσ: space of feasible robot configurations at stance σ

3-stance of LEMUR 3 stance of LEMUR Feasible motion at 4-stance

1. Contacts 2. Quasi-static equilibrium 3. No (self-)collision 4. Torques within bounds

Inverse Kinematics Problem

2/26/2012 3 Forward Kinematics

d d2

θ2

(x,y) d1

θ1

( ,y)

x = d1 cos θ1 + d2 cos(θ1+θ2) y = d1 sin θ1 + d2 sin(θ1+θ2)

Inverse Kinematics

d d2

θ2

(x,y) d1

θ1

( ,y)

θ2 = cos-1 x2 + y2 – d1

2 – d2 2

2d1d2

• x(d2sinθ2) + y(d1 + d2cosθ2)

y(d2sinθ2) + x(d1 + d2cosθ2) θ1 =

Inverse Kinematics

d d2 (x,y) d1 ( ,y)

θ2 = cos-1 x2 + y2 – d12 – d22 2d1d2

• x(d2sinθ2) + y(d1 + d2cosθ2)

y(d2sinθ2) + x(d1 + d2cosθ2) θ1 =

Two solutions

More Complicated Example

d d2

θ2

d3 (x,y)

θ

d1

θ1 θ3

Redundant linkage Infinite number of solutions Self-motion space

More Complicated Example

d d2

θ2

d3 (x,y)

θ

d1

θ3 θ1

More Complicated Example

d d2

θ2

d3 (x,y)

θ

d1

θ1 θ3

2/26/2012 4 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

Fσ

Equilibrium Constraint

CM

backstep highstep lieback

Equilibrium Test in 3D

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

2/26/2012 5 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

2/26/2012 6

Lazy Search Lazy Search Lazy Search

1. Sample position/orientation of the chassis at random in restricted area 2 S l IK f h li b

Configuration Sampling

34

• 2. Solve IK for each limb

making contact

• 3. Sample DOFs in free

limb at random

• 4. Test equilibrium

constraint

35

Need for Sensor Feedback