Multi-Limb Robots on Irregular Terrain

NASA/JPL’s LEMUR Robot

Only friction and internal degrees of freedom are used to achieve equilibrium

Other Climbing Robots Cutkosky, Stanford, 2004 NINJA II Hirose et al, 1991 Free-climbing vs. aid-climbing Talk about applications 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 Given a terrain model and a goal location Compute a motion path to reach the goal Sensing Planning waypoint 1 candidate contacts non-gaited motion path Robot

Overview Given a terrain model and a goal location Compute a motion path to reach the goal waypoint 2 Sensing Planning Execution waypoint 1

Key Concept: Stance Set of fixed robot-environment contacts 3-stance of LEMUR Set of fixed robot-environment contacts Fs: space of feasible robot configurations at stance s Contacts Quasi-static equilibrium No (self-)collision Torques within bounds Feasible motion at 4-stance

Inverse Kinematics Problem

Forward Kinematics q2 q1 d2 (x,y) d1 x = d1 cos q1 + d2 cos(q1+q2) y = d1 sin q1 + d2 sin(q1+q2)

Inverse Kinematics q2 q1 d2 (x,y) d1 x2 + y2 – d12 – d22 q2 = cos-1 -x(d2sinq2) + y(d1 + d2cosq2) y(d2sinq2) + x(d1 + d2cosq2) q1 =

Inverse Kinematics Two solutions d2 (x,y) d1 x2 + y2 – d12 – d22 q2 = cos-1 x2 + y2 – d12 – d22 2d1d2 -x(d2sinq2) + y(d1 + d2cosq2) y(d2sinq2) + x(d1 + d2cosq2) q1 = Two solutions

More Complicated Example q2 (x,y) d3 d2 q3 d1 q1 Redundant linkage Infinite number of solutions Self-motion space

More Complicated Example q2 (x,y) d3 d2 q3 d1 q1

More Complicated Example q2 (x,y) d3 d2 q3 d1 q1

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 Spend some time here explaining your problem in a bit more technical detail. (Basically, take this from Section 3.1 of your ISRR paper, leading up to the description of the One-Step Climbing Problem, which you can state with the next slide.) Also, here is where you can mention the similarities to re-grasping in a multi-finger hand, and to motion-planning methods for track and legged robots.

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

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 Sample position/orientation of the chassis at random in restricted area Solve IK for each limb making contact Sample DOFs in free limb at random Test equilibrium constraint

Need for Sensor Feedback