DARPA Robotics Challengewww.cs.cmu.edu/~cga/dw

Day 1

Real TimeFinals

Optimization All The Way Down

• Multi-level optimization:– Footstep Optimization (Discrete + Continuous) – Trajectory Optimization (Continuous)– Optimization-Based Inverse Dynamics: Greedy

continuous optimization (Quadratic Program = QP) for full body at the current instant.

Trials

Multi-Level Control• Trajectory: External forces at contacts drive

center of mass (COM).

Rotation is more complicated:– Constant angular momentum– Rigid body equivalent– General case

• QP: Redundancies and constraints resolved for full body behavior.

xmF

IIFr )(

0)( Fr

dtIdLFr /)()(

Trials

LIPM Trajectory Optimization

X vs, Time

Y vs. Time

COM

Footstep

Footstep

Footstep

COM

COM

X vs. Y

meters

Trials

Optimization-Based “Inverse Dynamics” (QP)

Objectives:• Dynamics• Task Objectives• COM Acceleration• Torque About COM• Reference Pose Tracking• Minimize Controls

Constraints:• Center of Pressure• Friction Cone• Joint Torque Limits

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q

Aw

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22

11

M. de Lasa, I. Mordatch, and A. Hertzmann, “Feature-Based Locomotion Controllers,” ACM Transactions on Graphics, vol. 29, 2010.

Stephens

Trials

Stuck on the door

Finals

Handling modeling error and external forces

Finals

Finals

Failed manipulation

Finals

Fall Predictors

Finals

A bad stepFinals

Why Dynamics Matters

Wheels win?• All wheeled/tracked robots plowed through

debris.• All other robots walked over rough terrain.• KAIST – walked on stairs• Nimbro, RoboSimian – no stairs• Leg/wheel hybrids good if there is a flat

floor somewhere under the pile of debris.• Wheeled/tracked vehicles fell: need to

consider dynamics, need to be able to get up (CHIMP, NimbRo), and get un-stuck.

Finals

Whole-Body Locomotion

• No robot used railings, walls, door frames, or objects in the environment for physical guidance, stabilization, or support.

• Some robots used arms to get out of the car.

Finals

Can Atlas Be Human Like?www.cs.cmu.edu/~cga/dw

• Slow (0.5m/s)• Slow (0.6s/step)• Short steps 0.35m

(half human 0.7m)• Flat foot walking• Bent knees• No heel strike or

toe push off• Fixed pelvis

orientation

• Minimal vertical COM acceleration -> GRF

• Minimal horizontal COM acc. -> GRF

• COP fixed at center of foot

• Not robust to external perturbations or modeling error.

• Soft ground, sand,…?

Baby Steps To Human-Like Walking

Current

Current