IntroductionKinodynamic PlanningOptimizing Control Quantifying metastability Stochasticity is clearly a fundamental characteristic for real-world walking.

Introduction Kinodynamic Planning Optimizing Control

Quantifying metastability

Stochasticity is clearly a fundamental characteristic for real-world walking systems.

Introduction Kinodynamic Planning Optimizing Control

Quantifying metastability

Stochasticity is clearly a fundamental characteristic for real-world walking systems.

How can we quantify its effects?

Cartoon version of metastability

Introduction Kinodynamic Planning Optimizing ControlQuantifying metastability

Cartoon version of metastability

not strictly stable misleading and incomplete to call unstable

Introduction Kinodynamic Planning Optimizing ControlQuantifying metastability

Rimless Wheel model

Model assumptions

• rigid, massless spokes• point mass at “hip”• collisions:

▪ instantaneous▪ inelastic

• pendular dynamics

Introduction Kinodynamic Planning Optimizing ControlQuantifying metastability

McGeer, 1990.

Coleman and Ruina, 2002.

Tedrake, 2005.

Deterministic case:• fixed-point analysis• return map

Rimless Wheel

sinsin4

2cos2

l

gn

sinsin4

2cos2

l

gn

n2cos

1, n

12, n

2, n

n

Return map for post-collision velocity

Introduction Kinodynamic Planning Optimizing ControlQuantifying metastability

Deterministic case:• fixed-point analysis• return map

Stochastic case?• probability densities• stochastic return map

Rimless Wheel

sinsin4

2cos2

l

gn

sinsin4

2cos2

l

gn

n2cos

1, n

12, n

2, n

n

Return map for post-collision velocity

Introduction Kinodynamic Planning Optimizing ControlQuantifying metastability

Rimless Wheel on rough terrain

Introduction Kinodynamic Planning Optimizing ControlQuantifying metastability

Introduction Kinodynamic Planning Quantifying metastability

Optimizing Control

Can we optimize control to maximize MFPT on stochastic (rough) terrain?

Introduction Kinodynamic Planning Quantifying metastability

Optimizing Control

Can we optimize control to maximize MFPT on stochastic (rough) terrain?

Yes! Use dynamic programming on our discrete models of dynamics :

Value Iteration

Actuated Compass Gait strategy

Basic underactuated control strategy:

• PD control in part sets step width

▪ leg inertia still makes underactuated coupling important

• pre-collision toe-off primary add energy

• passive toe pivot

Introduction Kinodynamic Planning Quantifying metastability Optimizing Control

Actuated Compass Gait strategy

Basic underactuated control strategy:

• PD control in part sets step width

▪ leg inertia still makes underactuated coupling important

• pre-collision toe-off primary add energy

• passive toe pivot

acrobot dynamics

Introduction Kinodynamic Planning Quantifying metastability Optimizing Control

Primary contributions – summary

Underactuated kinodynamic motion planning • dynamic, fast, repeatable: coupled dynamics

▪ : trot-walk and pacing motions▪ : dynamic lunge

Stochastic methods to quantify walking reliability• mean first-passage time (MFPT) metric for walking• efficient eigenanalysis for MFPT• system-wide MFPT exists for metastable systems

Policy optimization for rough terrain walking• capability of passive-dynamic approach• (suggestive) short-sighted control policy successes

00

Thanks!

Harvard

Microrobotics

Laboratory

Rob WoodJ. Peter Whitney Mike KarpelsonBen Finio

Pratheev SreetharanKatie Hoffman

Chris Oland Brandon Eum

Russ TedrakeNick RoyAlec SkholnikKhash Rohanimanesh

Sam PrenticeJohn RobertsOlivier ChatotSteve Proulx

Marc RaibertAl Rizzi Gabe NelsonAaron Saunders

Cassie MoreiraAdam Fastman

Kevin Blankespoor

LearningLocomotionProgram

Robert MandelbaumTom WagnerLarry Jackel

Jim PippineDoug Hacket

Adam Watson

Katie Byl Metastable Legged-Robot Locomotion

Thanks!

Harvard

Microrobotics

Laboratory

Rob WoodJ. Peter Whitney Mike KarpelsonBen Finio

Pratheev SreetharanKatie Hoffman

Chris Oland Brandon Eum

Russ TedrakeNick RoyAlec SkholnikKhash Rohanimanesh

Sam PrenticeJohn RobertsOlivier ChatotSteve Proulx

Marc RaibertAl Rizzi Gabe NelsonAaron Saunders

Cassie MoreiraAdam Fastman

Kevin Blankespoor

LearningLocomotionProgram

Robert MandelbaumTom WagnerLarry Jackel

Jim PippineDoug Hacket

Adam Watson

Katie Byl Metastable Legged-Robot Locomotion

Questions?

Additional slides

• Some future work directions

• Potential collaboration efforts

• Specific anticipated collaborators

• Funding source opportunities

• (Various details about technical presentation)

Future work – anticipated directions

General lessons (good and bad)? Failures happen Underactuated models can handle rough terrain Short-sighted walking strategies are effective Discretization only works for low-dimension systems Dynamics are coupled

Future work – anticipated directions

General lessons (good and bad)? Failures happen Underactuated models can handle rough terrain Short-sighted walking strategies are effective Discretization only works for low-dimension systems Dynamics are coupled

Plan for failure … but also plan for recovery!

• Multi-modal locomotion strategies

▪ Hop+flap+tumble; run+jump; climb+soar

• Failure analyses

▪ Predict likely impact scenarios (falling shouldn’t be fatal)

• Multi-robot failure analyses

▪ failure events likely to be correlated

Future work – anticipated directions

General lessons (good and bad)? Failures happen Underactuated models can handle rough terrain Short-sighted walking strategies are effective Discretization only works for low-dimension systems Dynamics are coupled

Study theoretical efficiency of real-world (stochastic) locomotion

• When are legs more efficient than wheels (on rough terrain)?

• Efficiency of flapping flight in highly agile regime?

Future work – anticipated directions

General lessons (good and bad)? Failures happen Underactuated models can handle rough terrain Short-sighted walking strategies are effective Discretization only works for low-dimension systems Dynamics are coupled

Further analysis of short-sighted planning

• For walking:

▪ each step naturally dissipates energy

• For other locomotion (flying, swimming, …):

▪ can designed, piece-wise control strategies give similar effect?

Future work – anticipated directions

General lessons (good and bad)? Failures happen Underactuated models can handle rough terrain Short-sighted walking strategies are effective Discretization only works for low-dimension systems Dynamics are coupled

Development of methods for higher degree-of-freedom systems

• Hierarchical strategies?

• Exploitation of short-sighted maneuvers/strategies

▪ Toward desirable neighborhoods in state space

▪ Sequential visits of these neighborhoods over time

• Development of evaluation techniques (for such strategies)

Future work – anticipated directions

General lessons (good and bad)? Failures happen Underactuated models can handle rough terrain Short-sighted walking strategies are effective Discretization only works for low-dimension systems Dynamics are coupled

Trajectory planning required through state space

• Example: flapping flight (segue to current work…)

▪ Exploit combination of active and passive stability

▪ Potential reduction of effect dimensionality– Identify “principal components” of motions

Current work – microrobotic fly control

Harvard

Microrobotics

Laboratory

PI: Rob Wood

Current work – microrobotic fly control

Srong motivation for underactuation (weight, power, complexity)• Good: perfect case example

Minimal # of actuators; simple models of lift and drag promising• Bad: many tangential challenges…

(power elec., onboard sensing and control, batteries…)• Ugly: to control a fly, you need to manufacture it, first!

Mesoscale = microscope, tweezers, folding and glue […repeat!]

Future work – potential collaborative efforts

Tremendous potential – e.g., enabling progress toward:

• Optimizing physical design of agile robots

• Mechanical design

• Actuation

• Sensing

• Complex system analysis / operations research

• Robustness of deployed robot teams

• Probability of communication loss, etc.

• Influences design of multi-agent dynamics

• Swarm strategies

• Hierarchical command strategy

• Analysis of human and animal near-limit-cycle gaits

• Identify causes and predict rates of failure (falling)

• Applications toward: rehab, aging, prosthetics

Some potential research collaborators

Russ Tedrake (MIT) Rob Wood (Harvard) Boston Dynamics (Al Rizzi, Rob Playter) Physical Sciences, Inc. (Tom Vanek) Equilibria (Samir Nayfeh) iRobot (Rodney Brooks, Joe Foley) Peko Hosoi (MIT) Olin College Mike Merznich (Posit Science) Physical Therapy Dept., UCSF (Nancy Byl) NASA/Ames

Funding opportunities

NSF

• Info. and Intell. Sys. (CISE/IIS)

• Dynamic Sys. And Control (Eng/CMMI/DSC)

• Early CAREER grant

• Course curriculum funding SBIR – enabling robotics technology DARPA – unmanned systems AFRL – flapping flight; UAVs ONR – mine detection; ship inspection NIH – prosthetic locomotion