SICB10 Talia Yuki Moore 1/7/2010 Adding Inertia and Mass to Test Stability Predictions in Rapid Running Insects Talia Yuki Moore*, Sam Burden, Shai Revzen, Robert Full PolyPEDAL Lab University of California Berkeley 1

SICB10 Talia Yuki Moore 1/7/2010 (Gerald and Buff Corsi, Visuals Unlimited) (Pauline Smith) (Tim Flach Stone/Getty Images) (Flagstaffotos) Animals compensate for large changes in mass and moment of inertia. Natural Changes in Moment of Inertia 2

SICB10 Talia Yuki Moore 1/7/2010 Differences in Body Mass & Form 3 Animals have evolved diverse and successful body forms that differ in mass and moment of inertia. (Aivar Mikko) (Sophia Moore) ( S. Reid)

SICB10 Talia Yuki Moore 1/7/2010 Different View of Stability Sagittal Plane Horizontal Plane

SICB10 Talia Yuki Moore 1/7/2010 Instability in the Horizontal Plane 5

SICB10 Talia Yuki Moore 1/7/2010 Instability in the Horizontal Plane 6

SICB10 Talia Yuki Moore 1/7/2010 Lateral Leg Spring (LLS) Template 3 Legs Acting as One Animal Schmitt & Holmes, (2000) Bouncing Side to Side

SICB10 Talia Yuki Moore 1/7/2010 Model Parameters  k m d Schmitt & Holmes (2000) - leg stiffness - leg length - center of pressure position - body mass - inertia - leg angle kLdmIkLdmI

SICB10 Talia Yuki Moore 1/7/2010 Input Parameters  k Schmitt, Holmes, Garcia, Razo & Full (2001) k = 2.25 Nm  = 1 rad I = kgm 2 L = 0.1 m m = kg

SICB10 Talia Yuki Moore 1/7/2010 Model State Variables  Rotational velocity  Body orientation  Heading v Velocity Schmitt, Holmes, Garcia, Razo & Full (2002)   

SICB10 Talia Yuki Moore 1/7/2010 Self-Stabilization 11 Passive, mechanical self-stabilizing with minimal neural feedback Heading Velocity Orientation Rotational Velocity Schmitt, Holmes,Garcia, Razo & Full (2002)

SICB10 Talia Yuki Moore 1/7/ Perturbation remaining per stride [Eigenvalue, ] Vary Body Mass Nondimensional Body Mass Animal More Stable Less Stable Schmitt, Holmes, Garcia, Razo & Full (2000) Stability of Body Orientation & Rotational Velocity to Lateral Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Vary Leg Angle - Stride Length Vary Leg Length- Sprawl Vary Leg Stiffness Perturbation remaining per stride [Eigenvalue, ] Nondimensional Leg angle Animal Nondimensional Leg length Animal Perturbation remaining per stride [Eigenvalue, ] Perturbation remaining per stride [Eigenvalue, ] Nondimensional Spring stiffness Animal Tuning for Self-Stabilization Schmitt, Holmes, Garcia, Razo & Full (2000) More Stable Less Stable More Stable Less Stable More Stable Less Stable 

SICB10 Talia Yuki Moore 1/7/2010 Perturbation remaining per stride [Eigenvalue, ] Moment of Inertia Nondimensional Moment of Inertia Animal More Stable Less Stable Animal & Inertia Hypothesis: A cockroach with added mass and increased moment of inertia will recover from perturbations slower and be unstable. 14 Schmitt, Holmes, Garcia, Razo & Full (2000)

SICB10 Talia Yuki Moore 1/7/2010 Mass Each cockroach was its own control Perturbation remaining per stride [Eigenvalue, ] Non-Dimensional Moment of Inertia More Stable Less Stable Control Mass Inertia Changing Moment of Inertia & Mass 15 Treatment

SICB10 Talia Yuki Moore 1/7/2010 Rapid Impulse Perturbation Device Evidence for Mechanical Feedback 16 Recovery begins <10ms after perturbation Jindrich and Full (2002) Slowed 30X Challenges fastest neural reflexes

SICB10 Talia Yuki Moore 1/7/2010 Platform accelerates laterally at 0.6±0.1 g in a 0.1 sec interval providing a 50±3 cm/sec specific impulse, then maintains velocity. Lateral Perturbation 17 Cockroach runs at: 31±6 cm/sec Stride Frequency: 12.5±1.7 Hz trackway camera diffuser mirror magnetic lock animal motion cart cart motion rail pulley mass cable elastic ground

SICB10 Talia Yuki Moore 1/7/2010 Lateral Perturbation Criteria for trial rejection: 1. >15 ° deviation in heading pre-perturbation 2. Contact with the cart sides 3. >50% Change in forward velocity pre-perturbation Cart impulse Equal and opposite impulse on animal Measured: 1. Distal tarsal (foot) position 2. Pitch, roll, yaw 3. Forward, lateral, rotational velocity 4. Heading, body orientation

SICB10 Talia Yuki Moore 1/7/2010 Real time Lateral Perturbation Experiment 19

SICB10 Talia Yuki Moore 1/7/2010 Slowed 40x Leg and Body Tracking 20 Cart Velocity

SICB10 Talia Yuki Moore 1/7/2010 Raw Data Model Residual Phase χ χ χ Compare Response to Pre-Perturbation Behavior 21 Onset of Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Residual Orientation Animals Recover Orientation Inertia Changes Body Orientation Less Peak Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Residual Forward Velocity All Treatments Decrease Speed Aft Fore Peak Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Carrier et al J. Experimental Biology Increase Moment of Inertia Limits Maneuverability 35% Decrease in Speed Horizontal Plane Instability Reject Lateral Leg Spring Prediction Increased Moment of Inertia Treatment Recovers & Does Not Lead to Instability Limit Maneuverability Decrease Speed

SICB10 Talia Yuki Moore 1/7/2010 Residual Roll 25 Mass Rolls Most Animals Overcompensate in Recovery Lean Into Impulse Roll From Impulse Peak Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Residual Pitch 26 Mass Pitches More than Inertia Animals Remain Pitched Down in Recovery Nose down Nose up Peak Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Residual Lateral Velocity Inertia Lateral Velocity Changes Less Animals Overcompensate & Move Into Perturbation Peak Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Residual Lateral Tarsal Position Inertia Recovery Slower Animals Overcompensate & Place Feet as if to Resist Next Perturbation Peak Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Overcompensation in Humans Welch and Ting (2009)

SICB10 Talia Yuki Moore 1/7/2010 Feedback Response Frequency Change Neural Feedback Residual Phase Time Tarsal Fore-Aft Position Mechanical Feedback No Frequency Change Frequency Change Revzen, Bishop-Moser, Spence, Full (2007) Perturbation Tarsal Fore-Aft Position Feedback - Mechanical, Neural or Both? Time Residual Phase

SICB10 Talia Yuki Moore 1/7/2010 No Frequency Change Supports Mechanical Feedback Residual Phase Response Mechanical Feedback Followed by Neural Feedback to the Central Pattern Generator Frequency Change Supports Neural Feedback Peak Perturbation

SICB10 Talia Yuki Moore 1/7/2010 Conclusions 1. Changes in body mass and form affect response to perturbations. Mechanical feedback important early in response. 2. Increased moment of inertia reduces and delays response to perturbation, but limits maneuverability. 3. Passive horizontal plane model (Lateral Leg Spring) is insufficient to explain response to lateral perturbations. Higher degree of freedom models needed. 32

SICB10 Talia Yuki Moore 1/7/2010 Three Dimensional Models Spring-Loaded Inverted Pendulum (SLIP) Lateral Leg Spring (LLS) Seipel 2005 Spring Loaded Inverted Pendulum (SLIP) Lateral Leg Spring (LLS)

SICB10 Talia Yuki Moore 1/7/2010 Conclusions 4. Hexapods overcompensate in recovery perhaps providing greater stability to another perturbation from the same direction. Neural feedback to CPG may assist. 5. Placement of payload in legged robots can learn from nature Changes in body mass and form affect response to perturbations. Mechanical feedback important early in response. 2. Increased moment of inertia reduces and delays response to perturbation, but limits maneuverability. 3. Passive horizontal plane model (Lateral Leg Spring) is insufficient to explain response to lateral perturbations. Higher degree of freedom models needed.

SICB10 Talia Yuki Moore 1/7/2010 Guidance, Input, and Advice: Berkeley Biomechanics Group Prof. Robert Full PolyPEDAL Lab Think Tanks, Matlab Wizards: Sam Burden Shai Revzen Tarsus Trackers: Debbie Li Brian McRae Cockroach Wrangler: Jessie Ding Acknowledgements 35