Outline. Outline. Recent Popular Legged Robots in Japan. Self-contained! Adaptive? Limit Cycle Based. What is legged locomotion?

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1 Neuromorphic Eng. Workshop, Telluride, 14 Jul Biological Inspired Legged Locomotion Control of a Robot Hiroshi Kimura Univ. of Electro-Communications Tokyo, Japan Katsuyoshi Tsujita Kyoto Univ. Japan Recent Popular Legged Robots in Japan 4 Self-contained! Adaptive? Just following the preprogrammed motion pattern What is legged locomotion? Manipulation of a Body 5 ZMP Based Zero Moment Point vs. Limit Cycle Based 6 Stabilization of Non-linear Oscillation ZMP ZMP dynamic walking hopping juggling Stable Limit Cycle on Phase Plane

2 ZMP Based 7 ZMP-based Motion Generation and Control 8 Acceleration Inertia force Gravity + COG In order to avoid falling down, realize the given trajectory as precise as possible. ZMP COP Control of a arm Avis & Ashimo [Japan, Feb. 2003] Johnnie [Germany, Jul. 2003] Limit Cycle Based 9 Limit Cycle based Motion Control 10 x Swinging phase Phase plane x Supporting phase To keep the stable oscillation, Switching supporting/swinging phases non-linearity TomCat [Jul. 2003] the upper bound of the cyclic period of walking Passive Dynamic Walking 11 Legged Locomotion on Irregular Terrain 12 A walking machine can walk down the slope without actuation. Conventional Method precise model trajectory planning control variety of irregularity Is the control necessary? Problem Autonomous Adaptation? (Cornel Univ 2000)

3 How we can learn from animals 13 Hypothesis on Legged Locomotion - principles of mechanism and motion - 14 Functions of Animals mimicking Robots low speed motion Robots Animals Functions of Animals analysis Principles Robots A lot of alternatives in mechanism, devices and control methods Examples of Not Mimicking Animals [Hirose : TITECH] 15 Hypothesis on Legged Locomotion - principles of mechanism and motion - low speed motion high speed motion 16 Robots Animals Robots Animals sucker wheel-leg special link mechanism pantograph, parallel,. A lot of alternatives Only few alternatives in mechanism, devices since dynamics is dominant and control methods The differences in the number of joints and actuators, etc. become not so important. Mechanical design Control method Good examples 17 Large Power Actuator Not Good Mechanical Design Energy consumption : Large Adaptability to irregular terrain : Small 18 independent of the number of legs Large Foot

4 Size of Foot vs. Adaptability to Irregular Terrain 19 Size of Contacting Surface 20 side view front view side view front view Influence of local shape of terrain : large Large Power Actuator Not Good Mechanical Design Energy consumption : Large Adaptability to irregular terrain : Small Gear Reduction Ratio : High Viscosity : Large Self Locked Mass and Inertia Moment of a Swinging Leg : Large Ac/Deceleration Torque Impact Force at Landing 21 independent of the number of legs Mechanical design Control method Good examples 22 Large Foot High Gain Feedback at the Swinging Leg Joints Control Methods According to the Speed [Blickhan & Full:1993], [Full & Koditschek:1999] 23 Why the role of sensor feedback becomes small in high speed locomotion? 24 good for control of ZMP-based posture Limit-Cycle-based Neural System low / medium speed walking Musculoskeletal System high speed running Kinetic energy is large and dominant. In the short cyclic period, the influence of actuator output is small, problem! motion cannot be stabilized by the direct actuation. main controller role of sensor feedback upper neural system (learning) large lower neural system (CPG + reflexes) visco-elasticity of muscles (self stabilization) small In the short cyclic period, the accumulation of errors is small, advantage! motion can be stabilized by the exchange of stance/swing phases. non-linear switching control

5 Stabilization of Forward Speed Angular Velocity Control around contact point independent of the number of legs Touchdown Angle Control 25 Stabilization of Forward Speed - Touchdown Angle Control - 26 by ankle joint torque, control the angular velocity of the supporting leg V Torque : Large Efficiency : low Needs large foot by touchdown angle, control the forward speed of the next stance phase V exchange of phases (switching) Stabilization using the gravity Torque : Small Efficiency : high touchdown angle Biper3 [1981] Miura & Shimoyama [IJRR:1984] like walking on stilts V Stabilization of Forward Speed - Touchdown Angle Control - 27 Raibert:1984 the neutral-point foot-placement algorithm Touchdown (Attacking) Angle in Running [Hackert, Witte & Fischer : AMAM2000] [Buehler, et al. : AMAM2003] 28 in biological system stepping reflex Biper3 [1981] Miura & Shimoyama [IJRR:1984] attacking angle speed [m/s] speed [m/s] touchdown angle [deg] Half Bound Running [Hackert, Witte & Fischer : AMAM2000] [Buehler, et al. : AMAM2003] Mechanical design Control method Good examples

6 Hopping Robots by Raibert [ ] 31 Hopping Robots Touchdown angle control by Raibert [ ] 32 Point contact Air spring Light weight leg and the body of large inertia moment Touchdown angle control, others Running on irregular terrain Quadruped & Hexapod Robots 33 Hexapod Robots 34 [SCOUT-II] [RHex] [Sprawlita] Point contact (Passive) compliant and light weight leg Analysis of self stabilization RHex (2000-) Sprawlita, (2000-) Self stabilization to stabilize the forward speed without measuring it Quadruped Robot: Tekken 2 axes rate gyro & Weight:3Kg 2 axes inclinometer 40cm Pitch Axis (3 joints) pitch Hip & Knee joints: active Ankle joint: passive Yaw Axis (1 joint) roll yaw 35 20cm Over an Obstacle of 20% Relative Height to a Leg 36 Light weight leg Small foot Small gear ratio: ~16 viscosity: small compliant joint contact sensor encoder Sensor based adaptive walking on irregular terrain Over an obstacle 4.0cm in height

7 H/L H L 1 self-contained or not self-contained Maneuverability 0.5 Humanoid Quadruped walking Tekken-I 0 without vision RHex 37 V : walking speed L : leg length H : unknown height Hexapod of an obstacle Sprawlita running Monopod by M.Raibert & J.K.Hodgins 0.5 Scout-II Froude number V gl with vision / for known H Characteristics of Legged Robots based on Dynamics and Biological Concepts Mechanical design good for medium & high speed locomotion adaptation to irregular terrain Short cyclic period : rhythmic motion Complicated trajectory planning and control are not necessary. 38 CPGs+ Reflexes Rolling motion feedback to CPGs 39 Control Methods According to the Speed good for control of main controller ZMP-based posture upper neural system (learning) [Blickhan & Full:1993], [Full & Koditschek:1999] Limit-Cycle-based Neural System low / medium speed walking lower neural system (CPG + reflexes) Musculoskeletal System high speed running visco-elasticity of muscles (self stabilization) 40 Locomotion Control Using Neural System Model [Northeastern Univ.] BISAM [by Ekeberg] [Kyoto Univ.] [by Taga] [by Ijspeert] [Iguana co.] 41 Physiology CPG (Central Pattern Generator) Entrainment among neurons of CPGs Entrainment with musculoskeleton Reflexes Negative feedback Positive feedback Higher Level 42 Patrush[UEC] By Grillner, Cohen, Pearson, Prochazka, Mori, Drew, et al.

8 What is Neural System Model Control? Rhythm Phase Difference between Legs Tuning of Muscle Tone Physiological Experiments Using Cats :.. S. Mori [1973].. CPGs Reflexes Computer Simulation & Robot Experiments Kimura [1994-] 43 Tuning of Muscle Tone Joint PD Control as a Tonic Stretch Reflex. trq = K1 (θ * θ ) K2 θ jnt jnt jnt jnt θ θ * jnt jnt ={ stance θ jnt swing Κ1 Κ1 jnt={ stance jnt Κ1 swing jnt desired state jnt virtual springdamper system present state 44 Change of Stiffness in Stance/Swing Phases 45 CPG (Central Pattern Generator) 46 large in the stance phase against the gravity Tekken[2001-] & Collie-2[1987] small in the swing phase for irregular terrain reduce the impact force stiffness muscle tone stance phase swing phase Muscle tone and stiffness of walking cats [Akazawa:1982] Σ Feed ei Feedfi Σ w ij y ej u0 extensor neuron of other N.O.'s flexor neuron of other N.O.'s w ij y fj u0 Neural Oscillator by Matsuoka[87] & Taga[91] Extensor Neuron, τ τ uei w fe u fi τ ei fi v ei ei v fi Flexor Neuron Excitatory Connection Inhibitory Connection fi, τ y i phase w hf Pace Trot w hf -1 < w hf < Neural Oscillator Matsuoka[87], Taga[91] time constant 47 Gaits 48 joint angle, body roll angle, etc. u{e,f}i : inner state of the neuron y{e,f}i : output of the neuron v{e,f}i : variable representing the self inhibition Trot: v = 0.6m/s, T = 0.35s Walk: v = 0.3m/s, T = 0.6s -0.7 w hf -0.3

9 Other Mobility 49 Motion Generation & Adaptation 50 Tuning of Muscle Tone torque output sensory feedback reflex Running in a bound gait Changing the direction Rhythm Generation (CPG: Central Pattern Generator) phase (stance/swing) output sensory feedback response Motion Adaptation & Sensory Feedback [Tekken:2001] the legs should be free to move forward during the first period of the swing phase, Passive ankle joint & Flexor reflex 51 Passive Ankle & Flexor Reflex 52 spring and lock mechanism contact & collision detect sensor Over an obstacle 2.0cm in height Motion Adaptation & Sensory Feedback [Tekken:2001] the legs should be free to move forward during the first period of the swing phase, Passive ankle joint & Flexor reflex 53 Vestibulospinal reflex/response for pitching 54 the legs should land reliably on the ground during the second period of the swing phase, Tonic labyrinthine response for rolling the phase difference between rolling motion of the body and pitching motion of legs should be maintained, Stepping reflex & Vestibulospinal reflex/response for pitching the average of the forward speed be kept constant, Slope of 10 degree inclination

10 Motion Adaptation & Sensory Feedback [Tekken:2001] the legs should be free to move forward during the first period of the swing phase, Passive ankle joint & Flexor reflex the legs should land reliably on the ground during the second period of the swing phase, Tonic labyrinthine response for rolling the phase difference between rolling motion of the body and pitching motion of legs should be maintained, Stepping reflex & Vestibulospinal reflex/response for pitching the average of the forward speed be kept constant, CPG network phase difference between legs be kept appropriately. 55 CPGs+ Reflexes Rolling motion feedback to CPGs 56 Waking in a long cyclic period is difficult to stabilize. 57 Tonic Labyrinthine Reflex for Rolling or Vestibular Reflex roll plane Nanzando s Medical Dic. 18 th edn. Principles of Neuro Science, 3 rd edn. 58 Trot T = 0.35s, easy Walk T = 0.6s, difficult Large rolling motion naturally generated disturbs pitching motion. Rolling motion feedback to CPG upward -inclined leg downward -inclined leg Roll Motion Feedback to CPG body roll angle δ Feed e.roll = (leg) k roll (body roll angle) Feed f.roll = - Feed e.roll < 0 59 Roll Motion Feedback to CPG 60 Right fore leg Left hind leg Right fore leg E -- F + Right hind leg E -- F + E -- F + Left fore leg E + F -- Left Hind leg E + F -- Without With F -- E + T = 0.3 sec. 1.3cm 17cm

11 Rolling Motion as Standard of Rhythm 61 Roll Motion Feedback to CPG 62 Pitching Motion of a Leg phase Rolling Motion of a Body angle phase (supporting / swinging) Rolling motion feedback to CPG Stabilizing a gait Adjusting phases of CPGs Excitatory Connection Inhibitory Connection Slope of 5 & 3 degree inclination Walking over Pebbles The values of all parameters are fixed for unknown terrain of medium degree of irregularity. H/L H L 1 Maneuverability RHex Hexapod Sprawlita 0.5 self-contained Humanoid Quadruped Monopod or walking Tekken-I not self-contained running Scout-II Froude number V without vision Energy Efficiency by M.Raibert & J.K.Hodgins gl with vision / for known H 65 Tekken-2 & Tekkn-1 66

12 Mechanically Variable Stiffness of Knee Joints 67 Tekken-2 68 Energy Consumption Specific Resistance = P/mgv OSU Hexapod PV II Tekken1 Walking(flat terrain) Tekken1 Runnig Hydraulic Quadruped Tekken1 Walking (irregular terrain) Big Muskie GE Quadruped ASV 1 Scout II ARL Monopod Tekken2 Walking(flat terrain) Human Running 1950 Cars Gravity Walker Human Walking Off-Road Vehicles Human cycling 1994 Cars Limiting Line modified from [Buehler, et al.:1999] Velocity [m/s] Discussion # What is Neural System Model Control? Equivalent? CPG (Central Pattern Generator) Interaction Reflexes Real Mechanism? ZMP Based Limit Cycle Based Feedforward compensation of gravity and inertia force Feedback correction of errors using sensor information Discussion #1 Motion Generation & Adaptation Phase diff. CPG outputs phase information (stance/swing phase). Hip joint angle, the body pitch and roll angle are input to CPGs as responses. PD controller outputs joint torque as reflexes. tonic labyrinthine response for rolling ktlrr LF LH Tuning of muscle tone θ swing θ stance - + interneurons + - α flexor motor neuron RF RH CPG - θ y i y i > 0 y i < 0 vestibule body body roll angle pitch angle Rhythm α spinal cord tonic stretch response θ vsr θ vsr θ vsr extensor motor neuron vestibulospinal reflex/response

13 Discussion # Autonomous Adaptive Walking Neural System Dynamics coupling Emergently Adaptive Mechanical System Dynamics Dynamic Walking interaction Environment by Taga[1991] Coupled Dynamic based Motion Generation dynamic walking on irregular terrain For desirable adaptation, we must construct neural system carefully. physics, biology, physiology, Discussion #2 How dynamics of mechanism is encoded into parameters of the neural system Relation between the leg length or the stiffness and the time constant of CPG! Choose the original cyclic period of CPG as O TCPG Reflexes / Responses? length of a leg mass / stiffness Discussion #3 argument (BC:2002) CPG Models Cruse, Ekeberg more sensor dependent & more decentralized more general cyclic period is determined by speed of the body and legs Taga, Kimura, Lewis, Tsujita&Tsuchiya, Ilg, non-linear oscillator time constant or standard cyclic period dynamics of mechanism is encoded into parameters of the neural system essential for dynamic walking by Kimura (IJRR2003) 75 Coupled Dynamics based Motion Generation adaptive walking on irregular terrain Neural System Dynamics coupling Mechanical System Dynamics interaction Environment gait transition visual adaptation Emergently Adaptive Dynamic Walking autonomous adaptation at levels from the lower spring-damper system to the higher vision system Future Works 78 Self-contained System & Outdoor Experiments Visual Adaptation Behavior Gait Transition Bipedal Locomotion

14 Future Works 79 Behavior and Tuning of Muscle Tone 80 Self-contained System & Outdoor Experiments Visual Adaptation Behavior Gait Transition [in Telluride, 2001] [of Kimura] Bipedal Locomotion [S. Mori:1996] [Prochazka:1988] Future Works Self-contained System & Outdoor Experiments Visual Adaptation Behavior Gait Transition By Tsujita-san Bipedal Locomotion 81 2 nd AMAM Int. Conf. on Adaptive Motion of Animals and Machines March , Kyoto Supported by Japan Science Promotion Society Biology, Physiology, Biomechanics, Robotics,. 3 rd AMAM in Germany on Sep Acknowledgment Ph.D Student Yasuhiro Fukuoka Y. Fukuoka, H. Kimura & A.H. Cohen Int. J. of Robotics Research, 2003 TEPCO AVICE & JST JSPS continued

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