9 b Locomotion Why dont more robots have

9 b Locomotion Why don’t more robots have legs? Robots learn to walk, right? How long does it take for a robot to learn to walk? How does walking compare to tracks and wheels? © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 1

9 b Biometric Locomotion Objectives • List the five types of biomimetic locomotion Types Crawling Sliding Legs -Balance -Leg events Summary • Given the number of legs, give the formula and compute the number of possible leg events • List the three virtual biped gaits • Define reference trajectory, ZMP, CPG • Explain the difference between static and dynamic stability in legged locomotion © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 2

9 b Types Crawling Sliding Legs -Balance -Leg events Summary Motivation • By this point, familiar with principles of organizing the software behind a reactive or behavioral robot system • But what about the mobility part? – Not a control course, but do need some familiarity © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 3

9 b General outline • Types Crawling Sliding Legs -Balance -Leg events Summary Biomimetic locomotion – Intro • Types of Biomimetic Locomotion • Why Legs – What make legs hard • More inclusive: footfall, • Reference trajectory, oscillation (gait) • Planning the oscillation: number of leg events – Gaits – Balance • Support polygon, zmp • Static Balance • Dynamic Balance – Generating gaits for legs with joints • GPG, motion capture • Learning – Alternative Legs – Typical Areas of AI Research © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) • Reference trajectory, learning, and CPG 4

9 b Biological Locomotion (Sweigert, Nourbakhsh) • Crawl- overcome friction through longitudingal vibration Types Crawling Sliding Legs -Balance -Leg events Summary • Sliding- overcome friction through transverse vibration • Running- overcome kinetic energy with oscillatory movement of multi-link pendulum • Jumping- overcome kinetic energy with oscillatory movement of multi-link pendulum • Walking- overcome gravity by rolling like a polygon © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 5

9 b The Most Famous Crawling Robot • Terminator Types Crawling Sliding Legs -Balance

9 b Second Most Famous Crawling Robot • Terminator. Bot, courtesy of Richard Voyles Types Crawling Sliding Legs -Balance -Leg events Summary © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 7

9 b Types Crawling Sliding Legs -Balance -Leg events Summary Sliding Snakes • http: //www. engin. umich. edu/research/mrl/urpr/Video /Best_of_OT-4_1 Mbs. wmv • http: //www. snakerobot. com/ – Hybrid: See under search and rescue, the Snoopy robot • Note the need for radio-control in snakes. The hybrid Snoopy has a camera on the mobile robot base to let the operator see © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 8

9 b Biological Locomotion (Sweigert, Nourbakhsh) • Crawl- overcome friction through longitudingal vibration Types Crawling Sliding Legs -Balance -Leg events Summary • Sliding- overcome friction through transverse vibration • Running- overcome kinetic energy with oscillatory movement of multi-link pendulum • Jumping- overcome kinetic energy with oscillatory movement of multi-link pendulum • Walking- overcome gravity by rolling like a polygon © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 9

9 b Biological Locomotion (Sweigert, Nourbakhsh) • Crawl- overcome friction through longitudingal vibration Types Crawling Sliding Legs -Balance -Leg events Summary LEGGED LOCOMOTION • Sliding- overcome friction through transverse vibration • Running- overcome kinetic energy with oscillatory movement of multi-link pendulum • Jumping- overcome kinetic energy with oscillatory movement of multi-link pendulum • Walking- overcome gravity by rolling like a polygon © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 10

9 b Wheels v. Biomimetic Locomotion • From Raibert – Only half earth is accessible by wheels Types Crawling Sliding Legs -Balance -Leg events Summary – Leg advantages • can find isolated footholds, whereas wheels are continuous • Provide active suspension – Not as energy intensive as other biological modes • • • Crawling/sliding Running Tires on soft ground Walking Railway wheels Increasing power demand © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 11

9 b What Makes Legs Hard • Reference trajectory • oscillation (gait) and foot placement – Where to place the foot and how to stay balanced • Planning the oscillation: number of leg events © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 12

9 b The Problem with Legs Want dynamic gaits, but… Types Crawling Sliding Legs -Balance -Leg events Summary • Degrees of freedom – Human leg has 7 (excluding toes) • Placing legs Left Right u - - d - u • 6 legs (hexapods like bees) d - – K=6 N=39, 916, 800 u u d d – Large number of possible leg events (from S&I) • N=(2 k-1)!, where k = #legs • Bipedal – K=2 N=6 © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 13

9 b So define gaits rather than plan leg events Gets worse when consider joints Use a gait, then add react to adjust foot fall to terrain. If terrain is too difficult, revert to “free gait” • Approach: reference trajectory and oscillation (gait) © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 14

9 b Gaits • Oscillations • Raibert’s virtual bipedal gaits • Central pattern generators

9 b Static Balance • Support polygon – Convex hull of the contact points center of mass (COM) • If COM is always in the support polygon, then statically balanced • First legged robots were statically balanced Support polygon © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 16

9 b Types Crawling Sliding Legs -Balance -Leg events Summary It’s All A Matter of Balance • “Static stability” means balance is always maintained with no need for motion for passive correction. Fairly rare in nature. • Static walking – Usually has >=6 legs, since must lift legs – Ex. Lobster – Ex. OSU hexapod, Odetics, Dante • Note also the body is always moving on a horizontal plane, no pushing up or down. This simplifies the control © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 17

9 b Odetics Odex 1 Types Crawling Sliding Legs -Balance -Leg events Summary ©

9 b Dante I, II Types Crawling Sliding Legs -Balance -Leg events Summary ©

9 b Zero Moment Point • But we’d like to have bipeds, where the support polygon can’t be maintained by contact Non-zero points because one leg is in the horizontal force air • Have to worry about swinging leg and putting it down where it won’t slip when weight is transferred to it • Think of the leg as an inverted pendulum Non-zero • Zero-moment point is the point horizontal force in the swinging where are the horizontal forces are balanced: the robot shouldn’t fall • Influenced by friction, type of foot Zero-moment point • © 2019 ZMP typically have a “stomp” to nd Robin Murphy Introduction to AI Robotics 2 Edition (MIT Press 2019) 20 get the flat footed

9 b Types Crawling Sliding Legs -Balance -Leg events Summary Ex. Dynamic Balance: Segway We’d prefer true dynamic balance where COM could be out of support polygon and all feet off the ground • CMU video (maybe take out) © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 21

9 b Raibert’s Solution • Virtual Biped Gaits. Consider only gaits involving pairs of legs (control two at a time), exploit symmetry Types Crawling Sliding Legs -Balance -Leg events Summary – Trot (diagonal) – Pacing (lateral) – Bounding (front, back pairs) © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 22

9 b © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT

9 b Quadraped Hopper http: //www. ai. mit. edu/projects/leglab/robots. html trot Types Crawling Sliding Legs -Balance -Leg events Summary pace bound © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 24

9 b One Leg as the Degenerative Case Types Crawling Sliding Legs -Balance -Leg

9 b But what about legs with joints? • Oscillation of that specific leg, two common methods for creating (Handbook) – CPG: CPG becomes an assemblage of CPG – Motion-capture © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 26

9 b Better Legs: Spring Flamingo Types Crawling Sliding Legs -Balance -Leg events Summary

9 b r. Hex: Legs Like a Cockroach (take out the joint: pendulum legs act as a spring, can replace as a leaf spring) Types Crawling Sliding Legs -Balance -Leg events Summary © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 28

9 b Biomimetic Robots • Bob Full’s work Types Crawling Sliding Legs -Balance -Leg events Summary – http: //www. berkeley. edu/news/media/releases/2002/09/rfull /robots. html – r. Hex and Gecko © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 29

9 b Big Dog http: //video. google. com/videoplay? docid=5349770802105160028 Types Crawling Sliding Legs -Balance -Leg events Summary © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 30

9 b Whegs (wheels and legs) http: //biorobots. cwru. edu/projects/whegs. html Types Crawling Sliding Legs -Balance -Leg events Summary © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 31

9 b Bipeds • Honda P 3 – “intelligent”, “mobility” as keywords for company’s future Types Crawling Sliding Legs -Balance -Leg events Summary • Honda Asimo – http: //world. honda. com/ASIMO/ © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 32

9 b AI Approach • In general, AI is rarely involved in walking research because the mechanics are like flight stability for UAVs – Instead focuses on generating the reference trajectory (where it should go) and what velocity (need to run, not walk) • Two exceptions – Learn to walk: Ghenghis – CPGs from the neuroethology and neural networks communities © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 33

9 b Summary: Biological Locomotion Types Crawling Sliding Legs -Balance -Leg events Summary • If a robot has a degree of freedom, you want to be accurately measure it (proprioception) or you won’t be able to control it • Wheels remain the most energy efficient form of locomotion for ground robots but legs are the most versatile • Legs don’t have to look like legs (r. Hex, whegs) • Gaits reduce the problem of planning of footfalls for dynamic balance; while AI is rarely engaged in legs, CPG is an natural extension of behavior-based robotics and reinforces the value of the tradition of exploiting biological and ethological conditions © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 34

9 b Time to watch Dante’s Peak? © 2019 Robin Murphy Introduction to AI

9 b Note: This is based on a 2010 lecture so “ 7” appears

9 b • To generate gaits start with a reference trajectory which gives a default movement, then adjust in real-time to external conditions like terrain – Option 1: motion capture – Option 2: bio-inspired central pattern generator • There appears to be neurons at the spinal cord that produce a cyclic pattern link. springer. com/article/10. 1007%2 FBF 00652227 or rhymic motion that doesn’t require inputs– swallowing, respiration, locomotion design self-oscillating systems (i. e. , without inputs, although the shape of the output is tunable through some parameters) from which synchronized periodic motions of the joints can be derived. Self-oscillating systems are ones that you add steady (non-periodic) power to them and they automatically create a periodic motion • Even though the idea of a CPG is bio-inspired, the most common CPG approach is to use a non-linear equation, Van der pol equation, developed for oscillations in electronics. – to create sinusoidal radio waves – Explain noise – Some challenges are • Van der pol equation requires a numerical method to solve • The CPG is for a joint and legs have multiple joints, so doing collections of CPGs © 2019 Robin Murphy Introduction to AI Robotics 2 nd Edition (MIT Press 2019) 37