Mobile Robots (Legged)(Take class notes)Legged mobile robots• Mobile robots are robots which can move• There are two types of mobile robots- Legged – two, four, six and eight legs- Wheeled – one, two, three and four wheels• Legged mobile robot has a longer history than manipulators- Professor Robert McGhee developed the first walking machine at USC in the 1960’ – he later joined OSU - At OSU he developed the hexapod walking robot OSU HexapodPhony PonyLegged robotsLegged robots were also developed by industry such as the Walking Truck by Ralph S. Mosher of General Electric under a commission from the US Army in 1966ASV (adaptive suspension vehicle) developed by OSU in the 80sHumanoid robots –booming in recent yearsSARCOSUSAToyotaJapanAISTJapanToyotaJapanHonda ASIMOJapanHUBOKoreaLegged robot fundamentals• Kinematics, inverse kinematics and dynamics of legged robots are similar to robot manipulators, but more complicated• Consider the body as a mobile “base” and each leg as a manipulator• You can attached a coordinate frame to each link of a limb using the Denavit-Hartenberg convention – do you still remember?XBZBYBZF1XF1YF1YN1XN1ZN1XEZEYEControl the motion• You need to specify the motion of the body first:- The position and orientation of the body in the earth frame:which is function of time • Then you can specify the position and orientation of each foot with respect to the body according to the required body motion: where m = 1, 2, 3, 4, 5, or 6• The goal is to achieve through the motions of individual feet• Collaborated motions of the feet form a gait)(tTBE1000)(FmzFmzFmzFmzFmyFmyFmyFmyFmxFmxFmxFmxFmBpaonpaonpaontT)(tTBEWalking gaits• Animals use a few types of gaits- Walk – trot; run – gallop: difference?- Gaits are naturally designed to achieve both stability and efficiency- In general animals use static or dynamic walking gaits: difference?- Static: center of gravity (COG) always falls in a supporting area- Dynamic: COG temporarily falls out of the supporting area periodically- Running is dynamicConsider a quadruped gait – using footprintsSupporting areaCOG projectionStability margin = shortest distance between the COG and the boundary of the supporting areaRight-right-left-leftRight-left-left-rightWhich one has better stability margin?Foot in the airUse trot gait- stability margin is smallDirection of motionDuty factor• Duty factor is the percentage of the a cycle which a foot is on the ground.• If the duty factor is greater than 50%, a gait considered as walk, while the one less than 50% is considered run• For the two quadruped gaits, the duty factor is greater than 75% - walk: RF: right forelimb, RH: right hindlimbRFLHRHLF25%50% 75% 100%Human biped locomotion• The first paper on human biped locomotion I read is:M. Saunders,V. T. Inman, and H. D. Eberhart, “The major determinants in normal and pathological gait,” Journal of Bone and Joint Surgery, Vol. 35-A, No. 3, July, 1953.• The paper analyzes the human locomotion as a phenomenon of the most extraordinarycomplexity using connected rigid bodies for illustration – six determinants in locomotionHuman locomotion – six determinantsCompass gaitSix determinants of human locomotion (1)• Pelvic rotation- The pelvis rotates about 4° in either direction during double support. As a result, the limbs are essentially lengthened in the would-be lowest point of the gait cycle to prevent a large drop of the COG• Pelvic tilt- The pelvis on the side of the swinging leg tilts about 4°–5°, which lowers COG at mid-stance• Knee flexion at mid-stance- The bending of the knee reduces the vertical elevation of the body at mid-stance by shortening the hip-to-ankle distanceSix determinants of human locomotion (2)• Foot and ankle motion- Ankle motions smooth the pathway of the COG during stance phase• Knee motion- When the ankle is depressed, the knee extends, and when the ankle is elevated, the knee flexes. Knee motion in this way smooths the pathway of the center of mass and thus conserves energy. • Lateral pelvic displacement- Displacement of pelvic towards the stance foot to make sure that the COG is supported by the foot • Human locomotion is much more complicated than we thought• The purpose is to make your locomotion most efficientHumanoid robotsWABOT-1 – Wasada Un. CURBi Robot – now at OSU• Humanoid robot was first developed in Japan in 1973• In the U.S. first one was CURBi developed in 1986Zero moment point (ZMP)• Zero moment point (ZMP) is a classical concept and has been used in the programing and control of humanoid robots for a long time.• It specifies a point, about which the moments of the ground reaction forces, the inertia force, and the gravity forces are zero. • If the ZMP is in the supporting area, the humanoid robot is stable; otherwise, it is not• A humanoid robot cannot be in the none stable case for too longZMP EquationsNewton-Euler equations:    󰇗• The ground reaction force is responsible for providing and  in the opposite direction • Since is related to the reference point X, the point Z is defined as ZMP if :0=  =  FZMPGround reaction forcenxyLegged robot examples• Hubo crosses over 2x4 and 4x4 barsLegged robot