Robotics (Locomotion) Winter 1393 Bonab University

Transcription

1 Robotics (Locomotion) Winter 1393 Bonab University

2 Locomotion Movement or the ability to move Locomotion Locomotion mechanisms used in biological systems: -Successful in harsh environments -Inspired most engineered locomotion systems Exception: wheels However, Our walking ~= rolling polygon 2

3 Locomotion Can we copy nature? Locomotion Extremely difficult because: Mechanical complexity is achieved by: Structural replication (cell division) like: millipede Man-made structure: fabrication=individual Miniaturization : extremely difficult Nature s energy storage and activation (torque, response time, And conversion efficiency) unachievable Example: insects (robust) Such limitations locomotion choice: Wheeled (simpler, suitable for flat ground) Small # of legs ( higher DOFs mechanical complexity) 3

4 Locomotion -- efficiency Locomotion on flat surfaces wheeled locomotion 1-2 orders of magnitude more efficient than legged locomotion Example: railway with rolling friction = ideal But, as the ground gets softer!! Legged locomotion = only point contacts A biped walking system ~= by a rolling polygon, with sides = d to the span of the step. As the step size decreases circle/wheel 4

5 Locomotion -- efficiency Locomotion Efficiency of wheeled locomotion depends on: Environment (specially on ground) Flatness Hardness Efficiency of legged locomotion depends on: Mass (that robot needs to support at all parts of gait) Leg Body So, it s clear why nature chooses legged rough/unstructured env. (insect vertical variation > 10 it s height) Human environments = engineered, smooth surfaces so, choice= wheeled Recently, for more natural outdoor environments hybrid 5

6 General Considerations (all forms of mobile robot locomotion) Locomotion Locomotion vs. Manipulation both study: Actuators generate interaction forces Mechanisms desired kinematic & dynamic properties Key issues for locomotion: stability - number and geometry of contact points - center of gravity - static/dynamic stability - inclination of terrain characteristics of contact - contact point/path size and shape - angle of contact - friction type of environment - structure - medium, (e.g. water, air, soft or hard ground) 6

7 Legged Mobile Robots Legged Legged locomotion = a series of point contacts between the robot & ground Advantages: Adaptability Maneuverability in rough terrain Quality of the ground: does not matter Cross holes so long as its reach exceeds the width Example of manipulation: Dung beetle Potential to manipulate objects in the environment with great skill, e.g. Disadvantages: power and mechanical complexity (Leg, which may include several DoF, must be capable of sustaining part/whole weight) high maneuverability = forces in different directions (if leg has enough DoFs) 7

8 Leg configurations and stability Legged Some biologically successful legged systems Large animals (reptiles, mammals): 4-legs Insects >= 6-legs Some mammals perfected for 2-leg locom. Humans can even jump on 1-leg (balance) Price = complex active control In contrast: 3-legged static stability (stool : balance without motion, passive) Arrangement of the legs of various animals Robot: static walk (need to lift legs) = need 6-legs (a tripod of legs in touch with ground at all times) Insects/spiders, Mammals, Human Standing/walking after birth is more difficult 6-legs 4-legs 2-legs Video demonstrating tripod walk 8 Static walking with six legs

9 Variety of successful legs: from very simple to complicated Legged Complexity of individual legs Caterpillar (1-DoF) Hydraulic pressure extends leg Release in pressure + single tensile muscle retracts leg Complex overall locomotion Two robotic legs (with 3-DoFs): leg is extended using hydraulic pressure Human leg: (> 7 major DoFs) Further actuation at toes > 15 muscle groups, 8-complex joints 9

10 Variety of successful legs: Example Legged 3-DoF cockroach leg 10

11 Leg DoFs needed to Move Legged At least 2-DoFs needed Lift Swing forward More common is adding 1-dof for adding complex maneuvers 4 th is in recent walking robots at ankle In general: adding dof = increase maneuverability Range of terrains Different gaits Main disadvantage: Added energy, control, and mass And leg coordination / gait control 11 2-types of gaits in a 4-legged robot, static walking is impossible:

12 Possible gaits Legged Gait: a sequence of lift and release events for the individual legs. For a mobile robot with k legs: 1. lift right leg; 2. lift left leg; 3. release right leg; 4. release left leg; 5. lift both legs together; 6. release both legs together. K=6: 12

13 Examples of walking robots: One-legged Legged 13 No high-volume industrial application (legged), but important research 1-leg Minimizes mass No leg coordination Maximizes advantage of legged motion (1 contact point vs. whole track) So, suitable for the roughest terrain Hopper running start cross a gap > its stride Multilegged can t run limited to gap = its reach Major challenge: balance Not only static walk = impossible Static stability while stationary = impossible Active balance: 1-Change centre of gravity, 2-Corrective forces

14 Examples of walking robots: One-legged Legged Raibert hopper (well-known single legged hopping robot) Actuators: hydraulic (large off-board pump) Continuous corrections (body attitude, velocity) By adjusting leg angle Not very energy efficient 14

15 Examples of walking robots: One-legged Legged 2D single bow leg hopper More energy efficient Hydraulic actuator bow leg (85% of landing energy is returned, means: Stable hopping with 15%) 1 battery set 20 minutes of hop controls velocity by changing the angle of the leg to the body at the hip An important aspect in hopping robots: Duality: mechanics vs. controls Mechanical design can help simplify control Dynamic stability with more passivity The 2D single bow leg hopper from CMU 15 Video: Robots from MIT s Leg Lab

16 Examples of walking robots: 2-legged Legged Past 10 years: many successful bipedal robots demonstrated: Walking-run Jumping Up-down stairs Even aerial tricks In the commercial sector: Honda Sony significant advances highly capable 2-leg robots They both designed: Servos for small power joints Great: power/weight (small & strong) Intelligent (with sensors, so compliant actuation) Honda Sony 16

17 Examples of walking robots: 2-legged (Sony SDR-4X II) Legged Result of research begun in 1997 Objective: motion/ communication entertainment (dancing & singing) 38 DOF 7 microphones fine sound localization Person recognition (image) Stereo map reconstruction Speech recognition (limited) For this goal, Sony spent considerable effort designing a motion prototyping application system to enable engineers to script dances in a straightforward manner 17 NAO biped robot video

18 Examples of walking robots: 2-legged (Honda P2) Legged Long history Asimo P2 Much larger than Sony SDR-4X Practical mobility in the human world of stairs The first robot that famously (biomimetic): stair up/down Goal: not entertainment, but human aids in society Height ~= humans operate in their world (say, control light switches) important feature (2-leg robots): anthropomorphic shape Can have same approximate dimensions as humans Makes them excellent vehicles for research in human-robot interaction 18

19 Examples of walking robots: 2-legged Legged WABIAN-2R developed at Waseda University in Japan designed to emulate human motion (even to dance like a human) DOF= leg:6x2, foot:1x2(passive), waist:2, trunk:2, arm:7x2, hand:3x2, Neck:3 Spring flamingo of MIT: Springs in series with leg actuators = More elastic gait Combined with kneecaps Very biomimetic 2-leg robots: can only be statically stable within some limits must perform continuous balance-correcting even when standing still 19

20 Examples of walking robots: 4-legged Legged Standing still = passively stable, walking remains challenging (CoG needs to be actively shifted during gait) Sony invested several $million on AIBO: 20

21 Examples of walking robots: 4-legged (AIBO, artificial dog from Sony) Legged Sony produced: A new robot operating system that is near real-time New geared servomotors: Sufficiently high torque to support the robot Yet back drivable for safety A color vision system -> AIBO can chase a brightly colored ball function for 1-hour -> recharging > 60,000 units sold in the first year ~ $ leg: the potential to serve as effective artifacts for research in human-robot interaction: As a pet (might develop an emotional relationship) They can emulate learning and maturation (AIBO does) 21

22 Examples of walking robots: 6-legged (hexapods) Legged Extremely popular for their static stability in walking So, less control complexity In most cases, each leg has 3DOF: hip flexion, knee flexion, & hip abduction 22 Plustech developed the first applicationdriven walking robot Lauron II, a hexapod platform developed at the University of Karlsruhe, Germany

23 Examples of walking robots: 6-legged (hexapods) Legged Genghis is a commercially available hobby robot has six legs, each 2DOF provided by hobby servos (hip flexion - hip abduction) Such robots has less maneuverability in rough terrain but performs quite well on flat ground. Straightforward arrangement of servomotors, straight legs -> easily built Insects (the most successful locomoting creatures on earth), excel at traversing all forms of terrain with 6-legs, even upside down. Genghis, one of the most famous walking robots from MIT, uses hobby servomotors as its actuators The gap of capability (insects-robots) is still huge Not lack of DOF in robots Insects combine few active DOFs with passive structures (microscopic barbs, textured pads) -> grip strength 23

24 Wheeled Mobile robots Wheeled Wheeled locomotion: the design space Wheel design Wheel geometry Stability Maneuverability Controllability Wheeled locomotion: case studies Synchro drive Omnidirectional drive (locomotion) with three spherical wheels with four Swedish wheels with four castor wheels and eight motors Tracked slip/skid locomotion Walking wheels Uranus from CMU Nomad X4000 Has 4 castor Wheels all -steered -driven 24

25 Wheeled Mobile robots: Design space - wheel design Wheeled 4 basic wheel types (large effect on the overall kinematics) (a) Standard wheel 2DOF; rotation around the (motorized) wheel axle and the contact point b) castor wheel: 2DOF; rotation around an offset steering joint c) Swedish wheel: 3DOF; rotation around the (motorized) wheel axle, around the rollers, and around the contact point (d) Ball or spherical Highly directional steering 25

26 Wheeled Mobile robots: Design space - wheel geometry Wheeled Choice of wheel Types Arrangement, or wheel geometry strongly linked affects: Maneuverability Controllability Stability Why not common car configuration (Ackerman)? 26

27 Wheeled Mobile robots: Design space - wheel geometry Wheeled 27

28 Wheeled Mobile robots: Design space - wheel geometry Wheeled 28

29 Wheeled Mobile robots: Design space - Stability Wheeled Minimum # wheel for stability? Surprisingly, 2 (CoM below axle) But wheel diameter = impractically large Dynamics (high enough torque) can also cause instability Conventionally, static (Not dynamic) stability requires 3-wheels CoG be contained in the triangle of contacts Otherwise it needs controller to be stabilized Stability further improves by adding wheels But we ll need flexible suspension on uneven terrain Cye does vacuum and deliveries 29

30 Wheeled Mobile robots: Design space - Maneuverability Wheeled Maneuverability: Overall DoF that robot can manipulate: Mobility Steerability Omnidirectional Robot? Can move at any time in any direction on the ground plane (x,y) Regardless of robot s orientation around it s vertical axix requires wheels to move in more than just 1-direction So, usually employ powered Swedish (Mecanum) or spherical wheels 30

31 Wheeled Mobile robots: Design space - Maneuverability Wheeled Examples of robot direction based on wheels rotation: Uranus: uses four Swedish wheels to rotate and translate independently and without constraints 31

32 Wheeled Mobile robots: Design space - Maneuverability Wheeled A disadvantage for Swedish/spherical wheels: Limited ground clearance (mechanical limitations) A solution: 4-castor wheels: All actively translated All actively steered -> truly omnidirectional (although robot moves with this steering) Other classes of robots are highly popular: High maneuverability slightly inferior to Omnidirectional: Motion in any direction: May require initial rotation If a circular robot with rotation axis at the centre, footprint also won t change The simplest is 2-wheel differential drive 1-2 more contact points for improved stability Ackerman config. (lower maneuverability) Turning diameter > car Moving sideways very difficult advantage: its directionality -> very good lateral stability in high-speed turns (popular) 32

33 Wheeled Mobile robots: Design space - Controllability Wheeled Controllability vs. Maneuverability (inverse correlation) E.g., 4-castor wheel -> significant processing (desired rotational/translational velocities -> individual wheel commands) Omnidirectional designs greater DOF at the wheel (the Swedish wheel has a set of free rollers) -> accumulation of slippage -> reduce dead-reckoning accuracy increase the design complexity For specific direction of travel: Ackerman: just lock the steering 2-wheel diff. drive : Challenging for the 2 motors to have the same velocity profile Variations between wheels, motors, environmental differences Uranus: even more difficult Summary: no ideal configuration maximizes 33 Stability Maneuverability Controllability -> Design based on: Application

34 Wheeled Mobile robots: Case studies Wheeled 1-Synchro drive: Popular for indoor applications Only 2-motors Translation motor Steering motor No direct way of reorienting the chassis It drifts with time (uneven tire slippage) Rotational dead reckoning problem Can add extra motor for this purpose Omnidirectional, but orientation of chassis is not controllable Dead reckoning: True omnidirectional < Synch. < Ackerman Closest wheel starts spinning first (single belt for translation) B21r: sold with such capability 34

35 Wheeled Mobile robots: Case studies Wheeled 2-Omnidirectional drive: Complete maneuverability = high interest In any direction (x,y,θ) holonomic (Every DoF is controllable) a) With 3 spherical wheels Suspended by 3 contact points (2 bearing, 1 by wheel connected to motor axle) Simple design, but limited to flat surfaces & small loads b) With 4 Swedish wheels (or with 3 90 o wheel because we have 3 DoF in the plane) One motor for each wheel Direction & relative speed of each motor omnidirectionality Even can simultaneously rotate around its vertical axis One application: Mobile manipulator (gross motion by robot chassis) c) With 4 castor wheels & 8 motors Requires precise synchronization and coordination for Precise motion (x,y,θ) 35 XR4000 from Nomadic

36 Wheeled Mobile robots: Case studies Wheeled 3-Tracked slip/skid locomotion: Assumption in wheel configurations: wheels are not allowed to skid Alternatively: reorient the robot by spinning wheels that are facing the same direction at different speeds in opposite directions Example: army tank, Nanokhod Large ground contact patches better: maneuverability in loose terrains traction Disadvantage: changing orientation (=skidding turn) Most of the track must slide Exact centre of turn is difficult to predict Dead reckoning: inaccurate Power efficiency: good on loose train, bad otherwise 36

37 Walking wheels Walking robots: best maneuverability in rough terrain Inefficient on flat ground & need sophisticated control Hybrid solutions: combining adaptability of legs efficiency of wheels Example: Shrimp: 6 motorized wheels Front-back motors are steered 4 on the side help steering by speed control Personal rover Actively shifts CoM By identifying the terrain Then moving the boom 37 Shrimp, an all-terrain robot with outstanding passive climbing abilities (EPFL)

38 Supplement Locomotion 38

39 Extra explanation Mecanum Wheel Figure 2 provides a top view of a (rectangular) vehicle featuring four Mecanum wheels, along with its attached coordinate system (x,y), the origin of which is assumed to be the geometrical centre of the rectangle; the wheels are identifed by the numbers 1 : : : 4, starting from the right-bottom corner (i.e., from the right-rear wheel of the vehicle) and proceeding in the counter-clockwise direction. The angular velocities w1:::4 are designed positive for translational motion in the forward direction (increasing y). 39

40 Extra explanation Mecanum Wheel The driving (motor) force (thrust) ~Fi acting on wheel i of the vehicle (chosen to be wheel 2), along with its decomposition into one force ( ~Fi;p) parallel to the rotational axis of the roller (which is in contact with the ground at that moment) and one in the transverse direction ( ~Fi;t), are shown in Fig. 3. The angle between the transverse direction and the rotational plane of the wheel is denoted as α [0,π ). (The quantity sin α is also known as the efficiency of the wheel'.) Since the rollers rotate freely around their axle, there is no traction along the transverse direction; therefore, the force ~Fi;t can safely be ignored when studying the motion of the vehicle. The relation between Fi;p and Fi (indicating the corresponding moduli of the two vectors) reads as: Fi;p = Fi sin α. 40 The rollers shown are assumed to be those corresponding to the lower part of the wheel, part of which is in contact with the ground.

41 Extra explanation Mecanum Wheel Finally, the only relevant force, Fi,p, may be decomposed into forces along the axes of the attached coordinate system (see Fig. 4). The geometry dictates that Fi,x = Fi,p cos α= Fi sin α cos α and Fi,y = Fi,p sin α = Fi sin 2 α. 41 The rollers shown are assumed to be those corresponding to the lower part of the wheel, part of which is in contact with the ground.

42 Control scheme for mobile robots Locomotion Main bodies of knowledge associated with mobile robotics 42