Kungl Tekniska Högskolan

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1 Centre for Autonomous Systems Kungl Tekniska Högskolan March 22, 2006

2 Outline Wheel

3 The overall system layout

4 : those found in nature

5 found in nature Difficult to imitate technically Technical systems often use wheels or caterpillars/tracks Rolling is more efficient, but not found in nature Nature never invented the wheel! However the movement of walking biped is close to rolling

6 Biped Walking Biped walking mechanism not to far from real rolling rolling of a polygon with side length equal to step length the smaller the step the closer approximation to a circle However, full rolling not developed in nature

7 Passive walking examples Video of passive walking example Video of real passive walking system (Steve) Video of passive walking system (Delft)

8 Walking or rolling? Number of actuators Structural complexity Control Expense Energy sufficient Terrain characteristics Movement of the system Movement of COG Extra loss

9 RoboTrac A Hybrid Vehicle

10 Characterisation of locomotion concept Physical interaction between the vehicle and its environment is concerned with the interaction forces and the actuators that generate them Most important issues include: Stability Contact characteristics Type of environment

11 Mobile systems with legs Walking machines Fewer legs complicated locomotion stability requires at least 3 legs During walking some legs are in the air Thus a reduction in stability Static walking requires at least 4 legs (and simple gaits)

12 Number of joint for each leg (DOF: Degrees of freedom) A minimum of 2 DOF is required to move a leg A lift and a swing motion Sliding free motion in more than 1 direction is not possible In many cases a leg has 3 DOF With 4-DOF an ankle joint can be added Increased walking stability Increase in mechanical complexity and control

13 Control of a walking robot Motion control should provide leg movements that generate the desired body motion. Control must consider: The control gait: the sequencing of leg movement Control of foot placement Control body movement for supporting legs

14 Leg control patterns Legs have two major states: 1 Stance: One the ground 2 Fly: in the air moving to a new postion Fly phase has three main components 1 Lift phase: leaving the gound 2 Transfer: moving to a new position 3 Landing: smooth placement on the ground

15 Example 3 DOF Leg design

16 Gaits Gaits determine the sequence of configurations of the legs Gaits can be divided into two main classes 1 Periodic gaits, which repeat the same sequence of movements 2 Non-periodic or free gaits, which have no periodicity in the control, could be controlled by layout of environment

17 The number of possible gaits? The gait is characterised as the sequence of lift and release events of individual legs it depends on the number of legs the number of possible events N for a walking machine with k legs is: N = (2k 1)! For the biped walker (k=2) the possible events are 3! = 6 lift left leg, lift right leg, release left leg, release right leg, light both legs, release both legs For a robot with 6 legs the number of gaits are: 11! =

18 Most obvious 4 legged gaits

19 Static gaits for 6 legged vehicle

20 Walking vs Running Motion of a legged system is called walking if in all instances at least one leg is supporting the body If there are instances where no legs are on the ground it is called running Walking can be statically or dynamically stable Running is always dynamically stable

21 Stability Stability means the capability to maintain the body posture given the control patterns Statically stable walking implies that the posture can be achieved even if the legs are frozen / the motion is stoppped at any time, without loss of stability Dynamic stability implies that stability can only be achieved through active control of the leg motion. Statically stable systems can be controlled using kinematic models. Dynamic walking or running requires use of dynamical models.

22 Stability Define Centre of Mass as P CM (t) The A SUP (t) is the area of support Stable walking: P CM (t) A SUP (t) t Dynamic walking: P CM (t) / A SUP (t) t Stability margin: min P CM A SUB

23 Examples of walking machines So far limited industrial applications of walking A popular research field An excellent overview from the clawar project Video of 1 legged example

24 Honda P2-6 Humanoid Max speed: 2km/h Autonomy: 15 minutes Weight: 210 kg Height: 1.82 m Leg DOF: 2 * 6 Arm DOF: 2 * 7 Video 1 Video 2

25 Bipedal MIT Leg Lab has developed a number of biped robots Spring flamingo (a large simple walker) The M2 robot for walking humanoid (Video example) The early two legged systems by Raibert (Video)

26 Humanoid s A highly popular topic in japan More than 65 robots at present on display Wabian built at Waseda University Weight: 107 kg Autonomy: none Height: 1.66 m DOF in total: 43

27 Walking robots with four legs - Quadrupeds A highly popular toy ( copies sold) Involves an advanced control design has vision, ranging, sound, orientation sensors Has a separate league in the RoboCup tournament (Example video)

28 TITAN-VIII a Quadruped Developed by Hirose at Univ of Tokyo Weight: 19 kg Height: 0.25 m DOF: 4 * 3

29 WARP KTH Walking Machine Early test platform Weight: 225 kg Height: 0.7 m Length: 1.1 m Autonomy: 15 min DOF: 4 * 3

30 Hexapods six legged robots Most popular due to the statically stable walking Ex: Ohio walker Speed: 2.3 m/s Weight: 3.2 t Height: 3 m Length: 5.2 m Legs: 6 DOF: 6 * 3

31 Lauron II Hexapod Univ of Karlsruhe Speed: 0.5 m/s Weight: 6 kg Height: 0.3 m Length: 0.7 m Legs: 6 DOF: 6 * 3 Power: 10 W

32 Genghis Subsumption Platforms i/mit AI Weight: 4 kg Autonomy: 30 min Length: 0.4 m Height: 0.15 m Speed: 0.1 m/s

33 Systems with wheels Wheels is often a good solution in particular indoor Three wheels enough to guarantee stability More than three wheels requires suspension Wheel configuration and type depends upon the application

34 Types of wheels There are four types of wheels Standard wheel: two degrees of freedom rotation around motorized axle and the contact point Castor wheel: three degrees of freedom: wheel axle, contact point and castor axle

35 Types of wheels II Swedish wheel: three degrees of freedom - motorized wheel axles, rollers, and contact point (Video) Ball or spherical wheel: suspension not yet technically solved

36 Characteristics of wheeled systems Stability of vehicle is guaranteed with three wheels, i.e. P CM (t) A SUP (t) t Four wheels improves stability if suspended Bigger wheels Handling of larger obstacles Imposes extra torque and higher reduction in gear ratio Most arrangements are non-holonomic (see Lecture 3) Control is more complex (Video commercial)

37 Wheel arrangements Two wheels Three wheels

38 Wheel arrangements II Four wheels

39 Synchro Drive All wheels are driven synchronously by one motor Defines speed All wheels are steered synchronously by second motor Define direction of motion orientation of inertial frame remains the same

40 Differential drive setup Two wheeled or possible two wheels and a castor Control of each wheel independently Control discussed in lecture 3

41 Bicycle drive Two wheeled with one wheel control of direction Only dynamically stable

42 Catarpillar / Tracked vehicles Frequently used in rough terrain Requires skid steering Poor control of motion. Requires external sensors for accurate control

43 Hybrid Mix of contact configurations (small / large configuration) Developed for Mars Exploration (ESA) by Mecanex and EPFL Named the SpaceCat Walking with wheels (Video)

44 SHRIMP wheeled climbing Passive handling of rough terrain 6 wheels for stability Size 60 x 20 cm Overcomes obstacles upto double wheel diameter

45 SHRIMP Motion

46 /Discussion Different types of locomotion Well suited for unstructured terrain Power efficiency still an issue Suited for planar surfaces Different configurations control varies (see Lecture 3) Tracked Suited for rough terrain Skid steering poses a challenge to control Intelligent design is key to design of an efficient system

47 Lecture Schedule Mon. March / Q2 (Kinematic modelling) Thu. March / E3 (Lab session 2) Mon. April / E2 (Sensors/Features) Thu. April / Q2 (Mapping/Estimation) Thu April / Q33 (Planning and Integration)

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