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Robot Locomotion Henrik I Robot Locomotion Christensen Robot Locomotion Henrik I Robot Locomotion Christensen Introduction Concepts Henrik I Christensen Legged Wheeled Summary Centre for Autonomous Systems Kungl Tekniska H¨ogskolan [email protected] March 22, 2006 Outline Robot Locomotion Henrik I Christensen Introduction Concepts Legged Concepts Wheeled Legged Locomotion Summary Wheel Locomotion The overall system layout Robot Locomotion Henrik I Christensen Introduction Concepts Legged Wheeled Summary Locomotion Concepts: those found in nature Robot Locomotion Henrik I Christensen Introduction Concepts Legged Wheeled Summary Locomotion Concepts Robot Locomotion Henrik I Christensen Introduction Concepts Concepts found in nature Legged Difficult to imitate technically Wheeled Technical systems often use wheels or caterpillars/tracks Summary Rolling is more efficient, but not found in nature Nature never invented the wheel! However the movement of walking biped is close to rolling Biped Walking Robot Locomotion Henrik I Christensen Introduction Biped walking mechanism Concepts not to far from real rolling Legged rolling of a polygon with side Wheeled length equal to step length Summary the smaller the step the closer approximation to a circle However, full rolling not developed in nature Passive walking examples Robot Locomotion Henrik I Christensen Introduction Concepts Legged Video of passive walking example Wheeled Video of real passive walking system (Steve) Summary Video of passive walking system (Delft) Walking or rolling? Robot Locomotion Henrik I Christensen Introduction Number of actuators Concepts Structural complexity Legged Wheeled Control Expense Summary Energy sufficient Terrain characteristics Movement of the system Movement of COG Extra loss RoboTrac – A Hybrid Vehicle Robot Locomotion Henrik I Christensen Introduction Concepts Legged Wheeled Summary Characterisation of locomotion concept Robot Locomotion Henrik I Christensen Introduction Locomotion Concepts Physical interaction between the vehicle and its Legged environment Wheeled Locomotion is concerned with the interaction forces and Summary the actuators that generate them Most important issues include: Stability Contact characteristics Type of environment Mobile systems with legs – Walking machines Robot Locomotion Henrik I Christensen Fewer legs ⇒ complicated locomotion Introduction stability requires at least 3 legs Concepts Legged During walking some legs are in the air Wheeled Thus a reduction in stability Summary Static walking requires at least 4 legs (and simple gaits) Number of joint for each leg (DOF: Degrees of freedom) Robot Locomotion Henrik I Christensen Introduction A minimum of 2 DOF is required to move a leg Concepts Legged A lift and a swing motion Sliding free motion in more than 1 direction is not possible Wheeled Summary 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 Control of a walking robot Robot Locomotion Henrik I Christensen Introduction Concepts Motion control should provide leg movements that Legged generate the desired body motion. Wheeled Control must consider: Summary The control gait: the sequencing of leg movement Control of foot placement Control body movement for supporting legs Leg control patterns Robot Locomotion Henrik I Christensen Introduction Concepts Legs have two major states: Legged 1 Stance: One the ground 2 Wheeled Fly: in the air moving to a new postion Summary 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 Example 3 DOF Leg design Robot Locomotion Henrik I Christensen Introduction Concepts Legged Wheeled Summary Gaits Robot Locomotion Henrik I Christensen Introduction Concepts Gaits determine the sequence of configurations of the legs Legged Gaits can be divided into two main classes Wheeled 1 Periodic gaits, which repeat the same sequence of Summary movements 2 Non-periodic or free gaits, which have no periodicity in the control, could be controlled by layout of environment The number of possible gaits? Robot Locomotion Henrik I Christensen The gait is characterised as the sequence of lift and release Introduction events of individual legs Concepts it depends on the number of legs Legged the number of possible events N for a walking machine Wheeled with k legs is: Summary 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! = 39.916.800 Most obvious 4 legged gaits Robot Locomotion Henrik I Christensen Introduction Concepts Legged Wheeled Summary Static gaits for 6 legged vehicle Robot Locomotion Henrik I Christensen Introduction Concepts Legged Wheeled Summary Walking vs Running Robot Locomotion Henrik I Christensen Introduction Concepts Motion of a legged system is called walking if in all Legged instances at least one leg is supporting the body Wheeled If there are instances where no legs are on the ground it is Summary called running Walking can be statically or dynamically stable Running is always dynamically stable Stability Robot Locomotion Henrik I Christensen Stability means the capability to maintain the body Introduction posture given the control patterns Concepts Statically stable walking implies that the posture can be Legged achieved even if the legs are frozen / the motion is Wheeled Summary 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. Stability Robot Locomotion Henrik I Christensen Define Centre of Mass as Introduction PCM (t) Concepts The ASUP (t) is the area of Legged support Wheeled Summary Stable walking: ⇒ PCM (t) ∈ ASUP (t)∀t Dynamic walking: ⇒ PCM (t) ∈/ ASUP (t)∃t Stability margin: min kPCM − ASUB k Examples of walking machines Robot Locomotion Henrik I Christensen Introduction Concepts So far limited industrial applications of walking Legged A popular research field Wheeled Summary An excellent overview from the clawar project http://www.uwe.ac.uk/clawar Video of 1 legged example Honda P2-6 Humanoid Robot Locomotion Henrik I Christensen Max speed: 2km/h Introduction Concepts Autonomy: 15 minutes Legged Weight: 210 kg Wheeled Height: 1.82 m Summary Leg DOF: 2 * 6 Arm DOF: 2 * 7 Video 1 Video 2 Bipedal Robot Robot Locomotion Henrik I Christensen Introduction Concepts Legged MIT Leg Lab has developed a number of biped robots Wheeled Spring flamingo (a large simple walker) Summary The M2 robot for walking humanoid (Video example) The early two legged systems by Raibert (Video) Humanoid Robots Robot Locomotion Henrik I Christensen Introduction A highly popular topic in japan Concepts More than 65 robots at present Legged on display Wheeled Wabian built at Waseda Summary University Weight: 107 kg Autonomy: none Height: 1.66 m DOF in total: 43 Walking robots with four legs - Quadrupeds Robot Locomotion Henrik I Christensen A highly popular toy (300.000 Introduction copies sold) Concepts Involves an advanced control Legged design Wheeled Summary has vision, ranging, sound, orientation sensors Has a separate league in the RoboCup tournament (Example video) TITAN-VIII a Quadruped Robot Locomotion Henrik I Christensen Introduction Concepts Developed by Hirose at Univ of Legged Tokyo Wheeled Weight: 19 kg Summary Height: 0.25 m DOF: 4 * 3 WARP – KTH Walking Machine Robot Locomotion Henrik I Christensen Introduction Concepts Early test platform Legged Weight: 225 kg Wheeled Summary Height: 0.7 m Length: 1.1 m Autonomy: 15 min DOF: 4 * 3 Hexapods – six legged robots Robot Locomotion Henrik I Christensen Most popular due to the statically Introduction Concepts stable walking Legged Ex: Ohio walker Wheeled Speed: 2.3 m/s Summary Weight: 3.2 t Height: 3 m Length: 5.2 m Legs: 6 DOF: 6 * 3 Lauron II – Hexapod Robot Locomotion Henrik I Christensen Univ of Karlsruhe Introduction Concepts Speed: 0.5 m/s Legged Weight: 6 kg Wheeled Height: 0.3 m Summary Length: 0.7 m Legs: 6 DOF: 6 * 3 Power: 10 W Genghis – Subsumption Platforms Robot Locomotion Henrik I Christensen Introduction iRobot/MIT AI Concepts Legged Weight: 4 kg Wheeled Autonomy: 30 min Summary Length: 0.4 m Height: 0.15 m Speed: 0.1 m/s Systems with wheels Robot Locomotion Henrik I Christensen Introduction Concepts Wheels is often a good solution – in particular indoor Legged Three wheels enough to guarantee stability Wheeled Summary More than three wheels requires suspension Wheel configuration and type depends upon the application Types of wheels Robot Locomotion Henrik I Christensen Introduction There are four types of wheels Concepts Standard wheel: two degrees of Legged freedom – rotation around Wheeled motorized axle and the contact Summary point Castor wheel: three degrees of freedom: wheel axle, contact point and castor axle Types of wheels – II Robot Locomotion Henrik I Christensen Introduction Swedish wheel: three degrees of Concepts Legged freedom - motorized wheel Wheeled axles, rollers, and contact point Summary (Video) Ball or spherical wheel: suspension not yet technically solved Characteristics of wheeled systems Robot Locomotion Henrik I Christensen Introduction Stability of vehicle is guaranteed with three wheels, i.e. Concepts P (t) ∈ A (t) ∀t Legged CM SUP Wheeled Four wheels improves stability
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