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 if suspended Summary 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) Wheel arrangements
Robot Locomotion
Henrik I Christensen Two wheels
Introduction
Concepts
Legged
Wheeled Summary Three wheels Wheel arrangements – II
Robot Locomotion
Henrik I Christensen
Introduction Four wheels Concepts
Legged
Wheeled
Summary Synchro Drive
Robot Locomotion
Henrik I Christensen
Introduction All wheels are driven Concepts synchronously by one motor Legged Defines speed Wheeled All wheels are steered Summary synchronously by second motor Define direction of motion orientation of inertial frame remains the same Differential drive setup
Robot Locomotion
Henrik I Christensen Two wheeled or possible two wheels and a castor Introduction
Concepts Control of each wheel independently Legged Control discussed in lecture 3 Wheeled
Summary Bicycle drive
Robot Locomotion
Henrik I Christensen
Introduction Two wheeled with one wheel control of direction Concepts Only dynamically stable Legged
Wheeled
Summary Catarpillar / Tracked vehicles
Robot Locomotion
Henrik I Christensen
Introduction Concepts Frequently used in rough terrain Legged Requires skid steering Wheeled
Summary Poor control of motion. Requires external sensors for accurate control Hybrid Locomotion
Robot Locomotion
Henrik I Christensen
Introduction
Concepts Mix of contact configurations
Legged (small / large configuration) Wheeled Developed for Mars Exploration Summary (ESA) by Mecanex and EPFL Named the SpaceCat Walking with wheels (Video) SHRIMP – wheeled climbing
Robot Locomotion
Henrik I Christensen
Introduction Passive handling of rough Concepts
Legged terrain Wheeled 6 wheels for stability Summary Size 60 x 20 cm Overcomes obstacles upto double wheel diameter SHRIMP Motion
Robot Locomotion
Henrik I Christensen
Introduction
Concepts
Legged
Wheeled
Summary Summary/Discussion
Robot Locomotion
Henrik I Christensen Different types of locomotion Introduction Legged Concepts Well suited for unstructured terrain Legged Power efficiency still an issue Wheeled Wheeled Summary 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 Lecture Schedule
Robot Locomotion
Henrik I Christensen
Introduction Concepts Mon. March 27 @ 10–12 / Q2 (Kinematic modelling) Legged Thu. March 30 @ 10–12 / E3 (Lab session 2) Wheeled
Summary Mon. April 3 @ 10–12 / E2 (Sensors/Features) Thu. April 6 @ 15-17 / Q2 (Mapping/Estimation) Thu April 20 @ 10-12 / Q33 (Planning and Integration)