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 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 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 –

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)