Mobile Robots Locomotion Institute for Software Technology 1
Course Outline 1. Introduction to Mobile Robots 2. Locomotion 3. Sensors 4. Localization 5. Environment Modelling 6. Reactive Navigation 2
Today s Agenda Motivation for Locomotion Basic Definitions Legged Locomotion Wheeled Locomotion Properties of Locomotion and their Application Feedback Control 3
Literature Introduction to Autonomous Mobile Robots. 2 nd Edition. Roland Siegwart, Illah Reza Nourbakhsh, Davide Scaramuzza. MIT Press. 2011. Springer Handbook of Robotics. Bruno Siciliano and Oussama Khatib. Springer. 2008. 4
Again, Robotics is Easy perception modelling domain model environment model information extraction raw data planning task cognition reasoning path planning navigation path execution actuator commands behavior control sensing environment/world acting 5
Locomotion Oxford Dictionary: movement or the ability to move from one place to another 6
Locomotion a mobile robot needs locomotion has a long history in nature different optimizations for speed stability efficiency http://www.youtube.com/watch?v=tifowaz0eeg 7
Locomotion in Biological Systems [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] 8
biological locomotion is hard to replicate mechanical complexity duplication miniaturization actuation energy storage Inspiration by Nature [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] 9
Efficiency I [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] 10
Efficiency II [Sicillano, Khatib, 2008, Springer] 11
stability Key Issues of Locomotion number and geometry of contact points center of gravity static/dynamic stability inclination of the terrain characteristics of contact contact points/path size and shape angle of contact friction type of environment structure medium, e.g. water, air, soft or hard ground 12
Dimensionality the degree of freedom (DOF) of a workspace is its overall dimensionality on (flat) ground DOF=3 in the air or below water DOF=6 13
[Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] Institute for Software Technology 14 Legs versus Wheels
Zero Moment Point Movement (ZMP) commonly used method for stable walking ZMP is defined as that point on the ground at which the net moment of the inertial forces and the gravity has no component along the horizontal axes (Vukobratović and Branislav) [Sicillano, Khatib, 2008, Springer] 15
Zero Moment Point Movement suppose a legged robot comprising several bodies force vector acing on body (gravity plus external) angular velocity of body inertia tensor ( ) of body relative position of body to ZMP [Sicillano, Khatib, 2008, Springer] 0,0, 16
a robot able to use ZMP needs: there are at least six fully actuated joints for each leg the joints are position controlled the feet are equipped with force sensors, which are used to measure the ZMP Requirements for ZMP http://www.youtube.com/watch?v=3aouq1_e--k 17
Wheel Types standard castor Swedish spherical Side View Front View Top View [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] 18
Typical Arrangements (2 and 3 Wheels) 2 Wheels 3 Wheels [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] 19
Typical Arrangements ( 4 Wheels) [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] http://www.youtube.com/watch?v=xzkc4ez8gye http://www.youtube.com/watch?v=8sh1a511_q4 20
NASA Mars Rover - Rocker-Bogie hybrid between walking and driving allows to climb obstacles reduce movement of body Advanced Mechanisms [Nasa/JPL] http://www.youtube.com/watch?v=bc441bv1wfc 21
Other Forms of Locomotion in the air below water http://www.youtube.com/watch?v=4erebkj_3py http://www.youtube.com/watch?v=9vm-gq9_h9i 22
Homogeneous Transformation we need a transformation between the motion in the reference frame and the robot frame the transformation depend on the global angle,,,, cos sin 0 sin cos 0 0 0 1 23
Kinematic Constraints an arrangement comprises wheels of different types each wheel provides an individual velocity and individual parameters, e.g. steering anlge to determine the maneuverability of an attunement we use 2 sorts of constraints rolling constraints: all motions in the wheel plane have to be accompanied with the appropriate wheel spin sliding constraints: the motion orthogonal to the wheel has to be zero 24
Fixed Standard Wheel,, sin cos cos 0RKC [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] cos sin 0SKC 25
Steered Standard Wheel same as fixed standard wheel expect steering is now a function of time,, [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] sin cos cos 0RKC cos sin 0SKC 26
Swedish Wheel [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] sin cos cos cos 0 RKC cos sin sin 0SKC 27
Spherical Wheel same as fixed standard wheel expect steering is now a free variable [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] sin cos cos 0RKC cos sin 0SKC 28
Combining the Constraints I the wheel arrangement comprises fixed and steerable wheels, denotes the steering angles while denotes all fixed angles denotes wheel speed of the fixed wheels while denotes wheel speed of the steered wheels, denotes the combination 29
Combining the Constraints II Rolling Constraints 0with Sliding Constraints 0 0 0 0 0 0 0with All Together 0 and 30
Maneuverability we can use the constraints to investigate the mobility potential of a robot the degree of mobility is defined as: 3 represents the number of DOF that can immediately manipulated by changes in the wheel velocities related to the location of the instantaneous center of rotation (ICR) the degree of steerability is defined as: 0 2 depends on the number of steerable wheels robot maneuverability related to the DOF a robot is able to manipulate 31
Application of Constraints 32
Automatic Reconfigurable Omni-Drive [Brandstötter, Hofbauer, Steinbauer, Wotawa IROS 2007] 33
Automatic Reconfigurable Omni-Drive motor 1 fails motor 2 fails motor 3 fails 34
[Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] Institute for Software Technology 35 (Non)-Holomorphic
Feedback Control move a differential drive to a goal non-holonomic constraints we need differential inverse kinematics lim 0 [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] 36
Control Law + 3, 8, 1.5 [Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press] 37
Questions? Thank you! 38