Dipartimento di Elettronica, Informazione e Bioingegneria Robotics

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Augusta Dixon
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1 Dipartimento di Eettronica, Informazione e Bioingegneria Robotics Basic mechanica 015

2 1 - mechanics subsystem MECHANICS (arm, whees, ) subsystem PROCESS (task, environment) Mobiity degrees Materias Geometry subsystem ACTUATORS (motors, artificia musces, ) subsystem SENSORS (interna and externa) OPERATOR Kinematics Dynamics subsystem CONTROL (contro oop, transformations, subsystem PLANNING (path, grasps, trajectories)

3 Rigid body assumptions Robots have to move rigid bodies The robots are assembed from rigid parts Rigid transformations (that preserve the distance between the points in the body) are apt to describe the actions Rigid transformations are aso usefu to contro the robot structure

4 mobiity How many are the degrees of mobiity of a free rigid body? 3 in the pane (x, y, θ) 6 in space (x, y, z, ρ, θ, φ) y theta x z

5 Mobiity of mechanisms Mechanism = a chain composed of inks and joints, fixed at one end How many are the degrees of mobiity of a mechanism with N inks? Each rigid body has 6; 6 * N if N bodies have no constraints but constraints reduce the number How to compute them?: Operative criterion Grueber criterion

6 Operative criterion Idea whee, ony roing: M = 1 Seria panar mechanism, 4 ink: M = 3 Fixed structure. M = 0

7 Grueber criterion Fora mechanismofn inks M = 6*N - #constraints according to Grueber M = 3*(N -1) *#P1 -#P P1 joints with 1 degree of mobiity P joints with degree of mobiity M = 3(4-1) (3) 0 = 3

Up-down 1. Open-cose a itte 1. @ base (Up-down & side-to-side).

8 More compex exampe How many mobiity degrees has the human hand? part Wrist Pam Finger s Thumb Tota Do F 1 4* Side-to-side. Up-down 1. Open-cose a itte base (Up-down & side-to-side). each of two joints base (attached to visibe joints

9 Mechanica chain: inks Any geometry exampes: Com ponenti, m obiità, Z strutture Z1 Z1 Z Parae Orthog ona

10 Mechanica chain: joints 1 degree of mobiity: kinds Z rotary joints Z Z1 prismatic joints Z

11 Compex joints 3 rotations Gimba Spherica joints (no singuarity) rotations universa

12 Mobiity, degrees of freedom, actuators The variabes that individuate position and orientation of an object are caed degrees of freedom. Robot manipuator Degrees of freedom (dof) = number of independent variabes reated to joints positions to specify to define the position of a the inks of the structure Actuators: to reach a position DOFs can be actuated Usuay dof = number actuators Robot with dof > number actuators are caed underactuated m = 6 dof = 6 actuators=6

13 Manipuators architecture The mechanica design may depend on the task Consider a robot arm To reach any point in a 3D space (position) the robot needs at east 3 dof To reach any point in a 3D space with any orientation it needs other 3 dof COMMON SOLUTION: 3 dof in the arm to reach the position 3 dof in the wrist to reach orientation

14 Hoonomic, non hoonomic, redundant hoonomic robot => the robot has a number of controabe DOFs equa to the number of mobiity degrees Number dof = M Non hoonomic robot = the robot has a number of controabe DOFs smaer than the number of mobiity degrees Number dof < M Redundant robot = the robot has a number of controabe DOFs greater than the number of mobiity degrees Number dof > M

15 Configuration Space The set of a the possibe positions that an object can have is caed configuration space (C-space)

16 Work space vs C-space Work space The rea space R 3 - R for panar robots Configuration space The space of a the objects/robot configurations Degrees of freedom Number of parameters necessary and sufficient to define a point in the configuration space

workspace A manipuator is a sequentia open chain 6 dof every position can be reached with a specified orientation industria robots usuay dof < 6 difficut tasks dof > 6 Work space = the set of

17 workspace A manipuator is a sequentia open chain 6 dof every position can be reached with a specified orientation industria robots usuay dof < 6 difficut tasks dof > 6 Work space = the set of points that the robot can reach Reachabe work space = where the end effector can arrive with at east one orientation Dexterous work space = where the end effector can arrive in any orientation

18 Cartesian (TTT) 3 prismatic joints move aong x, y, z axes Arm or gantry architecture PRO: The transformation between Cartesian and joint space is inear decouped movements simpe contro inear transformations Aegro DEA-GE

19 Workspace cartesian Workspace is cubic Coarse and fine assemby

20 Cyindrica (RTT) Asse 3 Asse 1 Asse R pus orthogona T Rotation joints are ess expensive than prismatic joints The transformation between Cartesian and joint space is inear ony in Z

21 workspace cyindrica Working space is (part of) a cyinder Limited movements, a arge voume aong the main axis is out of reach

22 Spheric or poar (RRT) Asse 1 R joints and after a prismatic one Asse 3 The hand is oriented to the externa space Used in weding (sadatura). Asse In the fig, Stanford Arm (1974).

23 workspace spheric Part of a sphere The transformation between Cartesian and joint space is not inear

24 Articuated (RRR) Asse 3 R Simiar to human arm Rotation joints are ess expensive More human ike movements (but human arm is redundant) Asse 1 Asse 3 Puma CRS

25 workspace articuated Part of a sphere The transformation between Cartesian and joint space is not inear

26 SCARA (seective compiant assemby robot arm) Asse 1 Asse Asse 3 R with parae axes, 1 T Good to work from top to bottom Decouped the transformations Cartesian joint space Z is inear X and Y not inear A the motors are in the base ink

27 workspace SCARA Part of a cyinder

28 Wrist of industria robot Yaw Ro, Pitch e Yaw (roio beccheggio e imbardata). Z Ro rot (Z) The ast inks are used to orient the end effector 3 are necessary o obtain any orientation The 3 axes may intersect in one point Ro Pitch Y Yaw rot (X) X Pitch rot (Y)

29 Rotations in Cartesian space Z ro z Y pitch X yaw

30 Gripper or hand simpe gripper Compex hands Barrett hand, Utah MIT

An industria gripper - WSG50 With the WSG 50, SCHUNK is now abe to offer a sensitive gripper that can be controed via Ethernet TCP/IP in addition to Profibus DP.

31 An industria gripper - WSG50 With the WSG 50, SCHUNK is now abe to offer a sensitive gripper that can be controed via Ethernet TCP/IP in addition to Profibus DP. It aso has an integrated Web server for configuration and diagnostics that makes programming, putting it into operation, remote maintenance, and updating, simpe. Sensors are integrated in the gripper jaws which enabe the WSG 50 gripper to measure the forces that occur during gripping. This feature makes it the idea too for handing sensitive sampes in aboratories, pharmaceuticas, research faciities, and for measuring and testing appications. The WSG 50 gripper has a stroke of 110 mm and a variabe gripping force between 1 and 10 N with a gripping speed of 850 mm/s.

32 Grasp in humans and robots Human graspings are cassified and depend on the task Industria robots with a simpe gripper have imited ways to manipuate objects (friction cones computed in or 3 points)

33 human motor patterns (short ist from Cutkosky)

34 Eectronics and car industry On to manipuators

35 terminoogy Andrè-Marie Ampère proposed in 1834 the name kinematics for a new science dedicated to everything that can be said about the different sorts of motions independent of the forces that can produce them. Dynamics - from Greek δυναμικός powerfu, is the mathematica anaysis of the motion of bodies as a resut of impressed forces A trajectory is the path that a moving object foows through space as a function of time.

Dinamics motion equations Trajectory computation tempora aw to

36 Study of manipuator motion kinematics - reationships between the independent joint variabes θ and the Cartesian variabes x Dinamics motion equations Trajectory computation tempora aw to move the end effector Contro get the correct movement in the rea system

37 Direct and inverse kinematics ink parameters joint vaues: ϑ 1 (t),... ϑ n (t) Direct kinematics end effector position (x, y, z), and orientation (ϕ, θ, ξ ) ink parameters joint vaues: ϑ1(t),..., ϑn (t) Inverse kinematics

38 Kinematic computations in the robot system subsystem MECHANICS (arm, whees, ) subsystem ACTUATORS (motors, artificia musces, ) subsystem CONTROL (contro oop, transformations, subsystem PROCESS (task, environment) subsystem SENSORS (interna and externa) subsystem PLANNING (path, grasps, trajectories) Ideay panning is in Cartesian space the contro subsystem receives the Cartesian target and transforms it in joint space through Inverse Kinematics. the contro subsystem is aware of the joint position (through interna sensors) and uses the Direct Kinematics to compute the Cartesian position of the end effector OPERATOR

39 Direct kinematics (DK) The arm is initiay aigned aong x o; It moves the first ink of θ 1 and the second ink of θ. QUESTION: What is now the Cartesian position of the end effector? Soutions: 1. Geometric approach on the pane. Agebric approach using coordinates transformations.

40 DK Geometric ad-hoc method The probem is reduced to a set of probems in the pane - trigonometric soutions θ1 θ 1 θ θ θ 3 θ3?

41 DK of RR panar y 1 θ working space for compete rotations of the joints θ1 x θ1 {0, ±180 } θ {0, ±180 } DK x=1 cos(θ1) + cos(θ1+θ) y=1 sen(θ1) + sen(θ1+θ)

42 IK of RR panar - 1 ( ) ( ) ( ) C C S C S C C S C = = = + + = + y x ( ) 1 1 y x C + = 1 ϑ ϑ 1 α To find ϑ ( ) + = y x cos ϑ soutions for θ + sign for ebow down - sign for ebow up x, y

43 IK of RR panar - To find ϑ1: set Δθ=θ1+α tan Δθ= y/x tan(α ) = S/( 1 + C) tan θ1 = tan Δθ -tan α y 1 θ (x, y) then: θ1 α θ Δθ θ1 x ϑ1 = tan 1 y x tan S C

44 5dof exampes j j 3 j 4 j 5 Minimover, CRS55 a the inks are on a pane j 1 L3 θ 4 L θ 3 j 4 L1 j 3 Z θ j x

45 6 dof exampes CRS 460 (articuated) 3 dof wrist Puma 560 (articuated)

46 DK Agebraic method Genera representation of kinematic chains Find a soution 1. using homogeneous coordinates Assign the reference systems using a (quasi) agorithmic method. Denavit Hartemberg

47 Further readings

EEE 187: Robotics Summary 2

1 EEE 187: Robotics Summary 2 09/05/2017 Robotic system components A robotic system has three major components: Actuators: the muscles of the robot Sensors: provide information about the environment and