doc02CFIC - LaDiSpe - Politecnico di Torino
download 
Reclamo Transcript
02CFIC - LaDiSpe - Politecnico di Torino
What is an industrial robot? RO OBOTIC CA – 01CFIDV 02CFIC CY A robot is … A kinematic chain A multi-body dynamical system A system with motors and drives A system with digital and analogic sensors An electronic system A supervised and controlled system A software driven system Therefore … a mechatronic system Basilio Bona – DAUIN – Politecnico di Torino 002/1 OBOTIC CA – 01CFIDV 02CFIC CY RO Industrial robotics Scope: object manipulation Robots are often called 9 Industrial Manipulators 9 Robots/robotic arms Usuallyy the robot base is fixed or moves along rails The previous COMAU robot at LabRob Basilio Bona – DAUIN – Politecnico di Torino 002/2 RO OBOTIC CA – 01CFIDV 02CFIC CY Prerequisites Read Chapter 2 of the textbook Reference systems y Vectors Matrices Rotations, translations, roto-translations Homogeneous g representation p of vectors and matrices Basilio Bona – DAUIN – Politecnico di Torino 003/3 Reference Systems/Frames RO OBOTIC CA – 01CFIDV 02CFIC CY Three unit vectors (versors) mutually orthogonal in 3D space Right-hand reference frames (RHRF) obey right hand rule Color code RGB k k = i×j right hand rule j i When the fingers go from i to j the thumb is aligned with k Basilio Bona – DAUIN – Politecnico di Torino 003/4 Reference Systems/Frames RO OBOTIC CA – 01CFIDV 02CFIC CY We call this the “cavatappi” (corkscrew) rule k = i×j Ri j i This is also called a CARTESIAN FRAME Basilio Bona – DAUIN – Politecnico di Torino 003/5 RO OBOTIC CA – 01CFIDV 02CFIC CY Reference frames and rigid bodies Every rigid E i id body b d is i defined d fi d by b a RHRF, RHRF the so-called body frame (BF) All points in the rigid body are defined by suitable vectors in the body frame Basilio Bona – DAUIN – Politecnico di Torino 003/6 RO OBOTIC CA – 01CFIDV 02CFIC CY Vectors and Matrices Introductory notes on vectors and matrices can be found here VECTORS http://www.ladispe.polito.it/Meccatronica/01CFI/2008-09/Slides/Vettori.pdf htt // l di lit it/M t i /01CFI/2008 09/Slid /V tt i df http://www.ladispe.polito.it/Meccatronica/download/Appunti_matrici_vettori.pdf MATRICES http://www.ladispe.polito.it/Meccatronica/01CFI/2008-09/Slides/Matrici.pdf Basilio Bona – DAUIN – Politecnico di Torino 003/7 RO OBOTIC CA – 01CFIDV 02CFIC CY Kinematics Kinematics allow to represent positions, velocities and accelerations of multibody points, independently from the causes that generate them (i.e., (i e forces and torques) In order to describe the kinematics of manipulators or mobile robots, it is necessary to define the concept of kinematic chain A kinematic chain is a series of ideal arms connected by ideal joints Flexible Arm M = 9.5 [g], J = 0.547 [Kgmm^2], L = 2.5 [cm] M = 102 [g], J = 530 [Kgmm^2], L = 25 [cm] M = 192 [g], J = 3595 [Kgmm^2], L = 47.5 [cm] Basilio Bona – DAUIN – Politecnico di Torino 003/8 RO OBOTIC CA – 01CFIDV 02CFIC CY Is the human arm a kinematic chain? Wi t Wrist Arm What is this? The human arm + wrist has 7 dof A redundant arm But it is not ideal, since it is composed by muscles, bones and other tissues, tissues is not a rigid body body, the joint are elastic, etc. Basilio Bona – DAUIN – Politecnico di Torino 003/9 RO OBOTIC CA – 01CFIDV 02CFIC CY Kinematic chain A kinematic chain KC is composed by a variable number of Arms/links (rigid and ideal) Joints (rigid and ideal) It is defined only as a geometric entity (no mass, friction, etc.) It has degrees of motion and degrees of freedom (DOF) One must be able to fix on each arm a RF -> DH conventions One must be b able bl to describe d b every possible point in a given RF Basilio Bona – DAUIN – Politecnico di Torino 003/10 RO OBOTIC CA – 01CFIDV 02CFIC CY Kinematic chain A multi-body structure composed by ideal rigid arms/links (no mass and other dynamic properties), linked to other arms by ideal joints that allow a relative motion between two successive arms Joints 4, 4 5, 5 6 Link 3 Joint 3 Arm 2 Arm 1 Joint 2 Joint 1 Joints allow a single degree of motion between connected links Joints may be – Rotoidal or rotation or rotational joints allow a relative rotation between arms – Prismatic or translation joints allow a relative translation between arms Basilio Bona – DAUIN – Politecnico di Torino 003/11 Kinematic chain RO OBOTIC CA – 01CFIDV 02CFIC CY wrist shoulder shoulder wrist Basilio Bona – DAUIN – Politecnico di Torino 003/12 Rotation Joints RO OBOTIC CA – 01CFIDV 02CFIC CY How we draw joints and links? Rotation joints are draw in 3D perspective as small cylinders with axes aligned along each rotation axis k j i Rotation joints are draw in 2D as small circles or small hourglasses axis is normal to the plane pointing toward the observer k i Basilio Bona – DAUIN – Politecnico di Torino j 003/13 RO OBOTIC CA – 01CFIDV 02CFIC CY Example Basilio Bona – DAUIN – Politecnico di Torino 003/14 RO OBOTIC CA – 01CFIDV 02CFIC CY Prismatic Joints Prismatic joints are draw in 3D perspective as small boxes with each axis aligned along the translation axis Prismatic joints are draw in 2D as small squares with a point in their centres or as small rectangles with a line showing the two successive links k i Basilio Bona – DAUIN – Politecnico di Torino j 003/15 RO OBOTIC CA – 01CFIDV 02CFIC CY Example Basilio Bona – DAUIN – Politecnico di Torino 003/16 RO OBOTIC CA – 01CFIDV 02CFIC CY Another example Basilio Bona – DAUIN – Politecnico di Torino 003/17 RO OBOTIC CA – 01CFIDV 02CFIC CY Kinematic chain The COMAU robot seen as an ideal kinematic chain Basilio Bona – DAUIN – Politecnico di Torino 003/18 RO OBOTIC CA – 01CFIDV 02CFIC CY Kinematic representation q6 q5 q4 q3 q2 The jjoint motion produces p a motion in Cartesian 3D space. One must be able to describe the relation between the two representations q1 Joint space vs Task space Basilio Bona – DAUIN – Politecnico di Torino 003/19 RO OBOTIC CY CA – 01CFIDV 02CFIC Joint space and task space Task Space (Cartesian) z Joint space \ 6 q3 direct \ x y n i inverse q1 q2 direct kinematics is easier than inverse kinematics Basilio Bona – DAUIN – Politecnico di Torino 003/20 RO OBOTIC CA – 01CFIDV 02CFIC CY Task Space Task Space Operational Space Workspace p Are synonymous Basilio Bona – DAUIN – Politecnico di Torino 003/21 RO OBOTIC CA – 01CFIDV 02CFIC CY Degrees of motion and degrees of freedom The degrees of motion (dom, (dom as they are called) count the number of prismatic/rotation joints (active, i.e., motor-driven or passive) The degrees of freedom (dof, as they are called) count the number of free parameters of the considered body Dofs may be referred to manipulator, when they count what it can do with its center point, point or to the task when measure what is required by the application Basilio Bona – DAUIN – Politecnico di Torino 003/22 Degrees of motion and degrees of freedom RO OBOTIC CA – 01CFIDV 02CFIC CY Joint 3 TCP Tool Center Point Joint 1 Joint 4 Joint 2 Base The KC has 4 degrees of motion since there are 4 rotating joints An object in a plane has only 3 dof (two positions + one angle) 4-3 3 = 1). Therefore this KC is redundant (redundancy 4 If the task requires only the object positioning, with no particular constraint on orientation, i t ti the th dof d f will ill reduce d tto 2 and d th the redundancy d d increases i to t 4-2=2 42 2 Basilio Bona – DAUIN – Politecnico di Torino 003/23 Often one reads that a robot control is able to manage, e.g., 8 dof. This sentence should be correctly understood, since it means that the robot is able RO OBOTIC CA – 01CFIDV 02CFIC CY to control 8 degrees of motion. In the example below the robot has 5 dof and 5 dom, and the additional 3 dom on the rotating fixture are useful only for part machining. The task on parts on the rotating fixtures requires 5 or 6 dof. Example E l off a robot b t with ith a slave l rotating t ti fixture fi t with additional degrees of motion Basilio Bona – DAUIN – Politecnico di Torino 003/24 In this example the robot has 5 dom, + 1 of the translating base + 2 of the two otat g fixtures. tu es rotating RO OBOTIC CA – 01CFIDV 02CFIC CY In total 5+1+2=8 dom, and the task maybe 5 or 6 dof Robot with a translating base Basilio Bona – DAUIN – Politecnico di Torino 003/25
