Wheeled Mobile Robot Introduction - 1 PDF

General Introductions Mechatronics Applications2 Lecture No. 1 Dr. Eng. Essa Alghannam March 2024 Ph.D. Degree in Mechatronics Engineering  Syllabus Mobile robot (differential – omniwheels & mecanum – Car Like Robot)...

General Introductions Mechatronics Applications2 Lecture No. 1 Dr. Eng. Essa Alghannam March 2024 Ph.D. Degree in Mechatronics Engineering  Syllabus Mobile robot (differential – omniwheels & mecanum – Car Like Robot) Path planning (A* – Dijkstra – PF ) Motion control using Cosine switch control Driving DC motors with encoder (PID) Tishreen University Dr. Eng. Essa Alghannam  PROJECT (60) 3 STUDENTS Collaboration Individual accountability Keep your plan realistic Prepare a project timeline Divide the project into tasks, and tasks into subtasks Write, write and write (TEMPLATE) Be creative Tishreen University Dr. Eng. Essa Alghannam Tishreen University Dr. Eng. Essa Alghannam  What To Look For Your Project Number and Types of Wheels - chassis Payload: How much weight the robot can lift. Speed: How fast the robot can position. This depends on the speed of the motors used. Acceleration: How quickly a robot can accelerate. Environment dimension: This is the region of space a robot can reach. Electrical study. (battery – circuits – sensors - micro controller – sch and pcb) Accuracy- Repeatability Tishreen University Dr. Eng. Essa Alghannam  Degree of freedom Degree of freedom (also called the mobility M) of a system can be defined as: Degree of Freedom the number of inputs which need to be provided in order to create a predictable output; also: the number of independent coordinates required to define its position. In general, the term Degrees of Freedom (DOF) is used to describe the number of parameters needed to specify the spatial pose of a rigid body or system. Tishreen University Dr. Eng. Essa Alghannam  Where is the box? Where is the car? Attach a reference local frame on car (𝐱, 𝐲, 𝛟) describes location A rigid body moving in 2d space has: 3 equations and 6 unknowns ⇒ 3 free A rigid body moving in 3d space has: parameters 3 equations and 9 unknowns ⇒ 6 free parameters 2 parameters for position x, y 3 parameters for position x, y, z 1 parameters for orientation 3 parameters for orientation Tait–Bryan angles or Euler Tishreen University Dr. Eng. Essa Alghannam  Mobility The fixed body has zero degrees of freedom relative to itself. The free body has 6 degrees of freedom in 3D space. The free body has 3 degrees of freedom in 2D space. Consider a system of n nonconnected rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. include the fixed body: the count of bodies is n+1 Mobility is independent of the choice of the body that forms the fixed frame. Then the degree-of-freedom of the unconstrained system of N = n + 1 is Tishreen University Dr. Eng. Essa Alghannam  Motion Constraints A rigid body moving in 3d space has 6 degrees of freedom BUT Joints (kinematic pair) that connect bodies in this system remove degrees of freedom and reduce mobility. Tishreen University Dr. Eng. Essa Alghannam  Gruebler’s Formula or the Mobility Formula The mobility formula counts the number of parameters that define the configuration of a set of rigid bodies that are constrained by joints connecting these bodies. Anytime there is a joint connecting two rigid Planar movement bodies the number of parameters goes down by: Spatial version: Two if the joint is 1 dof One if the joint is 2 dof Zero if the joint is 3 dof N: the number of links (including the fixed link). 𝑗: the number of joints. fi : DOF of joint i. Tishreen University Dr. Eng. Essa Alghannam  Planar movement where: M = degree of freedom or mobility L = number of links J1 = number of 1DOF (full) joints J2 = number of 2 DOF (half) joints Spatial version: Kutzbach mobility equation for spatial linkages A one-freedom joint removes 5 DOF, a two-freedom joint removes 4 DOF, etc. Grounding a link removes 6 DOF. Tishreen University Dr. Eng. Essa Alghannam Tishreen University Dr. Eng. Essa Alghannam  M=3(3-1)-2*0-1 M=3(3-1-1)+2 Tishreen University Dr. Eng. Essa Alghannam  M=3(8-1-10)+10 M=3(8-1)-2*10-0 Tishreen University Dr. Eng. Essa Alghannam  M=3(6-1-8)+9=0 M=3(6-1)-2*7-1 Tishreen University Dr. Eng. Essa Alghannam Tishreen University Dr. Eng. Essa Alghannam Tishreen University Dr. Eng. Essa Alghannam Tishreen University Dr. Eng. Essa Alghannam Tishreen University Dr. Eng. Essa Alghannam Tishreen University Dr. Eng. Essa Alghannam  End-effector configuration End-effector coordinate SE(3): 3D Transformations. The group of all transformations in the 3D Cartesian space is. (SE: special Euclidean group). Transformations consist of a rotation and a translation. Roll, pitch yaw Tishreen University Dr. Eng. Essa Alghannam  They are described as: Translational Moving forward and backward on the X-axis. (Surge) Moving left and right on the Y-axis. (Sway) Moving up and down on the Z-axis. (Heave) Rotational Tilting side to side on the X-axis. (Roll) Tilting forward and backward on the Y-axis. (Pitch) Turning left and right on the Z-axis. (Yaw) Tishreen University Dr. Eng. Essa Alghannam  Describes the robot end effector poses Describes the joint coordinates of the robot The robot has two kinds of degrees of freedom: The degree of freedom of configuration space and it is equal to the number of joints the robot has. The dimension of configuration space. The degree of freedom of task space is equal to dimension of task space 2D : 3 (x,y,angle) 3D : 6 (x,y,z,3 angles) Tishreen University Dr. Eng. Essa Alghannam  In 3d space: A robot that has mechanisms to control all 6 physical DOF is said to be holonomic. A robot with fewer controllable DOF than total DOF is said to be non-holonomic, and a robot with more controllable DOF than total DOF (such as the robot snake) is said to be redundant. Tishreen University Dr. Eng. Essa Alghannam  Rotation about Cartesian axes - about z axe the coordinates of a point relative to the new effector coordinate system the coordinates of a point relative to the old coordinate z1 z system  →x1 → y1 → → z1 → →  x. x z1. x  − s x 1 y1. x   x  x1   c 0   x1   → → → → → →  y  = 1R  y  =  s 0   y1  z1. y  c y1 0 R = y x1. y   0  1   1 y1. y   z → → → → → →   z   z1   0 0 1   z1  Ɵ  x1. z y1. z z1. z  90-Ɵ y   Ɵ → → → → → → x1. x = 1.1.c− = c y1. x = c− ( +90− + ) = − s z1. x = 0 x → → x1 → → → → x1. y = 1.1.c90− = s z1. y = 0 y1. y = c− = c → → → → x1. z = 1.1c90 = 0 → → z1. z = 1 y1. z = 0 ci − si 0 0 x = x1c − y1s + 0.z1   Rot ( z ,i ) =  i y = x1s + y1c + 0.z1 s ci 0 0 0 1 0 z = 0.x1 − 0. y1 + 1.z1  0  Tishreen University Dr. Eng. Essa Alghannam  0 0 0 1   1 0 0 0  c i 0 s i 0 ci − si 0 0 0 c − si 0      Rot ( x,  i ) =  Rot ( y,  i ) =  i 0 1 0 0 Rot ( z ,i ) =  i s ci 0 0 0 s 0  − s 0 0  ci   i 0 c i  0 1 0   i 0 0 0 1   0 0 0 1   0 0 0 1  Recall that rotation matrices are orthogonal therefore Tishreen University Dr. Eng. Essa Alghannam ‫انتهت المحاضرة‬