Three Wheeled Omnidirectional Robot : Motion Analysis

A Three-wheeled omnidirectional robot is capable to moving in any given direction without rotating by giving velocities to the three wheels in a certain ratio.
All motors are situated at an angle of 120 degrees from each other.
fB , fL , fR  are for back , left and right wheel respectively. ax and ay are accelerations in XR and YR axis in Robot frame and w is the angular velocity in Robot frame.

Hence putting the values of alpha and making it into a matrix form we get :
As we need to obtain the f values, we will invert the matrix.
We need  ax , ay and w is the world frame, so we apply transformation. The transformation angle is  α1 = 30 degrees.
 Putting this in the previous equation,
Multiplying the two matrices, we get the final relation as :
For example, if you want to move the robot along X axis(world frame), put 
axW = 1 ,
ayW = 0 ,
w = 0
You will get the ratio of velocities as : 1 : -2 : 1 .
Which means if you give 1 unit velocity to left wheel (forward) , 2 unit velocity to back wheel (backwards) and 1 unit velocity to right wheel (forward), the robot will move along X axis.

Comments

Post a Comment

Popular posts from this blog

The move_base ROS node

Image
move_base package provides the move_base node which is a major element of ROS Navigation stack. It moves the robot from its current position to a goal position. When path planning is done, the user gives uses the 2D Nav Goal in RVIZ to specify the goal position and orientation. This position (x,y,z) and orientation(x,y,z,w) are actually published in move_base/goal topic. The move_base node links together a global and local planner to accomplish its global navigation task. The Global Planner It is in charge of calculating the safe path in order to arrive at goal pose. Note that the path is calculated before the robot starts moving so it will not take into account the laser readings while moving i.e. unscanned obstacles that are not in the map. Navfn Planner The Navfn planner is the most commonly used global planner for ROS Navigation. It uses Dijkstra's algorithm in order to calculate the shortest path between the initial pose and the goal pose. Carrot Planner This plann...
Read more

Overview of ATmega328P

Image
While reading about the ATmega328, I came a across a lot of stuff which I would like to share here. There is a humongous amount of information available in its datasheet. Introduction ATmega328 is a single chip micro-controller created by Atmel. It has a In-System Self-programmable Flash memory of 32 KB, SRAM of 2 KB (2048 bytes) and EEPROM of 1 KB (1024 bytes). It has a 8-bit AVR CPU type which means they can process data in 8-bit chunk as its data bus is 8-bit wide.   It contains 23 general purpose I/O pins and 32 general purpose working registers. It has 32 single-byte registers and 8-bit RISC (reduced instruction set computer) devices and hence the name 328. The P is for ' picoPower '. It has 3 flexible timer/counter with compare modes, internal and external interupts , 6-channel 10-bit A/D converter , programmable watch dog timer with internal oscillator and 5 software selectable power saving modes. Digital communication peripherals include 1-USART, 2-SPI and 1-...
Read more