The Denavit-Hartenberg (DH) parameters are a set of four parameters used to
describe the kinematics and geometry of a rigid body in robotics. They were
introduced by Jacques Denavit and Richard Hartenberg in the 1950s.
The DH parameters consist of:
1. The length of the link, denoted by "d", which is the distance between two
consecutive joints along the z-axis.
2. The twist angle, denoted by "θ", which is the angle between two consecutive
links measured about the z-axis.
3. The offset, denoted by "a", which is the distance between the two consecutive
joints along the x-axis.
4. The joint angle, denoted by "α", which is the angle between two consecutive
links measured about the x-axis.
By specifying the DH parameters for each joint in a robot arm, it is possible to
compute the position and orientation of the end effector of the arm with respect to a
fixed reference frame. This is useful for controlling the motion of the robot and
planning its trajectory.
Forward kinematics analysis is a method used in robotics and biomechanics to
determine the position and orientation of an end effector (the part of a robotic
system that interacts with the environment) given the joint angles and lengths of the
system's links.
In other words, forward kinematics calculates the position and orientation of a
robot's end effector based on the angles and lengths of its joints. This analysis is
essential in robotics for planning and control of motion, as it helps to determine the
required movements of each joint to achieve a desired end effector position and
orientation.
Forward kinematics is often used in conjunction with inverse kinematics, which is the
opposite problem of determining the joint angles required to achieve a desired end
effector position and orientation.
The Newton-Euler approach, also known as the Newton-Euler equations of motion, is
a mathematical method used to compute the motion and forces of a rigid body or a
mechanical system. It is named after Sir Isaac Newton and Leonhard Euler, two
prominent mathematicians who made significant contributions to the field of
classical mechanics.
The Newton-Euler approach is based on Newton's second law of motion, which
states that the acceleration of an object is directly proportional to the net force
acting on it and inversely proportional to its mass. The approach uses a set of
equations that relate the forces, moments, and motion of a rigid body to each other,
allowing engineers and scientists to analyze and predict the behavior of mechanical
systems.
The key idea behind the Newton-Euler approach is to use a set of recursive equations
that relate the acceleration, velocity, and position of a body to the forces and
moments acting on it. These equations, known as the recursive Newton-Euler
equations, can be used to compute the motion and forces of a mechanical system
given the external forces acting on it and the inertial properties of its components.
The Lagrange-Euler approach, also known as the Lagrangian mechanics, is a
mathematical framework used to model the motion of mechanical systems in physics
and engineering. It is based on the principle of least action, which states that the
path taken by a system between two points in time is the one that minimizes the
action (the integral of the Lagrangian over time).
In robotics, the Lagrange-Euler approach is often used in joint space to derive the
equations of motion for a robot manipulator. The approach uses the Lagrangian,
which is the difference between the kinetic energy and the potential energy of a
system, to derive the equations of motion.
To use the Lagrange-Euler approach in joint space, the following steps are typically
followed:
1. Define the Lagrangian of the system, which is the difference between the
kinetic energy and potential energy of the robot manipulator.
2. Derive the Euler-Lagrange equations of motion, which are a set of secondorder differential equations that describe the dynamics of the system.
3. Use the Euler-Lagrange equations to solve for the joint torques required to
achieve a desired motion or trajectory.
A proportional–integral–derivative controller (PID controller or three-term controller) is
a control loop mechanism employing feedback that is widely used in industrial control
systems and a variety of other applications requiring continuously modulated control. A PID
controller continuously calculates an error value
as the difference between a
desired setpoint (SP) and a measured process variable (PV) and applies a correction based
on proportional, integral, and derivative terms (denoted P, I, and D respectively), hence the
name.
A PID controller is a type of feedback controller commonly used in engineering and
control systems to regulate and control a process or system. The name PID stands for
Proportional-Integral-Derivative, which refers to the three terms that make up the
controller.
The proportional term of a PID controller is proportional to the current error, which is
the difference between the desired setpoint and the current value of the process
variable. The proportional term produces an output that is directly proportional to
the error, and it is used to adjust the control input in proportion to the error.
The integral term of a PID controller is proportional to the accumulated error over
time. This term helps to eliminate steady-state error, which is the difference between
the setpoint and the actual value of the process variable when the error is zero. The
integral term produces an output that is proportional to the integral of the error over
time, and it is used to correct for slow changes in the process.
An Omni robot is a type of mobile robot that uses omni-directional wheels or
holonomic wheels to move in any direction without changing the orientation of the
robot. The wheels used in an Omni robot are typically arranged in a triangular or
square pattern to provide stability and maneuverability.
The working principle of an Omni robot is based on the differential drive system.
Each wheel of the robot is independently controlled by a motor and can rotate in any
direction, allowing the robot to move in any direction and rotate in place.
To control the movement of an Omni robot, a control system is used to calculate the
required speed and direction of each wheel based on the desired motion of the
robot. This control system can be implemented using various methods, including PID
controllers, fuzzy logic, or neural networks.
In an Omni robot, the control system calculates the required speed and direction of
each wheel based on the desired motion of the robot. The speeds of the wheels are
adjusted using the differential drive system to achieve the desired motion, such as
moving forward, backward, or sideways, or rotating in place.
Omni robots are commonly used in applications that require precise and agile movement,
such as in warehouses, hospitals, or research facilities. They are particularly useful for
navigating in narrow spaces or confined areas where traditional wheeled robots may have
difficulty maneuvering.
Robotics is an applied engineering science
that has been referred to as a combination
of machine tool technology and computer
science. It includes machine design,
production theory, micro electronics,
computer programming & artificial
intelligence.
Mechatronics, is an interdisciplinary
branch of engineering that focuses
on the integration of mechanical,
electrical and electronic engineering
systems, and also includes a
combination of robotics, electronics,
computer science,
telecommunications, systems,
control, and product engineering.