In this section of the course, we are going to see one of the most important concepts in robotics.
This is the dynamic model of the robot, in our case, robotic manipulators.
So let's get started.
What is the dynamic model of the robot?
The dynamic model of the robot provides us a description of the relationship between joint forces,
alteryx and the motion of the structure, namely position, velocity and acceleration of the robot limbs
and joints.
We can separate two kind of robot dynamic model, namely direct model.
And the inverse model.
What is the direct model?
Indirect modeling?
We have the knowledge of joint talks and joint positions and velocities, and we want to determine the
joint accelerations.
As you can see from the equation, F is nothing but a nonlinear function of joint positions, velocities
and talks of the V foreign joint accelerations.
We can integrate it to find new joint positions and velocities in inverse model.
As the name suggests, we do the opposite of the direct model.
So we are given desired joint positions, velocities and accelerations, and we want to calculate join
talks for forces that must be applied in order to get the desired motion.
These are joint accelerations.
Velocities and positions are obtained by choosing desired trajectory to be tracked.
It will be more clear to you when we see trajectory planning during modelling, we will make some assumptions
in order to simplify the problem.
First of all, we will discard the flexibilities in robot manipulator and accept each part of it as
a rigid body.
Secondly, we will consult the joints almost ideal, so there is no backlash or any other issues, except
we will take into account only joint frictions.
Okay, at this moment, you may ask, or maybe not, why it's interesting for us to get a dynamic model
of the manipulator.
This will be more clear to you further in the course.
But let me briefly give you some points.
First, we use it for simulation of robots, which is very important because the robots are precious
and we want first to simulate them and then apply in the real world.
During simulation, we will need joint positions, velocities and acceleration to provide correct motion
to our robot.
We will need to work to simulate further advanced concepts.
Then we will use the robot dynamic model excessively in design of control algorithms, which we will
see in future topics.
Control algorithms are very fundamental concepts for robotics because in order to do any user field
work with robots, we have to first be able to control them properly.
During this phase, you will see how important is robot dynamic model for us and also for analysis of
manipulator structures.
Because by robot dynamic model, we can get the talks that are induced in joins due to contact forces
with the environment.
Internal stress and Taubes endurance and so on, which are important for us during design phase of gears
drivers and so on.
We can obtain dynamic model of robot by using two very popular methods, namely a little Lagrange and
Newton formulation in Illinois Lagrange mode method.
The robot is considered as a whole, so because of that, we cannot get internal forces and stress in
joints.
But this method is more initiative.
You can inspect and understand physical meaning of each element in the robot dynamic model because model
is obtained analytically.
However, the method is not computationally efficient because you get model in symbolic form and then
do replacements to get a numerical result, which is time consuming in yet a major method.
Each link is considered as a rigid body and by using free body diagram and forward and backward recursion
method, the model is obtained.
However, be careful.
This model is numerical.
Namely, you get numerical results at the end instead of symbolic, as in a little like range method.
Because of that, this algorithm is much efficient.
Additionally, you can get internal forces and stress between each limb.
Howard.
This method of modeling is not initiative in order to grasp the physical meaning of each term.
The last thing I want to note is that while these two methods are completely different, the result
obtained is the same, so you can use either a little grounds or need some method based on the task
requirements.