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letmoon
07-16-2012, 02:45 AM
Hello everyone,

I am working on a middle size (about 40kg) differential drive system. I've already established the kinematics model of it, and now I am continuing work on the dynamics model. Actually, I don't have a good background at physics even the fundamentals. Thus, I felt a little difficult to deal with that. I have some question that I can not answer my self till now. I need your help, and appreciate it very much.

I just think that Kinematics model lets us to operate the robot in a mathematical way. After that had been built, we can drive the robot to move by specifying the velocities in each direction. Thus, it is easy to test that whether a kinematics model is right or not. And it is easy to be build by quoting equations from those published reference papers.

Similarly, it may be easy as well to build a dynamic model of a robot as what we did for the kinematics model, reading papers and quoting equations. However, how can we test a dynamic model? There is one thing that I am wondering. You know, a dynamic model contains the force balance including forces and torques. Thus, I don't know how can I verify it even if we know that we can use a series of correct equations from one paper. Do I need to design a controller? And what is the relationship between kinematics model and dynamics model?

PS: I am using an 3-wheel omnidirectional mobile robot to simulate the 2-wheel differential drive model. It is already a full-fledged robot with APIs. I mean that I need not to do anything for this robot. Thus, what I should do if I want to test a dynamics model of the differential drive system on it.

Thanks very much.

tician
07-18-2012, 12:19 AM
Doing a little copy-paste from a previous response of mine in the "Let's Discuss Kinematics, Shall We?" (http://forums.trossenrobotics.com/showthread.php?3497-Let-s-Discuss-Kinematics-Shall-We) thread that seems appropriate.


<pedantry> Kinematics is the half of dynamics describing just the motion of an object (path of travel and time taken). What you are referring to as 'DYNAMICS' is kinetics, the other half of dynamics which describes the effects of mass (gravity and inertia) and external forces on an object. </pedantry>


When you say kinematics model, I am assuming you mean the relationships between number of rotations of the motor shaft, the distance the wheels will travel, and the distance/rotation the center of the robot will travel (e.g. left motor rotates 64 times with a 64:1 gear train so the "R"-diameter wheel rotates only once, moving the "W" wide bot forward and right some distance while rotating some angle related to the values "R" and "W" using little more than simple geometry/trigonometry).

What I think you are looking for is the kinetics model, which adds additional components to the overall dynamic model. These components include but are not limited to the mass of the bot (how inertia affects acceleration when starting and stopping) and the friction (force transfer) between the wheels and the ground. An IMU might come in handy if you cannot directly measure the torque applied to the wheels, as it will allow you to measure the accelerations experienced by the bot when moving under different control conditions (full speed ahead will give one acceleration value, while half-speed will give another).

I'm a bit sleep deprived, generally messed up in the head, and I haven't used my Mech-E skills in a while, so I'm not entirely sure how you would accurately simulate a differential drive bot with a three omni-wheeled bot. Probably have to scale for the different wheel-bases and add/remove mass on the omni-wheeled bot to match (although the use of omni-wheels does create differences in friction effects versus two plain differentially driven wheels). MIT OpenCourseWare for Dynamics (http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/) might be a good place to start, but might be a bit too much if you have no physics background at all. Still better than looking through random published papers for equations that probably don't make sense in your scenario.

letmoon
09-20-2012, 03:21 AM
Thanks, tician.
Now, I have a generalized dynamic model of the differential drive-type robot. And I found it is just tested by a control algorithm, path following or trajectory tracking, in most of papers. But I don't understand very much about control. Thus, I wonder if there is a simple method which is available for testing a dynamic model.

jwatte
09-20-2012, 12:03 PM
Typically, you use a dynamics simulator. There exist some very high-end models used by car manufacturers and heavy equipment designers. There exist mid-range simulators used for things like movie effects (some are built into tools like 3ds Max or Maya) as well as mechanical design in tools like Inventor or SolidWorks. And there exists low-end systems used for computer games and robotics undergrad classes.

So, you have to first pick the tool to use, and then port your model to that tool. For an example of tools, you might look into the "Bullet Physics" library: http://bulletphysics.org/wordpress/ or the simulation built-into Inventor: http://www.youtube.com/watch?v=504xOZcfcbM
N (http://www.youtube.com/watch?v=504xOZcfcbM)ote that these systems have very specific requirements for how you integrate your model. You may have to transform the form you have your current model in, to the terms used by the simulation. Anything from friction to restitution to flexure of joints is modeled differently in the different packages, and to get results from real-world effects like elastic deformation of your chassis, you may have to push the simpler models outside of their comfort area.