This is an excellent and informative presentation. It is one of the clearest, most accurate and complete treatments of the kinematics of the various wheeled vehicle configurations that I have seen. Once one understands the kinematics, it is straightforward to arrive at a kinematic analysis of other configurations. (Omni wheels, for example.)
Thanks for the wonderful presentation. Yet there are few remarks to mention: At 26:06 (, Forward Kinematics), y(t) should be equal to the integral of v(t)Sin(theta.t). Also, why the robot position is computed according to ICC and not directly from x(t) to x(t+1)? I think the R matrix needed more explanation.
Hi, Could some tell me what does the R in 26:28 mean? There is no any notation on the slide so I'm a bit confused. The only thing I'm sure is that R is either a scalar or a 2*2matrix. Thanks!
R is a rotation matrix around the z axis. Just google it. You'll find that this matrix has dimension 3x3 with real numbers. r11 = cos(w·deltaT), r12 = -sin(w·deltaT), r13 = 0, r21 = sin(w·deltaT), r22 = cos(w·deltaT), r23 = 0, r31 = 0, r32 = 0, r31 = 1. The slides are using vector notation. So the term (w·deltaT) represents the rotation around a z-axis that passes through the ICC with the positive direction going from the video towards your eyes (Use the right hand ruleS to determine positive/negative directions and positive/negative rotations). First, a vector subtraction is performed (x_t - x_icc, again in vector form), so the reference coordinate frame from which you are applying the rotation (w·deltaT) is located at the ICC. Then the rotation around the mentioned z-axis is done, a finally you add the vector x_icc again to express the result, vector x_t+1, with respect the coordinate frame world. Hope this explanation helps.
