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.
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.)
Thank you soo much. I am wishing to hear more from you
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.
Very helpful content
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.
Shouldn't R be a 2D Rotation Matrix. Row 1 should have cos and -sin and Row 2 sin and cos terms.