Question

HW 12 problem 1part b and c once you find the Psimp(t,t) matrix how does that relate to each of the joint angles? Since Psimp(t,t) is a 3x8 matrix. I see that a=Psimp(t,t)*[pi;pv;pf]

Answer 1

Yes that last part is right. Using that equation for each of the joints, you can figure out the coefficients of your cubic polynomial. So in the equation you wrote above\[a = \left(\begin{matrix}a_0 \\ a_1\\a_2\\a_3\\b_0\\b_1\\b_2\\b_3\end{matrix}\right)\]

Answer 2

Would pv be considered the halfway point?

Answer 3

Yes pv is the waypoint. In this case, it's the point at t=2.5

Answer 4

Do I use the bo, b1, b2 b3 terms for anything?

Answer 5

Yes. There is a cubic trajectory that goes from ge(0) to ge(2.5) and another cubic trajectory that goes from ge(2.5) to ge(5). The first one uses a0-a3. The second one uses b0-b3

Answer 6

So it is going to be like a piece wise function?

Answer 7

Yes.