i am trying to find the inverse kinematics for quadrotor with 2Dof robotic arm, which has first joint rotation axis perpendicular with second joint. So, for the inverse kinematics i use two equations
theta 1 = atan2(z,y)
theta 2 = atan2(x, (sqrt(z^2 + y^2)-L1)), where x,y,z are end effector position
If I use these two solution in jacobean matrix for finding the joint velocities: thetadot = pinv(J)*(x,y,z)dot, at some point i have singular configuration. For finding the determinent of jacobean matrix, i consider the the determinant of the (J'*J) because my jacobean is a 3 * 2 matrix.
So my questions are
- are two equations for finding theta 1 and theta 2 correct?
- how can I avoid the singular configuration?
- when the jacobean matrix is zero, how can i find the joint velocities?