# Can a Jacobian matrix be used to derive joint angles from end-effector linear and rotational velocity (without a filter)?

I have a 2-link, 2 degree of freedom robotic arm, that only measures linear acceleration at each link(through an accelerometer), and rotational velocity on each joint (through a gyroscope).

I know that through using the Jacobian matrix, I can compute link velocity and acceleration from joint angles, and through the inverse of the matrix I can compute joint velocities from joint angles and link acceleration.

However, I am not sure if I can compute joint angles using only the link linear and rotational acceleration? I am aware that the joint angle could be estimated by integrating the joint velocities (and applying some sort of filter), but is there an algebraic way this can be computed? It doesn't seem likely to me.

Joint angles can be determined by looking at the gravity vector of each accelerometer.

The paper Low-cost Accelerometers for Robotic Manipulator Perception by Morgan Quigley, Reuben Brewer, Sai P. Soundararaj, Vijay Pradeep, Quoc Le, and Andrew Y. Ng describes exactly what you are attempting to accomplish.

• Thanks for the paper, I will look into that (although I was trying to avoid filters, but it looks like that might not be possible). By looking at the gravity vector, do you mean the arctangent equations here (robotics.stackexchange.com/questions/4677/…)? Commented May 11, 2015 at 12:43
• A 3 axis accelerometer just sitting on the desk will return 1g straight down.
– Ben
Commented May 13, 2015 at 14:14
• Yes, I understand, find the components of the acceleration vector (when its stationary). Commented May 13, 2015 at 15:54