To calculate the geometric Jacobian at any point on a manipulator, it is essential to understand the role of the Jacobian matrix in robotics. This matrix relates joint velocities to the linear and angular velocities of the end-effector, helping to understand how joint movements affect the end-effector's position and orientation.
Calculating the Jacobian for an arbitrary point that is not part of the robot's kinematic chain or a defined body may lack direct physical significance in terms of controlling or understanding the robot's motion. In control and motion planning, the focus is typically on the velocities at the end-effector or other significant points.
Arbitrary Point Calculation:
- If an arbitrary point is important for a specific task, it can be meaningful to add this point as a body in the model. Compute the Jacobian for the new body to describe how joint movements affect its motion.
Implementation:
Modify the rigid body model by inserting a new body representing the point of interest
For further guidance, refer to the following documentation:
RigidBodyTree:
addBody Method
Hope it helps!
