Admittance controller for an operational point wrt to a force sensor. It can be a point of the model (hand) or not (created operational point: an object in the hand of the robot) Which is closed to a force sensor (for instance the right or left wrist ft)
Simple test: the task is defined to be e_2 = .5 . e'.e, with e the mother task. The jacobian is then J_2 = e'.J, J being the jacobian of the mother task
The goal of this entity is to ensure that the maximal torque will not be exceeded during a grasping task. If the maximal torque is reached, then the current position of the gripper is kept
Integrates an ODE. If Y is the output and X the input, the following equation is integrated: a_p * d(p)Y / dt^p + .... + a_0 Y = b_m * d(m)X / dt^m + ... . b_0 X a_i are the coefficients of the denominator of the associated transfer function between X and Y, while the b_i are those of the numerator
Integrates an ODE using a naive Euler integration. TODO: change the integration method. For the moment, the highest derivative of the output signal is computed using the previous values of the other derivatives and the input signal, then integrated n times, which will most certainly induce a huge drift for ODEs with a high order at the denominator
![\[ g(e) = a \frac{\tanh(-b(||e|| - d)) + 1}{2} + c \]](form_63.png)