# PageControlAlgorithms The robot is a complex polyarticulated and motored system. In robotics we genrally need to control the position of each articulation through a convenient plnned tool trajectory. Position control loops are responsible to make the measred position cosed to the target position.

Hence, we need at least the follwing components:

• Position control loop
• Trajectory calculator

### Control loop

The position control loop is the chosen regulator that uses the measred position and computes the control value to make it close to the position target. This is called the control algorithm.

Basic controllers
The basic controllers can be as simple as the P, PD or PID controllers. The PID controller is  the simplest and the easiest controller to implement.

• The proportional parameter Kp, improves the system dynamic and the stiffness of the controller,
• The derivative parameter Td improves the damping and contributes to avoid the response overshoot,
• The integral parameter Ti assures the static error cancellation and makes the stiffness higher.

Controllers based on the dynamic models
1-Precomputed Feedforward controller

A lot of controllers are available an allows the improvement of the control performances. Most of these controllers are model based. The most known and used controller is the precomputed feedforward torque controller. We precompute the the corresponding torque with respect to the actual trajectory point (position, velocity and acceleration) and we use the obtained value with conjunction with a differential closed loop control value (figure below).

Here is the genralized expression of the inverse dynamic model Here is the principle of a precomputed feedforward torque controller :

In open-loop we will have the following control scheme : In closed-loop we will have the following control scheme : 2-Decoupling nonlinear linearizin controller

The concept of the nonlinear linariing controller is to compensate the entire non linearities in order to obtain a linear input-output trasfert. This linear transfert is as simple as double integrators for each articulation.

Computation summary:  3. Non linear sliding mode control

(to be completed soon)

4. Non linearizing control with perturbation estimation

(to be completed soon)