Force estimation with Luenberger-Sliding observers

Two lines are showed in the upper image of this video. In blue, the estimated total force and in red, the measured force. This video shows how the Luenberger-Sliding observer manages to estimate external forces during a compression task.

Sliding observers are a special application of the first developed sliding control. This type of control is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous signal that forces the system to “slide” along a cross-section of the system’s normal behaviour.

The state-feedback control law is not a continuous function of the time and it can switch between two different continuous functions depending on the state of the system’s variables. The motion of the system is designed so that in each of the zones the system moves towards the adjacent region with a different control structure and so the ultimate trajectory will not exist entirely within one control structure. It is said that the system will slide along the boundaries of the control structures. This movement is called sliding mode and the geometrical locus consisting of the boundaries is called the sliding hyper-surface.

During a  experimental test, the KRAFT manipulator was commanded to different poses carrying an elastic interface and the ATI force/torque sensor between the interface and the last link. The objective of this test is to validate my force estimation approach based on Luenberger-Sliding observers and to extract conclusions. During this test the robot was moved in free space by a human operator. At intermediate points of its trajectory the robot was forced to compress the spring against the horizontal surface.

During the development of this work, it was found that the only use of a Luenberger observer does not provide accurate results when the robot model is not perfectly known, which most of the cases are. Real tests were implemented on the Kraft manipulator, showing that incorrect torque offsets were performed when the model was not perfectly known. The inaccuracies found when implementing only Luenberger observers (I will show them in a future post) led my research through the search of a more robust estimator which was not affected in such a way by the modelling errors. The sliding observers were found to be an extremely effective solution with easiness of implementation.  The main disadvantage of this observer was the chattering action which provoked a switching around the zero torque which created a high level of noise. This chattering action was corrected with a coefficient depending on the value of the Luenberger observer in a way that the Sliding strength was made softer when less external forces were observed and stronger when they become bigger. This proposed solution gave good results allowing the Sliding action to reduce the offset error almost totally with minimum chattering.

One can appreciate big differences with respect the basic version of the observer. Offsets and unmodelled torques have almost disappeared, resulting on a clearer shape. The main difference between the two observers presented here lies in the correct estimation during absence of external forces. No offset forces are estimated for Luenberger-Sliding which however tend to appear without the sliding action.

During the tests performed based on spring compression, the average error on force estimation during the impact was 7% for Luenberger and 10% for Luenberger-Sliding. The direct comparison is not totally fair since the offset errors on the Luenberger observer tend to decrease the error observed during the impact, i.e. the estimation is moved upwards. Thus, good results have been achieved and a promising solution has been identified to be used as a force estimator.