Applications of Robust Descriptor Kalman Filter in Robotics

In this chapter we are interested in designing estimators for the internal variables of two kind of robots, wheeled mobile and robotic leg prosthesis, based on a recently developed robust descriptor Kalman filter. The proposed approach is reasonable since descriptor formulation can cope with algebraic restrictions on system’s signals. Further, the recursiveness of this class of filter is useful for on-line applications. Different procedures have been used to deal with mobile robots localization problem. Measurement systems based on odometric, inertial sensors and ultrasounds are selfcontained, simple to use, and able to guarantee a high data rate. However, the problem of these systems is that they integrate the relative increments, and the localization errors considerably grow over time if an appropriate sensor fusion algorithm is not used, see for instance [17], [18] and references therein. The examples developed in these references do not take into account robust approaches, in the line we are proposing here. In the context of robotic leg prosthesis, we deal with the development of devices for above knee amputees. Robotic prosthesis are devices intended to replace parts of the human body. They should be able to sense the environment and complain with the movement of the body in such a way to aid the user to perform the most common tasks. This is a very interesting and current research topic [7]. Environment sensing is one of the most difficult tasks, mainly in the case of leg prosthesis because of the great diversity of walking conditions and terrains. The use of Electromyographic (EMG) signal processing for detecting the main properties of the walking terrain is the focus of [15]. However, in the case of above knee prosthesis, there is no EMG signal available to allow automatic reorientation of the robotic foot. When the foot of a robotic leg is not in contact with ground, its configuration should be estimated to allow its control with respect to ground. This can be useful for controlling its orientation, mainly in the end of phase where the foot is not in contact with ground. In this chapter, it is shown a solution for this problem using multisensor data fusion by a robust descriptor Kalman filter. This chapter is divided in three main parts. In the first part we present basic definitions and concepts of descriptor systems and some examples to clarify the use of this kind of approach. In the second part we present three algorithms for the computation of the O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg