Maricela Figueroa

Inverse kinematics of a mobile robot

The problem of kinematics is to describe the motion of the robotic system without consideration of the forces and torques causing the motion. This paper presents two methods to obtain the inverse kinematics of a mobile robot. In the first method, two rows of the forward kinematics are selected, the inverse of these two rows is obtained, and later the inverse matrix is combined with the third row of the forward kinematics. In the second method, the pseudo-inverse matrix of the forward kinematics matrix is obtained. The comparison result of the two proposed methods is presented. Two simulations show the effectiveness of the proposed inverse kinematics algorithm.

Robust fault diagnosis of disturbed linear systems via a sliding mode high order differentiator

A fault estimator for linear systems affected by disturbances is proposed. Faults appearing explicitly in the state equation and in the system output (actuator faults and sensor faults) are considered. With this design neither the estimation of the state vector nor the estimation of the disturbances is required, implying that the structural conditions are less restrictive than the ones required to design an unknown input observer. Furthermore, the number of unknown inputs (faults plus disturbances) may be greater than the number of outputs. The faults are written as an algebraic expression of a high-order derivative of a function depending on the output. Thus, the reconstruction of the fault signals is carried out by means of a sliding mode high-order differentiator, which requires the derivative of the faults to have a bounded norm.

An observer with controller to detect and reject disturbances

In this paper, a novel states observer is designed. This observer not only estimates the states, but also detects the disturbances by creating estimated signals. Then, both the observed states and detected disturbances are used in a control law to reject the disturbances, avoiding the requirement to know the states and disturbances. The observer is designed by the combination of the poles assignation and geometric techniques. Both the observer and controller work simultaneously. The proposed method is applied in an active suspension system and a liquid-level hydraulic system.

Dynamic model with sensor and actuator for an articulated robotic arm

In this paper, the dynamic model with sensor and actuator for the articulated robotic arm is obtained by using the combination of the structural, the sensor, and the actuator dynamic models. The proposed approach is validated comparing the simulation results against the experimental results.

Quadratic optimal controller to stabilise symmetrical systems

ABSTRACT In this paper, we design a controller for stabilising a control system. The technique used for designing the controller includes a linear regulator and an asymptotical observer which form the controller. The linear regulator designed is a feedback of estimated states and also it must minimise a quadratic performance index. The gain matrix of optimal feedback is obtained by solving the Riccati equation, whilst the gain observer matrix is computed by making use of symmetrical systems properties. The properties of symmetrical systems allow us to find the optimal gain matrix of the observer without solving the dual Riccati equation, we only need to compute the matrices of controllability and observability. Having calculated the gain matrices of regulator and of observer, we proceeded to compute the transfer function of the observer-based controller.

Quasipolynomials and the structure at infinity of linear systems with delay

In this paper is studied the structure at infinity of linear systems with delays and the transfer function is expressed as a quotient of quasipolynomials. To know the behaviour at infinity of the transfer function is studied the location of the roots of quasipolynomials in the extended complex plane. It also explores the concept of zero at infinity of a rational function, since the structure at infinity is related to the zeros at infinity of the transfer function. Subsequently, there is an application to the problem of disturbance rejection.