Joaquim A. Batlle

Consistent triangulation for mobile robot localization using discontinuous angular measurements

Localization is a fundamental operation for the navigation of mobile robots. The standard localization algorithms fuse external measurements of the environment with the odometric evolution of the robot pose to obtain its optimal estimation. In this work, we present a different approach to determine the pose using angular measurements discontinuously obtained in time. The presented method is based on an Extended Kalman Filter (EKF) with a state-vector composed of the external angular measurements. This algorithm keeps track of the angles between actual measurements from robot odometric information. This continuous angular estimation allows the consistent use of the triangulation methods to determine the robot pose at any time during its motion. The article reports experimental results that show the localization accuracy obtained by means of the presented approach. These results are compared to the ones obtained applying the EKF algorithm with the standard pose state-vector. For the experiments, an omnidirectional robotic platform with omnidirectional wheels is used.

Holonomy in mobile robots

The search for a simple and accurate odometry is a main concern when working with mobile robots. This article presents a general analysis of the problem and proposes a particular solution to improve the odometry. The three crucial kinematical aspects of mobile robots (mobility, control, and positioning) are reviewed in detail for vehicles based both in conventional and in omnidirectional wheels. The latter case is more suitable from a maneuvering point of view as it provides the robot frame with the three Degrees Of Freedom (DOF) of plane motion without singular configurations. Moreover, a suitable design of the omnidirectional wheels leads to a strictly invariant Jacobian matrix and thus to a linear control equation with constant coefficients. It is shown that such vehicles may have a holonomic behavior when moving under suitable kinematical restrictions without constraining their trajectory. In that case, the odometry is algebraic (instead of integrative) and thus more accurate. An application case is presented.

Mobile robot localization. Revisiting the triangulation methods

Localization is one of the fundamental problems in mobile robot navigation. In this context, triangulation is used to determine the robot pose from landmarks position and angular measurements. The method based on circle intersection is the preferred one because it is independent of the robot heading. Nevertheless, it becomes undetermined when the robot point is on the circumference that contains the landmarks used. To cope with it, a triangulation method based on straight lines intersection is presented in this paper. The robot heading angle, which is needed in this method, can be accurately determined by means of a geometrical procedure. The accuracy of the presented approach is evaluated and compared to that of alternative methods by means of experimental results and computer simulations.

Dynamic positioning of a mobile robot using a laser-based goniometer

Positioning is a fundamental problem in mobile robot navigation. Several approaches to cope with the dynamic positioning problem have been made. Most of them are based on the inconsistent use of the algorithm for static positioning enhanced by predictive algorithms. In this paper, a method that guarantees the consistent use of this algorithm at any time under dynamic condition is presented. It combines vehicle kinematics and laser-based goniometer data for real time simulation of the evolution of the straight lines between the laser-based goniometer and the set of artificial landmarks used.

Localization of a Mobile Robot With Omnidirectional Wheels Using Angular Kalman Filtering and Triangulation

Localization is one of the fundamental problems in mobile robot navigation. Several approaches to cope with the dynamic positioning problem have been made. Most of them use an extended Kalman filter (EKF) to estimate the robot pose –position and orientation– fusing both the robot odometry and external measurements. In this paper, an EKF is used to estimate the angles, relative to the robot frame, of the straight lines from a rotating laser scanner to a set of landmarks. By using this method angles are predicted, between actual laser measurements, by means of the time integration of its time derivative, which depends upon the robot kinematics. Once these angles are estimated, triangulation can be consistently applied at any time to determine the robot pose. In this work, a mobile robot with three omnidirectional wheels –that consist of two spherical rollers– is considered. Computer simulations showing the accuracy of this method are presented.

Calibration for mobile robots with an invariant Jacobian

The kinematics of some mobile robots is described through a strictly invariant Jacobian matrix [J]. This is the case for robots with three degrees of freedom and suitable omnidirectional wheels, and that for robots with conventional wheels and differential kinematics. This article proposes a calibration technique for the matrix [J] of such robots. It is based on four accurate configuration measurements associated with particular nominal motions where the generalized velocities maintain a constant proportional relationship. As a consequence, the nominal trajectories are arcs of circumference and may be part of the actual trajectories of the robot. An application example is presented.

Posicionamiento de Robots Móviles mediante un Filtro de Kalman Angular y Triangulación

En este articulo se presenta un metodo alternativo para solucionar el problema del posicionamiento dinamico de un robot. Se utiliza un filtro de Kalman extendido para estimar en cada instante los angulos, relativos al bastidor de un robot, de las rectas entre un escaner laser rotativo y un conjunto de reflectores. Una tecnica de posicionamiento usual es la que utiliza mediciones angulares de las rectas entre un punto del robot y puntos conocidos del entorno, obtenidas mediante un escaner laser rotativo. A partir de estas mediciones, los algoritmos de triangulacion determinan la posicion y la orientacion del robot movil. El metodo presentado, al prever los angulos entre mediciones reales del sensor laser, garantiza el uso consistente de la triangulacion en cualquier instante en condiciones dinamicas. Los resultados experimentales muestran la precision del metodo propuesto