CONTROL DE ROBOTS M ´OVILES MEDIANTE VISI ´ON OMNIDIRECCIONAL UTILIZANDO LA GEOMETR´IA DE TRES VISTAS

This work investigates the topic of visual control of mobile robots. Two elements of particular interest to us within this vast ﬁeld are the use of omnidirectional vision and multiple-view geometric models. Omnidirectional imaging provides very accurate angular information, although it is affected by signiﬁcant distortion in the radial direction, and a wide ﬁeld of view, which is advantageous for robot navigational tasks. Additionally, the geometric models relating different views of the environment allow to reject image feature-matching errors and make the visual control process more robust. We present two visual control techniques to be used on a robot moving on the ground plane. First, we propose a new method for visual homing. The technique employs a reference set of images of the environment previously acquired at different locations and the images taken by the robot during its motion. In order to take advantage of the qualities of omnidirectional vision, we deﬁne a purely angle-based approach, without requiring any distance information. This approach, taking the planar motion constraint into account, motivates the use of the 1D trifocal tensor. The additional geometric constraints enforced by the tensor, which can be computed from point correspondences between three views, improve the robustness of the method in the presence of mismatches. The interest of this proposal is that the designed control scheme computes the robot velocities only from angular information, being this very precise information. In addition, we present a procedure that computes the angular relations between all the views even if they are not directly related by feature matches. This approach can be classiﬁed as image based, given that neither pose estimation nor 3D information are needed. Then, the robot is guaranteed to converge to the target location without knowing the metric information about the trajectory followed. In some applications, such as obstacle avoidance, more information about the 3D motion can be needed. Taking this idea into account, we also present an omnidirectional visual control method based on sinusoidal inputs. We were motivated by the well-known mathematical properties of sinusoids and their smoothness, which makes them particularly suited for parking manoeuvres of car-like vehicles. We derive analytical expressions for the evolutions of the robot’s state variables under the sinusoidal-varying velocities deﬁned in our design, and we propose a state feedback control law based on those expressions. We describe a way to estimate the state of the robot (i.e. its position and orientation) from the 1D trifocal tensor computed between the goal, current and initial views. This sinusoidal-based control aligns the robot with the target; the depth correction is carried out in a second step, in which the control law is deﬁned directly in terms of the elements of the 1D trifocal tensor. The performance of the controllers is illustrated through simulations, and the feasibility of the proposed approaches is supported by the stability analysis and the results from simulations and experiments with real images.