Edgar Martínez García

By G. Santos-Medina, K.Y. Heras-Gaytán, E.A. Martínez-García, R. Torres-Córdoba and V. Carrillo-Saucedo

This chapter discusses the design and modelling of a spherical flying robot. The main objective is to control its hovering and omnidirectional mobility by controlling the air mass differential pressure between two asynchronous coaxial rotors that are aligned collinearly. The spherical robot design has embedded a gyroscopic mechanism of three rings that allow the rotors’ under-actuated mobility with 3DOF. The main objective of this study is to maintain the thrust force with nearly vertical direction. The change in pressure between rotors allows to vary the rotors’ tilt and pitch. The system uses special design propellers to improve the laminar air mass flux. A nonlinear fitting model automatically calibrates the rotors’ angular speed as a function of digital values. This model is the functional form that represents the reference input to control the rotors’ speed, validated by three types controllers: P, PI, and PID. The robot’s thrust and induced forces and flight mechanics are proposed and analysed. The simulation results show the feasibility of the approach.

Part of the book: Robot Control

By Jorge U. Reyes-Muñoz, Edgar A. Martínez-García, Ricardo Rodríguez-Jorge and Rafael Torres-Córdoba

This work presents the mechanical design and the kinematic navigation control system for a tricycle-wheeled robot (one drive-steer and two lateral fixed passive) with two underactuated mechanisms: a global compass and local evasive compass. The proposed goal-reference mechanism is inspired by the ancient Chinese south-seeking chariot (c. 200–265 CE) used as a navigation compass. The passive lateral wheels transmit an absolute angle from its differential speeds to automatically steer the front wheel. An obstacle-evasive compass mechanism is commutated for steering control when detecting nearby obstacles. The absolute and local compass mechanisms commutate each other to control to the robot’s steering wheel to reach a goal while avoiding collisions. A kinematic control law is described in terms of the robot’s geometric constraints and is combined with a set of first-order partial derivatives that allows interaction between the global and local steering mechanisms. Animated simulations and numerical computations about the robot’s mechanisms and trajectories in multi-obstacle scenarios validate the proposed kinematic control system and its feasibility.

Part of the book: Kinematics

By Edgar Alonso Martínez-García and Luz Abril Torres-Méndez

This chapter presents a four-wheel robot’s trajectory tracking model by an extended Kalman filter (EKF) estimator for visual odometry using a divergent trinocular visual sensor. The trinocular sensor is homemade and a specific observer model was developed to measure 3D key-points by combining multi-view cameras. The observer approaches a geometric model and the key-points are used as references for estimating the robot’s displacement. The robot’s displacement is estimated by triangulation of multiple pairs of environmental 3D key-points. The four-wheel drive (4WD) robot’s inverse/direct kinematic control law is combined with the visual observer, the visual odometry model, and the EKF. The robot’s control law is used to produce experimental locomotion statistical variances and is used as a prediction model in the EKF. The proposed dead-reckoning approach models the four asynchronous drives and the four damping suspensions. This chapter presents the deductions of models, formulations and their validation, as well as the experimental results on posture state estimation comparing the four-wheel dead-reckoning model, the visual observer, and the EKF with an external global positioning reference.

Part of the book: Applications of Mobile Robots

By Santiago de J. Favela Ortíz and Edgar A. Martínez García

This work discloses a kinematic control model to describe the geometry of motion of a two-wheeled biped’s limbs. Limb structure is based on a four-bar linkage useful to alleviate damping motion during self-balance. The robot self-balancing kinematics geometry combines with user-customized polynomial vector fields. The vector fields generate safe reference trajectories. Further, the robot is forced to track the reference path by a model-based time-variant recursive controller. The proposed formulation showed effectiveness and reliable performance through numerical simulations.

Part of the book: Motion Planning