Rafael Torres-Córdoba

Exponential fields formulation for WMR navigation

In this manuscript, an autonomous navigation algorithm for wheeled mobile robots WMR operating in dynamic environments indoors or structured outdoors is formulated. The planning scheme is of critical importance for autonomous navigational tasks in complex dynamic environments. In fast dynamic environments, path planning needs algorithms able to sense simultaneously a diversity of obstacles, and use such sensory information to improve real-time navigation control, while moving towards a desired goal destination. The framework tackles 4 issues. 1 Reformulation of the Social Force Model SFM adapted to WMR; 2 the cohesion of a general inertial scheme to represents motion in any coordinate system; 3 control of actuators rotational speed as a general model regardless kinematic restrictions; 4 assuming detection of features obstacles/goals, adaptive numeric weights are formulated to affect navigational exponential components. Simulation and experimental outdoors results are presented to show the feasibility of the proposed framework.

Dead-reckoning inverse and direct kinematic solution of a 4W independent driven rover

We tackle the problem of trajectory control of a four-wheel driven skid-steering (4WDSS) robotic platform with asynchronous wheels velocity. A practical mathematical formulation for solving inverse and direct kinematics is provided. This approach also includes the formulation and implementation of a home made arrange of accelerometers to infer robot displacements in global coordinates system. Although we provide a direct kinematics solution, we further establish an inverse kinematics formulation using four parameters to exert trajectory control, namely instantaneous linear velocity, angular velocity, and robot Z-turning axes. The formulation for robot angular velocity is given differently from other research approaches, where it is stated in terms of the robots geometry, which directly impacts the robots swift capability. Trajectory control is yielded by controlling the location of the robot turning Z-axis with respect to the instantaneous center of rotation by direct control of the wheels speeds.

Theory for two dimensional electron emission between parallel flat electrodes

The electron emission in space charge is limited for the case of a planar cathode; such emission is generated by using an approximation that models electric field formation by a dipole, which generates an oscillatory symmetrical density current j(x), minimum value is moved around the origin and calculated throughout the Poisson equation. Such value has been previously calculated based upon the already stated conditions for the two dimensional (2D) case. In our matter under study, it is stated that a symmetric oscillatory potential, namely, μ(x,y) is invariably generated; because of that the boundary conditions represented by both a barrier potential and a square potential will satisfy this potential as well. For the case of the square potential, it is taking into account either a potential is attractive or repulsive. In this study one of the principal problems is discussed. It is when the space charge creates a potential barrier that prohibits steady-state beam propagation. In this paper it is claimed to ...

A multi-configuration kinematic model for active drive/steer four-wheel robot structures

In this study, a general kinematic control law for automatic multi-configuration of four-wheel active drive/steer robots is proposed. This work presents models of four-wheel drive and steer (4WD4S) robotic systems with all-wheel active drive and steer simultaneously. This kinematic model comprises 12 degrees of freedom (DOFs) in a special design of a mechanical structure for each wheel. The control variables are wheel yaw, wheel roll, and suspension pitch by active/passive damper systems. The pitch angle implies that a wheels contact point translates its position over time collinear with the robots lateral sides. The formulation proposed involves the inference of the virtual z-turn axis (robots body rotation axis) to be used in the control of the robots posture by at least two acceleration measurements local to the robots body. The z-turn axis is deduced through a set of linear equations in which the number of equations is equal to the number of acceleration measurements. This research provides two main models for stability conditions. Finally, the results are sustained by different numerical simulations that validate the system with different locomotion configurations.

Neural control and coordination of decentralized transportation robots

This work presents the modeling, control architecture and simulation of a decentralized multi-robot system for transporting material in a warehouse. Each robot has a task scheduler comprising two different neural networks for task allocation and fault tolerance. The path planner consists of a first-order dynamical state equation to control the robot’s four-wheel asynchronous driving and steering, as well as a partial differential equation to coordinate speeds and arrival times. The task allocation and motion coordination combine the robot’s kinematic control law with a one-layer artificial neural network that classifies five-dimensional symbolic logical equations that define the state transitions between asynchronous events. These events include carry and fetch, material supply, robots stop, obstacle avoidance and battery state. Another multilayer artificial neural network reads the same state inputs for fault detection and recovery. The two neural systems feed forward a navigation planner, which uses a partial differential equation to coordinate the robot’s speed and its relaxation time with respect to the robot in front of it. The energy cost is measured by a Lagrangian function. The proposed planning control scheme was computationally validated through parallel computing simulations. The system is shown to be consistent, reliable and feasible, and it allows for fast navigational tasks.

Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir–Blodgett law

This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r)=φ(r(τ))) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle–beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r)=φ(r(τ))) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle–beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.

Space charge emission in cylindrical diode

In this paper, a mathematical model to describe cylindrical electron current emissions through a physics approximation method is presented. The proposed mathematical approximation consists of analyzing and solving the nonlinear Poissons equation, with some determined mathematical restrictions. Our findings tackle the problem when charge-space creates potential barrier that disable the steady-state of the beam propagation. In this problem, the potential barrier effects of electrons speed with zero velocity emitted through the virtual cathode happens. The interaction between particles and the virtual cathode have been to find the inter-atomic potentials as boundary conditions from a quantum mechanics perspective. Furthermore, a non-stationary spatial solution of the electrical potential between anode and cathode is presented. The proposed solution is a 2D differential equation that was linearized from the generalized Poisson equation. A single condition was used solely, throughout the radial boundary conditions of the current density formation.