Each module consists on a concurrent program. The Blackboard implements an AI Artificial Intelligence system that consists on the central Database and knows all other modules capabilities, and is responsible for the task planning and controlling the other modules. Conflicts can occur due to competition for accessing the database during the performance of tasks by the various sub-modules.
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The lower layers respond more quickly to stimuli of input sensors, while the higher layers answer more slowly. Each level consists of modules for task planning and execution, world modeling and sensory processing functional abstraction. The data flow is horizontal in each layer, while the control flow through the layers is vertical. Figure 3. The behavioral architectures have as their reference the architecture developed by Brooks and thus follow that line of architecture Gat, ; Kaelbling, The Subsumption Architecture Brooks, was based on the constructive simplicity to achieve high speed of response to environmental changes.
This architecture had totally different characteristics from those previously used for robot control. Unlike the AI planning techniques exploited by the scientific community of that time, which searched for task planners or problem solvers, Brooks Brooks, introduced a layered control architecture which allowed the robot to operate with incremental levels of competence.
Online Kinematic and Dynamic-State Estimation for Constrained Multibody Systems Based on IMUs
These layers are basically asynchronous modules that exchange information by communication channels. Each module is an example of a finite state machine. The result is a flexible and robust robot control architecture, which is shown in Figure 4. Although the architecture is interesting from the point of view of several behaviors concurrently acting in pursuit of a goal Brooks, , it is unclear how the robot could perform a task with conflicting behaviors.
For example, in a objects stacking task, the Avoiding Obstacles layer would repel the robot from the stack and therefore hinder the task execution, but on the other hand, if this layer is removed from the control architecture, then the robot would be vulnerable to moving or unexpected objects. This approach successfully deals with uncertainty and unpredictable environmental changes.
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Nonetheless, it is not clear how it works when the number of tasks increases, or when the diversity of the environment is increased, or even how it addresses the difficulty of determining the behavior arbitration Tuijman et al. A robot driven only by environmental stimuli may never find its goal due to possible conflicts between behaviors or systemic responses that may not be compatible with the goal.
Nonetheless, this architecture is interesting for applications that have restrictions on the dimensions and power consumption of the robot, or the impossibility of remote processing. As discussed previously, hybrid architectures combine features of both deliberative and reactive architectures. There are several ways to organize the reactive and deliberative subsystems in hybrid architectures, as saw in various architectures presented in recent years Ferguson, ; Gat, ; Kaelbling, Still, there is a small community that research on the approach of control architectures in three hierarchical layers, as shown on Figure 5.
The lowest layer operates according to the behavioral approach of Brooks Brooks, or are even purely reactive. The higher layer uses the planning systems and the world modeling of the deliberative approach. The intermediate layer is not well defined since it is a bridge between the two other layers Zelek, The lowest layer corresponds to the skills or behaviors chosen to accomplish certain tasks.
The middle layer performs the coordination of behaviors that are chosen according to the plan being executed. The highest layer accommodates the planning level based on the library of plans RAP. The basic concept is centered on the RAP library, which determines the behaviors and sensorial routines needed to execute the plan. A reactive planner employ information from a scenario descriptor and the RAP library to activate the required behaviors. This planner also monitors these behaviors and changes them according to the plan.
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Figure 6 illustrates this architecture. Simmons introduces deliberative components performing with layered reactive behavior for complex robots. In this control architecture, the deliberative components respond to normal situations while the reactive components respond to exceptional situations. Figure 7 shows the architecture. The discussion on choosing an appropriate architecture is within the context of deliberative and behavioral approaches, since the same task can be accomplished by different control architectures.
A comparative analysis of results obtained by two different architectures performing the same task must consider the restrictions imposed by the application Ferasoli Filho, If the environment is known or when the process will be repeated from time to time, the architecture may include the use of maps, or get it on the first mission to use on the following missions. As such, the architecture can rely on deliberative approaches. On the other hand, if the environment is unknown on every mission, the use or creation of maps is not interesting — unless the map building is the mission goal.
In this context, approaches based on behaviors may perform better than the deliberative approaches. The kinematics study is used for the design, simulation and control of robotic systems. The kinematics provides a mathematical analysis of robot motion without considering the forces that affect it. This analysis uses the relationship between the geometry of the robot, the control parameters and the system behavior in an environment.
There are different representations of position and orientation to solve kinematics problems. The study of kinematics is performed with the analysis of robot physical structure to generate a mathematical model which represents its behavior in the environment. The mobile robot can be distinguished by different platforms and an essential characteristic is the configuration and geometry of the structure body and wheels.
The mobile robots can be divided according to their mobility. The robot stability can be expressed by the center of gravity, the number of contact points and the environment features. The complete location of the robot in the global frame is defined by. The translation of the robot is defined as a P G vector that is composed of two vectors which are represented by coordinates of local P L and global Q 0 G reference system expressed as.
The rotational motion of the robot can be expressed from global coordinates to local coordinates using the orthogonal rotation matrix Eq. The kinematics is analyzed through two types of study: the forward kinematics and the inverse kinematics. The inverse kinematics predicts the robot caracteristics as wheels velocities, angles and other geometrical parameters through the calculation of the final speed and its orientation angle:.
In the kinematic analysis, the robot characteristics such as the type of wheels, the points of contact, the surface and effects of sliding or friction should be considered. In the case of a two-wheeled differential robot, as presented in Figure 8 , each wheel is controlled by an independent motor X G and Y G represents the global frame, while X L and Y L represents the local frame. The linear speed of each wheel is determined by the relationship between angular speed and radius of the wheel as.
The kinematics equations of the robot are expressed on the initial frame Eq. Therefore, with the matrix of the differential model shown in Eq.
Kinematic and Dynamic Issues in Sensor Based Control
The holonomic constraint is explained by Eq. Finally, with the direct kinematics it is possible to obtain the equations that allow any device to be programmed to recognize at every moment its own speed, position and orientation based on information from wheel speed and steering angle. The omnidirectional robot is a platform made up of three wheels in triangular configuration where the distance between these wheels is symmetric. Each wheel has an independent motor and can rotate around its own axis with respect to the point of contact with the surface.
The Figure 9 shows the three-wheeled omnidirectional robot configuration. X L and Y L are the fixed axis on the local frame in the robot coordinates; d 0 describes the current position of the local axis in relation to the global axis, d i describes the location of the center of a wheel from the local axis. In order to obtain the kinematic model of the robot, the analysis of the speed of each wheel must be determined in terms of the local speed and its make the transformation to the global frame. The speed of each wheel has components in X and Y directions.
The speed of each wheel is represented by the translation and rotation vectors in the robot frame. The position from the global frame P 0 G is added to the position transformation and orientation of the wheel. The transformation matrix is obtained and provides the angular velocity of each wheel in relation to the global frame speeds represented in Eq. The study of the movement dynamics analyzes the relationships between the forces of contact and the forces acting on the robot mechanisms, in addition to the study of the acceleration and resulting motion trajectories.
The kinematic model relates to the displacement, velocity, acceleration and time regardless of the cause of their movement, whereas the dynamic analysis relates to the generalized forces from the actuators, with the energy applied in the system Dudek, There are different proposals for the dynamic model of robot navigation, but the general shape of the dynamic study is the analysis of the forces and torques produced inside and outside of the system.
General equations of system motion, and the analysis of the system torques and energy allows developing the dynamic model of the robotic system.
For this analysis, it is important to consider the physical and geometrical characteristics of the system such as masses, sizes, diameters, among others which are represented in the moments of inertia and static and dynamic torques of the system. Each joint of a robot consists of a an actuator DC motor, AC motor, step motor associated with a speed reducer and transducers to measure position and velocity. These transducers can be absolute or incremental encoders at each joint.
The motion control of robots is a complex issue, since the movement of the mechanical structure is accomplished through rotation and translation of their joints that are controlled simultaneously, which hinders the dynamic coupling. Moreover, the behavior of the structure is strongly nonlinear and dependent on operating conditions. These conditions must be taken into account in the chosen control strategy.
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The desired trajectory is defined by position, speed, acceleration and orientation of, therefore it is necessary to make coordinate transformations with set times and with great complexity of calculations. Normally the robot control on only considers the kinematic model, so joints are not coupled, and the control of each joint is independent. Each robotic joint commonly includes a DC motor, the gear, reducer, transmission, bearing and encoder. The dynamic model of DC motor is expressed by the electrical coupling and mechanical equation as.
The joint model is shown in Figure The system without slip can be expressed by. The model presented above will be increased by the dynamic effect of reducing the loads of coupled system through the motor model and load-reducer as. The robot dynamics can be analyzed from the Lagrange equation, expressed in terms as.
The kinematic constraints are independent of time, and the matrix D represents the full range for a group of linearly independent vectors and the H q is the matrix associated with constraints of the system. The equation of motion is expressed with V1 and V2 as the linear velocities of the system in Eq.
The relationship between the parameters of inertia, information of the centripetal force and Coriolis effect, friction on surfaces, disturbances and unmodeled dynamics is expressed as. The dynamic analysis of the differential robot is a practical and basic model to develop the dynamic model of the omnidirectional robot. For the analysis of the dynamic model it is necessary to know the physical constraints of the system to get the array of restrictions, the matrix of inertia is expressed by the masses and dimensions of the robot with the geometrical characteristics of three-wheeled omnidirectional system.
Control for robots navigation has been developed primarily with the trajectory tracking, with the aim to follow follow certain paths by adjusting the speed and acceleration parameters of the system, which are generally described by position and velocity profiles. Control systems are developed in open loop or closed loop.
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