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Embedded Technology for Mobile Robotics

Mobile robot applications are popular in various domains such as security, surveillance, automation, agriculture, and space missions. While the autonomy and capability to perform complex tasks are being possible, it is always required to control the robot operations including low-level control of actuators and processing sensors. It is increasing demand of accommodating all the controls and processing on an embedded system to optimize power consumption, size, and/or cost. The performance of a robotic system not only depends on the attached sensors but also its controller design. Further, the implementation of controller and processing sensors largely contribute to the desired behavior of the robot. Hence, a great deal of importance is to be given for implementation aspects of the controller.

The embedded system solution provides a customized solution for a controller. This customization may target optimization for cost, power, size, speed, or combination of these. Furthermore, the controller on an embedded platform may be designed to achieve real-time requirements. A single platform may be used for multiple controllers working in synchronization. The synchronization or parallel triggering is easily achievable if the architecture for the controllers is designed on a single chip using either Application-Specific Integrated Circuit (ASIC) or Field Programmable Gate Array (FPGA) technology. However, one needs to learn designing architecture to best utilize these technologies.

There exists availability of cross-platforms like system generator for high-level programming platforms such as MatLab that makes the job easier for developing embedded controllers using high-level codes. But, unless the control engineer knows about the architectural features of an embedded platform, the advanced properties are difficult to choose. Learning to develop an elementary architecture details would enable a control engineer to optimize the implementation. Hence, the study of Embedded Control Systems (ECSs) involves not only designs of control methodologies but also concepts related to elementary knowledge of embedded requirements. This chapter covers ECSs, Mobile Robots as a system to be controlled, and Embedded Technologies used in existing mobile robots.

Figure 1.1 Block diagram of an embedded control system

1.1 Embedded Control System

The embedded controller referred here is the controller implemented on an embedded platform. Figure 1.1 illustrates a block diagram of an ECS where the controller is implemented on an embedded platform. The embedded controller is controlling a plant or a system which in our case is a mobile robot. In practice, the plant characteristic is often analog in nature.

The physics of the plant or system is typically modeled using transfer function if the system can be very well described by a linear system. The transfer function of the system describes the input-output relationship in the frequency domain. In particular, a transfer function is the ratio of Laplace transform of output to input of the system. The modern control theory represents a linear system as a state-space model. For representing a system, let the state vector of the system be , input vector to the system be , and output vector be . The state space representation of the linear system is now given by

where is system matrix, is input matrix, and is output matrix with appropriate dimensions. For a nonlinear system, the state-space representation is given by

where and are nonlinear functions. In an interesting and popular representation of state-space in mobile robotics, the input to system is the derivative of a variable. For example, input to the system is acceleration which is derivative of velocity. The double integrator model is then represented for state variables and state-space representation of the system is given by

Similarly, chained form of system description is also very popular and many controllers have been designed for the system in chained form. The input-to-state relation in the chained form of representing the three dimensional system for state vector and input vector is described by

In many cases, mobile robot models are represented in double integrator and chained form. Appropriate transformations are used for representing the mobile robot models in these standard forms. An appropriate transformation for control commands accordingly needs to be implemented on the embedded platform. Moreover, the controller design development depends on the application objectives and input-output relationship of the mobile robot represented as a system. While application-specific objectives for embedded implementations are discussed in Chapter 3, the system representation of various popular mobile robots is discussed next.

1.2 Mobile Robotics

There exists variety of mobile robotic platforms that facilitate autonomous and remotely controlled robotic applications. These can be categorized under wheeled robots, aerial vehicles, and underwater vehicles. These vehicles can further have generic categorization of their movements in 2D (planar) and 3D. While these robotic platforms are customized with various payloads like camera, manipulator arm, or application-specific sensors, the common functionality movement can be modeled by describing their kinematic model. The kinematic model provides the relationship between the vehicle velocities and commanded velocities. In this context, the kinematic models describing 2D and 3D motions are as follows.

1.2.1 Robot Model for 2D Motion

To develop robot model, let us consider a point mass moving in a planar environment. The plane is represented in - coordinate frame with a fixed origin as shown in Figure 1.2. Let the current position of the point representing the robot be described by its coordinates in the fixed - frame. Since the point robot is a moving point, it further needs a description to show its current orientation. Let the current orientation of the point robot be with respect to the -axis as shown in Figure 1.2. Now, 2D motion of the point robot is described by . In order to define the input-output relationship for controller design, the output is the 2D motion of the point robot while the input depends on the command given to the point robot. Accordingly the robot model is developed. Popular robot models and their descriptions are as follows:

Figure 1.2 A point moving in planar environment

1.2.1.1 Generic Model

Let the 2D motion of the robot be given by velocities in the body frame of reference -, where - frame is oriented in the forward direction of the robot (at an orientation ) with respect to the inertial frame of reference -. In particular, the velocities are surge-forward and sway-left as shown in Figure 1.3.

Knowing that the rotation by angle results in transforming a 2D point by matrix , which is given by

the kinematic model of generic 2D mobile robot is given by

While the generic model describes the commanded velocities in body frame of reference, the commanded velocities in 2D unicycle model are linear and angular velocities as described next.

1.2.1.2 Unicycle Model

Given that the commanded velocities are linear velocity and angular velocity , the model is obtained by relating the angular velocity with change in orientation projecting linear velocity on and axes. These - and -projections define the velocities and , respectively. Therefore,

Figure 1.3 Generic 2D robot model

The models of many mobile robots are derived from the unicycle model given by (1.6). Some examples are as follows:

• Differential-Drive Mobile Robot (DDMR).
• Bicycle.
• Car-like Mobile Robot (CMR).

1.2.1.3 Differential-Drive Mobile Robot or DDMR

In order to give the linear and angular motions to the mobile robot, two wheels of the robot in DDMR configuration are independently driven. These independently driven wheels are fixed to the robot's body in the same orientation on a common axis with a center-point as shown in Figure 1.4. Typically, there is a third caster wheel for balancing the robot which is not driven. Let and be the left and right wheel velocities, respectively. The wheels can move in forward as well as backward directions and, therefore, differential velocity renders the angular motion to the robot. For example, if the left and right wheels are driven by the same speed but in opposite direction, the DDMR rotates at the point ideally without any linear velocity. Figure 1.5 explains the rotation of the robot in anticlockwise and clockwise directions. The axis of rotation is the center of common axis of two wheels (point ). For the anticlockwise rotation of the DDMR at point (zero linear velocity), the left wheel is driven in forward direction while right wheel is driven in the reverse direction but with the same speed as that of left wheel as shown in Figure 1.5a. Similarly, Figure 1.5b illustrates the clockwise...