**1. Introduction**

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Demand on high precision motion systems has been increasing in recent years. Since performance of today's many mechanical systems requires high stiffness, fast motion and accurate positioning capability, parallel manipulators have gained popularity. Currently, parallel robots have been widely used several areas of industry such as manufacturing, medicine and defense. Some of these areas: precision laser cutting, micro machining, machine tool technology, flight simulators, helicopter runway, throwing platform of missiles, surgical operations. Some examples are shown in Figure 1. Unlike open-chain serial robots, parallel manipulators are composed of closed kinematic chain. There exist several parallel kinematic chains between base platform and end moving platform. Serial robots consist of a number of rigid links connected in serial so every actuator supports the weight of the successor links. This serial structure suffers from several disadvantages such as low precision, poor force exertion capability and low payload-to-weight-ratio. The parallel robot architecture eliminates these disadvantages. In this architecture, the load is shared by several parallel kinematic chains. This superior architecture provides high rigidity, high payload-to-weight-ratio, high positioning accuracy, low inertia of moving parts and a simpler solution of the inverse kinematics equations over the serial ones. Since high accuracy of parallel robots stems from load sharing of each actuator, there are no cumulative joint errors and deflections in the links. Under heavy loads, serial robots cannot perform precision positioning and oscillate at high-speeds. Positioning accuracy of parallel robots is high because the positioning error of the platform cannot exceed the average error of the legs positions. They can provide nanometer-level motion performance. But they have smaller workspace and singularities in their workspace.

The most widely used structure of a parallel robot is the Stewart platform (SP). It is a six degrees of freedom (DOF) positioning system that consists of a top plate (moving platform), a base plate (fixed base), and six extensible legs connecting the top plate to the bottom plate.

SP was invented as a flight simulator by Stewart in 1965 (Stewart, 1965). This platform contained three parallel linear actuators. Gough had previously suggested a tire test machine similar to Stewart's model (Bonev, 2003). In the test machine, six actuators were used as a mechanism driven in parallel. Gough, the first person, developed and utilized this type parallel structure. Therefore, SP is sometimes named as Stewart-Gough platform in the literature. Stewart's and Gough's original designs are shown in Figure 2.

Position Control and Trajectory Tracking of the Stewart Platform 181

non-linear equations. In the literature, solutions of the forward (Chen & Song, 1994; Liao et al., 1993; Merlet, 1992; Nauna et al., 1990) and the inverse (Fitcher, 1986; Kim & Chung, 1999;

In this study, design and development stages were given about position control and trajectory tracking of a 6 DOF-Stewart platform using Matlab/Simulink® and DS1103 real time controller. Matlab® (Mathworks Inc.) is a well known and one of the most popular technical computing software package that it is used in a wide area of applications from financial analysis to control designs. Matlab/Simulink® allows easiest way of programming and technical computing to its users. It enables simulations and real time applications of various systems. Third party co-developers improve its abilities allowing using hundreds of hardware. Dspace® company is one of the third party participate of Matlab® that produces rapid control prototyping and hardware-in-the-loop simulation units. DS1103 is a powerful

This chapter is organized in the following manner. System components and real-time controller board are introduced in section 2 and 3, respectively. Position and trajectory tracking control with PID and sliding mode controllers are described in section 4. Finally,

The system components are two main bodies (top and base plates), six linear motors, controller, space mouse, accelerometer, gyroscope, laser interferometer, force/torque sensor, power supply, emergency stop circuit and interface board. They are shown in Figure 3.

A simple emergency stop circuit was designed to protect the motors, when they move to out of the limits. This circuit controls the power supply which gives the energy to the motors

Sefrioui & Gosselin, 1993) kinematics has been given in detail (Kizir et al., 2011).

real time controller board for rapid control prototyping (Dspace Inc.).

experimental results are given in detail.

**2. Stewart platform system** 

Fig. 3. Stewart platform system

Fig. 1. Applications of the Stewart Platform: medical, manufacturing and flight simulator (Niesing, 2001; Merlet, 2006; Wikipedia)

Fig. 2. Stewart (a) and Gough (b) original design (Bonev, 2003)

SP was not attracted attention during the first 15 years since the first invention. Then, Hunt indicated the advantages of parallel robots. After 1983, researchers realized their high load carrying capacity and high positioning ability of these robots. Researchers were then started to study a detailed analysis of these structures. The widely used structure of SP, where top platform is connected to base platform using 6 linear axis with universal joints, was then developed (Hunt, 1983).

It is a well known fact that the solution of the forward kinematics problem is easier than the inverse kinematics problem for serial robot manipulators. On the other hand, this situation is the just opposite for a parallel robot. Inverse kinematics problem of parallel robot can be expressed as follows: position vector and rotation matrix in Cartesian space is given, and asked to find length of each link in joint space. It is relatively easy to find the link lengths because the position of the connecting points and the position and orientation of the moving platform is known. On the other hand, in the forward kinematics problem, the rotation matrix and position vector of the moving platform is computed with given the link lengths. Forward kinematic of the SP is very difficult problem since it requires the solution of many non-linear equations. In the literature, solutions of the forward (Chen & Song, 1994; Liao et al., 1993; Merlet, 1992; Nauna et al., 1990) and the inverse (Fitcher, 1986; Kim & Chung, 1999; Sefrioui & Gosselin, 1993) kinematics has been given in detail (Kizir et al., 2011).

In this study, design and development stages were given about position control and trajectory tracking of a 6 DOF-Stewart platform using Matlab/Simulink® and DS1103 real time controller. Matlab® (Mathworks Inc.) is a well known and one of the most popular technical computing software package that it is used in a wide area of applications from financial analysis to control designs. Matlab/Simulink® allows easiest way of programming and technical computing to its users. It enables simulations and real time applications of various systems. Third party co-developers improve its abilities allowing using hundreds of hardware. Dspace® company is one of the third party participate of Matlab® that produces rapid control prototyping and hardware-in-the-loop simulation units. DS1103 is a powerful real time controller board for rapid control prototyping (Dspace Inc.).

This chapter is organized in the following manner. System components and real-time controller board are introduced in section 2 and 3, respectively. Position and trajectory tracking control with PID and sliding mode controllers are described in section 4. Finally, experimental results are given in detail.
