Position Control and Trajectory Tracking of the Stewart Platform

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.